%0 Artikel
%@ 1742-7061
%A Linka, K.
%A Cavinato, C.
%A Humphrey, J.D.
%A Cyron, C.J.
%D 2022
%J Acta Biomaterialia
%N 2256
%P 63 - 72
%R doi:10.1016/j.actbio.2022.05.039
%T Predicting and understanding arterial elasticity from key microstructural features by bidirectional deep learning
%U https://dx.doi.org/10.1016/j.actbio.2022.05.039
%X Microstructural features and mechanical properties are closely related in all soft biological tissues. Both yet exhibit considerable inter-individual differences and are affected by factors such as aging and disease and its progression. Histological analysis, modern in situ imaging, and biomechanical testing have deepened our understanding of these complex interrelations, yet two key questions remain: (1) Given the specific microstructure, can one predict the macroscopic mechanical properties without mechanical testing? (2) Can one quantify individual contributions of the different microstructural features to the macroscopic mechanical properties in an automated, systematic and largely unbiased way? Here we propose a bidirectional deep learning architecture to address these two questions. Our architecture uses data from standard histological analyses, two-photon microscopy and biaxial biomechanical testing. Its capabilities are demonstrated by predicting with high accuracy () the evolving mechanical properties of the murine aorta during maturation and aging. Moreover, our architecture reveals that the extracellular matrix composition and organization are the most prominent factors governing the macroscopic mechanical properties of the tissues studied herein.
%0 Artikel
%@ 1094-3420
%A Kronbichler, M.
%A Sashko, D.
%A Munch, P.
%D 2022
%J The International Journal of High Performance Computing Applications
%N 3090
%R doi:10.1177/10943420221107880
%T Enhancing data locality of the conjugate gradient method for high-order matrix-free finite-element implementations
%U https://dx.doi.org/10.1177/10943420221107880
%X This work investigates a variant of the conjugate gradient (CG) method and embeds it into the context of high-order finite-element schemes with fast matrix-free operator evaluation and cheap preconditioners like the matrix diagonal. Relying on a data-dependency analysis and appropriate enumeration of degrees of freedom, we interleave the vector updates and inner products in a CG iteration with the matrix-vector product with only minor organizational overhead. As a result, around 90% of the vector entries of the three active vectors of the CG method are transferred from slow RAM memory exactly once per iteration, with all additional access hitting fast cache memory. Node-level performance analyses and scaling studies on up to 147k cores show that the CG method with the proposed performance optimizations is around two times faster than a standard CG solver as well as optimized pipelined CG and s-step CG methods for large sizes that exceed processor caches, and provides similar performance near the strong scaling limit.
%0 Artikel
%@ 1569-3953
%A Arndt, D.
%A Bangerth, W.
%A Feder, M.
%A Fehling, M.
%A Gassmöller, R.
%A Heister, T.
%A Heltai, L.
%A Kronbichler, M.
%A Maier, M.
%A Munch, P.
%A Pelteret, J.-P.
%A Sticko, S.
%A Turcksin, B.
%A Wells, D.
%D 2022
%J Journal of Numerical Mathematics
%N 2987
%P 231 - 246
%R doi:10.1515/jnma-2022-0054
%T The deal.II Library, Version 9.4
%U https://dx.doi.org/10.1515/jnma-2022-0054
3
%X This paper provides an overview of the new features of the finite element library deal.II, version 9.4.
%0 Artikel
%@ 2196-4378
%A Golshan, S.
%A Munch, P.
%A Gassmöller, R.
%A Kronbichler, M.
%A Blais, B.
%D 2022
%J Computational Particle Mechanics
%N 3078
%R doi:10.1007/s40571-022-00478-6
%T Lethe-DEM: an open-source parallel discrete element solver with load balancing
%U https://dx.doi.org/10.1007/s40571-022-00478-6
%X Approximately 75% of the raw material and 50% of the products in the chemical industry are granular materials. The discrete element method (DEM) provides detailed insights of phenomena at particle scale, and it is therefore often used for modeling granular materials. However, because DEM tracks the motion and contact of individual particles separately, its computational cost increases nonlinearly O(nplog(np)) – O(n2p) (depending on the algorithm) with the number of particles (np). In this article, we introduce a new open-source parallel DEM software with load balancing: Lethe-DEM. Lethe-DEM, a module of Lethe, consists of solvers for two-dimensional and three-dimensional DEM simulations. Load balancing allows Lethe-DEM to significantly increase the parallel efficiency by ≈25–70% depending on the granular simulation. We explain the fundamental modules of Lethe-DEM, its software architecture, and the governing equations. Furthermore, we verify Lethe-DEM with several tests including analytical solutions and comparison with other software. Comparisons with experiments in a flat-bottomed silo, wedge-shaped silo, and rotating drum validate Lethe-DEM. We investigate the strong and weak scaling of Lethe-DEM with 1≤nc≤192 and 32≤nc≤320 processes, respectively, with and without load balancing. The strong-scaling analysis is performed on the wedge-shaped silo and rotating drum simulations, while for the weak-scaling analysis, we use a dam-break simulation. The best scalability of Lethe-DEM is obtained in the range of 5000≤np/nc≤15,000. Finally, we demonstrate that large-scale simulations can be carried out with Lethe-DEM using the simulation of a three-dimensional cylindrical silo with np=4.3×106 on 320 cores.
%0 Artikel
%@ 0177-0667
%A Mossaiby, F.
%A Sheikhbahaei, P.
%A Shojaei, A.
%D 2022
%J Engineering with Computers
%N 3072
%R doi:10.1007/s00366-022-01656-z
%T Multi-adaptive coupling of finite element meshes with peridynamic grids: robust implementation and potential applications
%U https://dx.doi.org/10.1007/s00366-022-01656-z
%X Coupling of methods based on the classical continuum mechanics (CCM), with peridynamic (PD) models is a recent hot topic in the realm of computational mechanics. In the coupled models, to optimize the usage of computational resources, usually the application of PD (the more demanding procedure) is restricted to critical areas of the domain affected by discontinuities such as propagating cracks. The remaining parts of the domain are described by a more efficient CCM-based model such as the finite element method (FEM). Here, we develop a coupled FEM/PD model for dynamic fracture modeling. The proposed method simultaneously features the following: (1) it can adaptively change the coupling configuration throughout the simulation such that only critical zones, on the verge of crack nucleation/propagation, are tackled by the PD procedure, and (2) it appropriately supports different grid spacing of PD and FEM parts. We refer to a model possessing both the features as multi-adaptive. This is crucial for a highly efficient coupling scheme. The performance of the proposed method is analyzed in terms of accuracy and computational efficiency through different numerical examples. The results show that the proposed method is superior to using a refined PD model, since it provides the same level of accuracy at a much lower computational cost. As a novel application, we present the promising results of a crack propagation problem in an unbounded domain, solved using classical artificial boundary conditions on an outer FEM layer.
%0 Artikel
%@ 2296-8016
%A Sardhara, T.
%A Aydin, R.C.
%A Li, Y.
%A Piché, N.
%A Gauvin, R.
%A Cyron, C.J.
%A Ritter, M.
%D 2022
%J Frontiers in Materials
%N 2827
%P 837006
%R doi:10.3389/fmats.2022.837006
%T Training Deep Neural Networks to Reconstruct Nanoporous Structures From FIB Tomography Images Using Synthetic Training Data
%U https://dx.doi.org/10.3389/fmats.2022.837006
%X Focused ion beam (FIB) tomography is a destructive technique used to collect three-dimensional (3D) structural information at a resolution of a few nanometers. For FIB tomography, a material sample is degraded by layer-wise milling. After each layer, the current surface is imaged by a scanning electron microscope (SEM), providing a consecutive series of cross-sections of the three-dimensional material sample. Especially for nanoporous materials, the reconstruction of the 3D microstructure of the material, from the information collected during FIB tomography, is impaired by the so-called shine-through effect. This effect prevents a unique mapping between voxel intensity values and material phase (e.g., solid or void). It often substantially reduces the accuracy of conventional methods for image segmentation. Here we demonstrate how machine learning can be used to tackle this problem. A bottleneck in doing so is the availability of sufficient training data. To overcome this problem, we present a novel approach to generate synthetic training data in the form of FIB-SEM images generated by Monte Carlo simulations. Based on this approach, we compare the performance of different machine learning architectures for segmenting FIB tomography data of nanoporous materials. We demonstrate that two-dimensional (2D) convolutional neural network (CNN) architectures processing a group of adjacent slices as input data as well as 3D CNN perform best and can enhance the segmentation performance significantly.
%0 Artikel
%@ 0020-7403
%A Hermann, A.
%A Shojaei, A.
%A Steglich, D.
%A Höche, D.
%A Zeller-Plumhof, B.
%A Cyron, C.
%D 2022
%J International Journal of Mechanical Sciences
%N 2546
%P 107143
%R doi:10.1016/j.ijmecsci.2022.107143
%T Combining peridynamic and finite element simulations to capture the corrosion of degradable bone implants and to predict their residual strength
%U https://dx.doi.org/10.1016/j.ijmecsci.2022.107143
%X This paper proposes a computational framework to describe the biodegradation of magnesium (Mg)-based bone implants. It is based on a sequential combination of two models: an electrochemical corrosion model to compute the mass loss of the implant over several weeks combined with a mechanical model to assess its residual mechanical strength. The first model uses a peridynamic (PD) corrosion model to tackle the complex moving boundary of the corroding material in an efficient manner. The results of this corrosion simulation are mapped to a finite element (FE) model by way of a damage variable. Subsequently, the FE model is used for mechanical analysis. To use PD for such a complex problem, we proposed three innovative improvements compared to state-of-the-art PD models: (1) application of an adaptive multi-grid discretization in space and an implicit time-stepping algorithm enabling an efficient simulation of the complex implant geometry over prolonged periods, (2) novel non-local Dirichlet absorbing boundary conditions to truncate the simulation domain in the close neighborhood of the implant of interest without prohibitive losses of accuracy, and (3) selection of suitable non-local kernel functions and parameter calibration on the basis of experimental data by an evolutionary algorithm. We demonstrate that this framework can capture the loss of implant mass due to corrosion for typical alloys such as Mg-5Gd and Mg-10Gd. Moreover, we point out how this framework can be used in the future to predict the declining mechanical strength of bone screws subject to biocorrosion over several weeks.
%0 Artikel
%@ 0045-7825
%A Shojaei, A.
%A Hermann, A.
%A Cyron, C.
%A Seleson, P.
%A Silling, S.
%D 2022
%J Computer Methods in Applied Mechanics and Engineering
%N 1861
%P 114544
%R doi:10.1016/j.cma.2021.114544
%T A hybrid meshfree discretization to improve the numerical performance of peridynamic models
%U https://dx.doi.org/10.1016/j.cma.2021.114544
%X Efficient and accurate calculation of spatial integrals is of major interest in the numerical implementation of peridynamics (PD). The standard way to perform this calculation is a particle-based approach that discretizes the strong form of the PD governing equation. This approach has rapidly been adopted by the PD community since it offers some advantages. It is computationally cheaper than other available schemes, can conveniently handle material separation, and effectively deals with nonlinear PD models. Nevertheless, PD models are still computationally very expensive compared with those based on the classical continuum mechanics theory, particularly for large-scale problems in three dimensions. This results from the nonlocal nature of the PD theory which leads to interactions of each node of a discretized body with multiple surrounding nodes. Here, we propose a new approach to significantly boost the numerical efficiency of PD models. We propose a discretization scheme that employs a simple collocation procedure and is truly meshfree; i.e., it does not depend on any background integration cells. In contrast to the standard scheme, the proposed scheme requires a much smaller set of neighboring nodes (keeping the same physical length scale) to achieve a specific accuracy and is thus computationally more efficient. Our new scheme is applicable to the case of linear PD models and within neighborhoods where the solution can be approximated by smooth basis functions. Therefore, to fully exploit the advantages of both the standard and the proposed schemes, a hybrid discretization is presented that combines both approaches within an adaptive framework. The high performance of the developed framework is illustrated by several numerical examples, including brittle fracture and corrosion problems in two and three dimensions.
%0 Artikel
%@ 0022-1120
%A Fehn, N.
%A Kronbichler, M.
%A Munch, P.
%A Wall, W.
%D 2022
%J Journal of Fluid Mechanics
%N 1210
%P A40
%R doi:10.1017/jfm.2021.1003
%T Numerical evidence of anomalous energy dissipation in incompressible Euler flows: towards grid-converged results for the inviscid Taylor-Green problem
%U https://dx.doi.org/10.1017/jfm.2021.1003
%X The well-known energy dissipation anomaly in the inviscid limit, related to velocity singularities according to Onsager, still needs to be demonstrated by numerical experiments. The present work contributes to this topic through high-resolution numerical simulations of the inviscid three-dimensional Taylor–Green vortex problem using a novel high-order discontinuous Galerkin discretisation approach for the incompressible Euler equations. The main methodological ingredient is the use of a discretisation scheme with inbuilt dissipation mechanisms, as opposed to discretely energy-conserving schemes, which – by construction – rule out the occurrence of anomalous dissipation. We investigate effective spatial resolution up to 81923 (defined based on the 2π-periodic box) and make the interesting phenomenological observation that the kinetic energy evolution does not tend towards exact energy conservation for increasing spatial resolution of the numerical scheme, but that the sequence of discrete solutions seemingly converges to a solution with non-zero kinetic energy dissipation rate. Taking the fine-resolution simulation as a reference, we measure grid-convergence with a relative L2-error of 0.27% for the temporal evolution of the kinetic energy and 3.52% for the kinetic energy dissipation rate against the dissipative fine-resolution simulation. The present work raises the question of whether such results can be seen as a numerical confirmation of the famous energy dissipation anomaly. Due to the relation between anomalous energy dissipation and the occurrence of singularities for the incompressible Euler equations according to Onsager's conjecture, we elaborate on an indirect approach for the identification of finite-time singularities that relies on energy arguments.
%0 Artikel
%@ 2383-4536
%A Dipasquale, D.
%A Sarego, G.
%A Prapamonthon, P.
%A Yooyen, S.
%A Shojaei, A.
%D 2022
%J Journal of Applied and Computational Mechanics
%N 3031
%P 617 - 628
%R doi:10.22055/JACM.2021.38664.3264
%T A Stress Tensor-based Failure Criterion for Ordinary State-based Peridynamic Models
%U https://dx.doi.org/10.22055/JACM.2021.38664.3264
2
%X Peridynamics is a recent nonlocal theory of continuum mechanics that is suitable to describe fracture problems in solid mechanics. In this paper, a new failure criterion based on the stress field is developed by adopting the damage correspondence model in the ordinary state-based peridynamic theory. The proposed stress tensor-based failure criterion is capable of predicting more accurately crack propagation in the mixed mode I-II fracture problems different from other failure criteria in peridynamics. The effectiveness of the proposed model is demonstrated by performing several examples of mixed-mode dynamic fracture in brittle materials.
%0 Artikel
%@ 0177-0667
%A Fuchs, S.L.
%A Praegla, P.M.
%A Cyron, C.J.
%A Wall, W.A.
%A Meier, C.
%D 2022
%J Engineering with Computers
%N 3072
%R doi:10.1007/s00366-022-01724-4
%T A versatile SPH modeling framework for coupled microfluid-powder dynamics in additive manufacturing: binder jetting, material jetting, directed energy deposition and powder bed fusion
%U https://dx.doi.org/10.1007/s00366-022-01724-4
%X Many additive manufacturing (AM) technologies rely on powder feedstock, which is fused to form the final part either by melting or by chemical binding with subsequent sintering. In both cases, process stability and resulting part quality depend on dynamic interactions between powder particles and a fluid phase, i.e., molten metal or liquid binder. The present work proposes a versatile computational modeling framework for simulating such coupled microfluid-powder dynamics problems involving thermo-capillary flow and reversible phase transitions. In particular, a liquid and a gas phase are interacting with a solid phase that consists of a substrate and mobile powder particles while simultaneously considering temperature-dependent surface tension and wetting effects. In case of laser–metal interactions, the effect of rapid evaporation is incorporated through additional mechanical and thermal interface fluxes. All phase domains are spatially discretized using smoothed particle hydrodynamics. The method’s Lagrangian nature is beneficial in the context of dynamically changing interface topologies due to phase transitions and coupled microfluid-powder dynamics. Special care is taken in the formulation of phase transitions, which is crucial for the robustness of the computational scheme. While the underlying model equations are of a very general nature, the proposed framework is especially suitable for the mesoscale modeling of various AM processes. To this end, the generality and robustness of the computational modeling framework is demonstrated by several application-motivated examples representing the specific AM processes binder jetting, material jetting, directed energy deposition, and powder bed fusion. Among others, it is shown how the dynamic impact of droplets in binder jetting or the evaporation-induced recoil pressure in powder bed fusion leads to powder motion, distortion of the powder packing structure, and powder particle ejection.
%0 Artikel
%@ 2452-199X
%A Zeller-Plumhoff, B.
%A Laipple, D.
%A Slominska, H.
%A Iskhakova, K.
%A Longo, E.
%A Hermann, A.
%A Flenner, S.
%A Greving, I.
%A Storm, M.
%A Willumeit-Römer, R.
%D 2021
%J Bioactive Materials
%N 2757
%P 4368 - 4376
%R doi:10.1016/j.bioactmat.2021.04.009
%T Evaluating the morphology of the degradation layer of pure magnesium via 3D imaging at resolutions below 40 nm
%U https://dx.doi.org/10.1016/j.bioactmat.2021.04.009
12
%X Magnesium is attractive for the application as a temporary bone implant due to its inherent biodegradability, non-toxicity and suitable mechanical properties. The degradation process of magnesium in physiological environments is complex and is thought to be a diffusion-limited transport problem. We use a multi-scale imaging approach using micro computed tomography and transmission X-ray microscopy (TXM) at resolutions below 40 nm. Thus, we are able to evaluate the nanoporosity of the degradation layer and infer its impact on the degradation process of pure magnesium in two physiological solutions. Magnesium samples were degraded in simulated body fluid (SBF) or Dulbecco's modified Eagle's medium (DMEM) with 10% fetal bovine serum (FBS) for one to four weeks. TXM reveals the three-dimensional interconnected pore network within the degradation layer for both solutions. The pore network morphology and degradation layer composition are similar for all samples. By contrast, the degradation layer thickness in samples degraded in SBF was significantly higher and more inhomogeneous than in DMEM+10%FBS. Distinct features could be observed within the degradation layer of samples degraded in SBF, suggesting the formation of microgalvanic cells, which are not present in samples degraded in DMEM+10%FBS. The results suggest that the nanoporosity of the degradation layer and the resulting ion diffusion processes therein have a limited influence on the overall degradation process. This indicates that the influence of organic components on the dampening of the degradation rate by the suppression of microgalvanic degradation is much greater in the present study.
%0 Artikel
%@ 1617-7959
%A Eichinger, J.F.
%A Grill, M.J.
%A Kermani, I.D.
%A Aydin, R.C.
%A Wall, W.A.
%A Humphrey, J.D.
%A Cyron, C.J.
%D 2021
%J Biomechanics and Modeling in Mechanobiology
%N 2802
%P 1851 - 1870
%R doi:10.1007/s10237-021-01480-2
%T A computational framework for modeling cell–matrix interactions in soft biological tissues
%U https://dx.doi.org/10.1007/s10237-021-01480-2
%X Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.
%0 Artikel
%@ 0374-3535
%A Brandstaeter, S.
%A Fuchs, S.
%A Biehler, J.
%A Aydin, R.
%A Wall, W.
%A Cyron, C.
%D 2021
%J Journal of Elasticity
%N 2425
%P 191 - 221
%R doi:10.1007/s10659-021-09833-9
%T Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling
%U https://dx.doi.org/10.1007/s10659-021-09833-9
1-2
%X Growth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.
%0 Artikel
%@ 1063-4584
%A Linka, K.
%A Thüring, J.
%A Rieppo, L.
%A Aydin, R.
%A Cyron, C.
%A Kuhl, C.
%A Merhof, D.
%A Truhn, D.
%A Nebelung, S.
%D 2021
%J Osteoarthritis and Cartilage
%N 2967
%P 592-602
%R doi:10.1016/j.joca.2020.12.022
%T Machine learning-augmented and microspectroscopy-informed multiparametric MRI for the non-invasive prediction of articular cartilage composition
%U https://dx.doi.org/10.1016/j.joca.2020.12.022
4
%X Background
Articular cartilage degeneration is the hallmark change of osteoarthritis, a severely disabling disease with high prevalence and considerable socioeconomic and individual burden. Early, potentially reversible cartilage degeneration is characterized by distinct changes in cartilage composition and ultrastructure, while the tissue’s morphology remains largely unaltered. Hence, early degenerative changes may not be diagnosed by clinical standard diagnostic tools.
Methods
Against this background, this study introduces a novel method to determine the tissue composition non-invasively. Our method involves quantitative MRI parameters (i.e., T1, T1ρ, T2 and
maps), compositional reference measurements (i.e., microspectroscopically determined local proteoglycan [PG] and collagen [CO] contents) and machine learning techniques (i.e., artificial neural networks [ANNs] and multivariate linear models [MLMs]) on 17 histologically grossly intact human cartilage samples.
Results
Accuracy and precision were higher in ANN-based predictions than in MLM-based predictions and moderate-to-strong correlations were found between measured and predicted compositional parameters.
Conclusion
Once trained for the clinical setting, advanced machine learning techniques, in particular ANNs, may be used to non-invasively determine compositional features of cartilage based on quantitative MRI parameters with potential implications for the diagnosis of (early) degeneration and for the monitoring of therapeutic outcomes.
%0 Artikel
%@ 2296-8016
%A Ganesan, H.
%A Scheider, I.
%A Cyron, C.
%D 2021
%J Frontiers in Materials
%N 2827
%P 602567
%R doi:10.3389/fmats.2020.602567
%T Quantifying the High-Temperature Separation Behavior of Lamellar Interfaces in γ-Titanium Aluminide Under Tensile Loading by Molecular Dynamics
%U https://dx.doi.org/10.3389/fmats.2020.602567
%X γ-titanium aluminide (TiAl) alloys with fully lamellar microstructure possess excellent properties for high-temperature applications. Such fully lamellar microstructure has interfaces at different length scales. The separation behavior of the lamellae at these interfaces is crucial for the mechanical properties of the whole material. Unfortunately, quantifying it by experiments is difficult. Therefore, we use molecular dynamics (MD) simulations to this end. Specifically, we study the high-temperature separation behavior under tensile loading of the four different kinds of lamellar interfaces appearing in TiAl, namely, the γ/α2, γ/γPT, γ/γTT, and γ/γRB interfaces. In our simulations, we use two different atomistic interface models, a defect-free (Type-1) model and a model with preexisting voids (Type-2). Clearly, the latter is more physical but studying the former also helps to understand the role of defects. Our simulation results show that among the four interfaces studied, the γ/α2 interface possesses the highest yield strength, followed by the γ/γPT, γ/γTT, and γ/γRB interfaces. For Type-1 models, our simulations reveal failure at the interface for all γ/γ interfaces but not for the γ/α2 interface. By contrast, for Type-2 models, we observe for all the four interfaces failure at the interface. Our atomistic simulations provide important data to define the parameters of traction–separation laws and cohesive zone models, which can be used in the framework of continuum mechanical modeling of TiAl. Temperature-dependent model parameters were identified, and the complete traction–separation behavior was established, in which interface elasticity, interface plasticity, and interface damage could be distinguished. By carefully eliminating the contribution of bulk deformation from the interface behavior, we were able to quantify the contribution of interface plasticity and interface damage, which can also be related to the dislocation evolution and void nucleation in the atomistic simulations.
%0 Artikel
%@ 1530-6984
%A Giuntini, D.
%A Davydok, A.
%A Blankenburg, M.
%A Domènech, B.
%A Bor, B.
%A Li, M.
%A Scheider, I.
%A Krywka, C.
%A Müller, M.
%A Schneider, G.
%D 2021
%J Nano Letters
%N 1946
%P 2891 - 2897
%R doi:10.1021/acs.nanolett.0c05041
%T Deformation Behavior of Cross-Linked Supercrystalline Nanocomposites: An in Situ SAXS/WAXS Study during Uniaxial Compression
%U https://dx.doi.org/10.1021/acs.nanolett.0c05041
7
%X With the ever-expanding functional applications of supercrystalline nanocomposites (a relatively new category of materials consisting of organically functionalized nanoparticles arranged into periodic structures), it becomes necessary to ensure their structural stability and understand their deformation and failure mechanisms. Inducing the cross-linking of the functionalizing organic ligands, for instance, leads to a remarkable enhancement of the nanocomposites’ mechanical properties. It is however still unknown how the cross-linked organic phase redistributes applied loads, how the supercrystalline lattice accommodates the imposed deformations, and thus in general what phenomena govern the overall material’s mechanical response. This work elucidates these aspects for cross-linked supercrystalline nanocomposites through an in situ small- and wide-angle X-ray scattering study combined with uniaxial pressing. Because of this loading condition, it emerges that the cross-linked ligands effectively carry and distribute loads homogeneously throughout the nanocomposites, while the superlattice deforms via rotation, slip, and local defects generation.
%0 Artikel
%@ 1617-7959
%A Eichinger, J.
%A Haeusel, L.
%A Paukner, D.
%A Aydin, R.
%A Humphrey, J.
%A Cyron, C.
%D 2021
%J Biomechanics and Modeling in Mechanobiology
%N 2802
%P 833 - 850
%R doi:10.1007/s10237-021-01433-9
%T Mechanical homeostasis in tissue equivalents: a review
%U https://dx.doi.org/10.1007/s10237-021-01433-9
3
%X There is substantial evidence that growth and remodeling of load bearing soft biological tissues is to a large extent controlled by mechanical factors. Mechanical homeostasis, which describes the natural tendency of such tissues to establish, maintain, or restore a preferred mechanical state, is thought to be one mechanism by which such control is achieved across multiple scales. Yet, many questions remain regarding what promotes or prevents homeostasis. Tissue equivalents, such as collagen gels seeded with living cells, have become an important tool to address these open questions under well-defined, though limited, conditions. This article briefly reviews the current state of research in this area. It summarizes, categorizes, and compares experimental observations from the literature that focus on the development of tension in tissue equivalents. It focuses primarily on uniaxial and biaxial experimental studies, which are well-suited for quantifying interactions between mechanics and biology. The article concludes with a brief discussion of key questions for future research in this field.
%0 Artikel
%@ 2296-8016
%A Schnabel, J.
%A Scheider, I.
%D 2021
%J Frontiers in Materials
%N 2827
%P 581187
%R doi:10.3389/fmats.2020.581187
%T Crystal Plasticity Modeling of Creep in Alloys with Lamellar Microstructures at the Example of Fully Lamellar TiAl
%U https://dx.doi.org/10.3389/fmats.2020.581187
%X A crystal plasticity model of the creep behavior of alloys with lamellar microstructures is presented. The model is based on the additive decomposition of the plastic strain into a part that describes the instantaneous (i.e., high strain rate) plastic response due to loading above the yield point, and a part that captures the viscoplastic deformation at elevated temperatures. In order to reproduce the transition from the primary to the secondary creep stage in a physically meaningful way, the competition between work hardening and recovery is modeled in terms of the evolving dislocation density. The evolution model for the dislocation density is designed to account for the significantly different free path lengths of slip systems in lamellar microstructures depending on their orientation with respect to the lamella interface. The established model is applied to reproduce and critically discuss experimental findings on the creep behavior of polysynthetically twinned TiAl crystals. Although the presented crystal plasticity model is designed with the creep behavior of fully lamellar TiAl in mind, it is by no means limited to these specific alloys. The constitutive model and many of the discussed assumptions also apply to the creep behavior of other crystalline materials with lamellar microstructures.
%0 Artikel
%@ 2213-7467
%A Fuchs, S.
%A Meier, C.
%A Wall, W.
%A Cyron, C.
%D 2021
%J Advanced Modeling and Simulation in Engineering Sciences
%N 2996
%P 15
%R doi:10.1186/s40323-021-00200-w
%T An SPH framework for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions
%U https://dx.doi.org/10.1186/s40323-021-00200-w
1
%X The present work proposes an approach for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of multiple liquid or gas phases. All fields are spatially discretized using the method of smoothed particle hydrodynamics (SPH). This approach is especially suitable in the context of continually changing interface topologies and dynamic phase transitions without the need for additional methodological and computational effort for interface tracking as compared to mesh- or grid-based methods. Proposing a concept for the parallelization of the computational framework, in particular concerning a computationally efficient evaluation of rigid body motion, is an essential part of this work. Finally, the accuracy and robustness of the proposed framework is demonstrated by several numerical examples in two and three dimensions, involving multiple rigid bodies, two-phase flow, and reversible phase transitions, with a focus on two potential application scenarios in the fields of engineering and biomechanics: powder bed fusion additive manufacturing (PBFAM) and disintegration of food boluses in the human stomach. The efficiency of the parallel computational framework is demonstrated by a strong scaling analysis.
%0 Artikel
%@ 0021-9991
%A Linka, K.
%A Hillgärtner, M.
%A Abdolazizi, K.
%A Aydin, R.
%A Itskov, M.
%A Cyron, C.
%D 2021
%J Journal of Computational Physics
%N 1208
%P 110010
%R doi:10.1016/j.jcp.2020.110010
%T Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning
%U https://dx.doi.org/10.1016/j.jcp.2020.110010
%X In this paper we introduce constitutive artificial neural networks (CANNs), a novel machine learning architecture for data-driven modeling of the mechanical constitutive behavior of materials. CANNs are able to incorporate by their very design information from three different sources, namely stress-strain data, theoretical knowledge from materials theory, and diverse additional information (e.g., about microstructure or materials processing). CANNs can easily and efficiently be implemented in standard computational software. They require only a low-to-moderate amount of training data and training time to learn without human guidance the constitutive behavior also of complex nonlinear and anisotropic materials. Moreover, in a simple academic example we demonstrate how the input of microstructural data can endow CANNs with the ability to describe not only the behavior of known materials but to predict also the properties of new materials where no stress-strain data are available yet. This ability may be particularly useful for the future in-silico design of new materials. The developed source code of the CANN architecture and accompanying example data sets are available at https://github.com/ConstitutiveANN/CANN.
%0 Artikel
%@ 0045-7825
%A Fuchs, S.
%A Meier, C.
%A Wall, W.
%A Cyron, C.
%D 2021
%J Computer Methods in Applied Mechanics and Engineering
%N 1861
%P 113922
%R doi:10.1016/j.cma.2021.113922
%T A novel smoothed particle hydrodynamics and finite element coupling scheme for fluid–structure interaction: The sliding boundary particle approach
%U https://dx.doi.org/10.1016/j.cma.2021.113922
%X A novel numerical formulation for solving fluid–structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the structural field using the finite element method (FEM). As compared to fully mesh- or grid-based FSI frameworks, due to the Lagrangian nature of SPH this framework can be easily extended to account for more complex fluids consisting of multiple phases and dynamic phase transitions. Moreover, this approach facilitates the handling of large deformations of the fluid domain respectively the fluid–structure interface without additional methodological and computational efforts. In particular, to achieve an accurate representation of interaction forces between fluid particles and structural elements also for strongly curved interface geometries, the novel sliding boundary particle approach is proposed to ensure full support of SPH particles close to the interface. The coupling of the fluid and the structural field is based on a Dirichlet–Neumann partitioned approach, where the fluid field is the Dirichlet partition with prescribed interface displacements and the structural field is the Neumann partition subject to interface forces. To overcome instabilities inherent to weakly coupled schemes an iterative fixed-point coupling scheme is employed. Several numerical examples in form of well-known benchmark tests are considered to validate the accuracy, stability, and robustness of the proposed formulation. Finally, the filling process of a highly flexible thin-walled balloon-like container is studied, representing a model problem close to potential application scenarios of the proposed scheme in the field of biomechanics.
%0 Artikel
%@ 1742-5689
%A Holzapfel, G.
%A Linka, K.
%A Sherifova, S.
%A Cyron, C.
%D 2021
%J Journal of the Royal Society Interface
%N 2207
%P 20210411
%R doi:10.1098/rsif.2021.0411
%T Predictive constitutive modelling of arteries by deep learning
%U https://dx.doi.org/10.1098/rsif.2021.0411
182
%X The constitutive modelling of soft biological tissues has rapidly gained attention over the last 20 years. Current constitutive models can describe the mechanical properties of arterial tissue. Predicting these properties from microstructural information, however, remains an elusive goal. To address this challenge, we are introducing a novel hybrid modelling framework that combines advanced theoretical concepts with deep learning. It uses data from mechanical tests, histological analysis and images from second-harmonic generation. In this first proof of concept study, our hybrid modelling framework is trained with data from 27 tissue samples only. Even such a small amount of data is sufficient to be able to predict the stress–stretch curves of tissue samples with a median coefficient of determination of R2 = 0.97 from microstructural information, as long as one limits the scope to tissue samples whose mechanical properties remain in the range commonly encountered. This finding suggests that deep learning could have a transformative impact on the way we model the constitutive properties of soft biological tissues.
%0 Artikel
%@ 0098-3500
%A Munch, P.
%A Kormann, K.
%A Kronbichler, M.
%D 2021
%J ACM Transactions on Mathematical Software
%N 3007
%P 33
%R doi:10.1145/3469720
%T hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations
%U https://dx.doi.org/10.1145/3469720
4
%X This work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two up to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal.II to create complex low-dimensional meshes and to operate on them individually. These meshes are combined via a tensor product on the fly, and the library provides new special-purpose highly optimized matrix-free functions exploiting domain decomposition as well as shared memory via MPI-3.0 features. Both node-level performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores confirm the efficiency of the implementation. Results obtained with the library hyper.deal are reported for high-dimensional advection problems and for the solution of the Vlasov–Poisson equation in up to six-dimensional phase space.
%0 Artikel
%@ 1569-3953
%A Arndt, D.
%A Bangerth, W.
%A Blais, B.
%A Fehling, M.
%A Gassmöller, R.
%A Heister, T.
%A Heltai, L.
%A Kronbichler, M.
%A Köcher, U.
%A Maier, M.
%A Munch, P.
%A Pelteret, J.
%A Proell, S.
%A Simon, K.
%A Turcksin, B.
%A Wells, D.
%A Zhang, J.
%D 2021
%J Journal of Numerical Mathematics
%N 2987
%P 171 - 186
%R doi:10.1515/jnma-2021-0081
%T The deal.II library, Version 9.3
%U https://dx.doi.org/10.1515/jnma-2021-0081
3
%X This paper provides an overview of the new features of the finite element library deal.II, version 9.3.
%0 Artikel
%@ 0167-6636
%A Steglich, D.
%A Besson, J.
%D 2021
%J Mechanics of Materials
%N 2610
%P 104064
%R doi:10.1016/j.mechmat.2021.104064
%T Prediction of deformation and failure anisotropy for thin magnesium sheets under mixed-mode loading
%U https://dx.doi.org/10.1016/j.mechmat.2021.104064
%X The plastic deformation and the failure behavior of a third generation magnesium AZ31 sheet is studied under quasi-static tensile, compressive, and mixed mode loading conditions at room temperature. While the deformation anisotropy is found to be less pronounced compared to previously investigated rolled sheets of this alloy, a strong dependence of the failure strain on the sheets orientation is experienced. This failure anisotropy is further studied and quantified using mixed-mode tests realized using a modified Arcan fixture. The irreversible deformation is modeled in the framework of finite elements using two coupled anisotropic plastic potentials. The model parameters are calibrated using the global force-elongation record of the tested samples. For the prediction of failure, an uncoupled damage model based on transformation of strain rates is developed and applied. It is shown that this model is able to predict the observed edge failure of notched specimens with good accuracy. The model predictions for the smooth tensile tests are analyzed in detail by full-field FE analyses to understand the interaction between strain localization and predicted damage evolution.
%0 Artikel
%@ 1931-9401
%A Bor, B.
%A Giuntini, D.
%A Domènech, B.
%A Plunkett, A.
%A Kampferbeck, M.
%A Vossmeyer, T.
%A Weller, H.
%A Scheider, I.
%A Schneider, G.
%D 2021
%J Applied Physics Reviews
%N 3018
%P 031414
%R doi:10.1063/5.0056616
%T Constitutive and fracture behavior of ultra-strong supercrystalline nanocomposites
%U https://dx.doi.org/10.1063/5.0056616
3
%X Supercrystalline nanocomposites are a new class of hybrid and nanostructured materials that can reach exceptional mechanical strength and can be fabricated at low temperatures. Hierarchically arranged, they bridge the gap from the nano- to the macro-scale. Even though their mechanical properties are starting to be characterized, their constitutive behavior is still largely unexplored. Here, the mechanical behavior of supercrystalline nanocomposites of iron oxide nanoparticles, surface-functionalized with oleic acid and oleyl phosphate ligands, is investigated in both bending and compression, with loading–unloading tests. A new bar geometry is implemented to better detect deformation prior to unstable crack propagation, and notched bending bars are tested to evaluate fracture toughness. Micro-mechanical tests result in the values of strength and elastic modulus that are extremely high for supercrystals, reaching record-high numbers in the oleic acid-based nanocomposites, which also show a significant tension–compression asymmetry. The constitutive behavior of both materials is predominantly linear elastic, with some more marked nonlinearities arising in the oleyl phosphate-based nanocomposites. The fracture toughness of both types of nanocomposites, ∼0.3 MPa√m, suggests that extrinsic toughening, associated with both material composition and nanostructure, plays an important role. Fractographic observations reveal analogies with shear and cleavage in atomic crystals. The influence of material composition, nanostructure, and processing method on the mechanical behavior of the nanocomposites is analyzed.
%0 Artikel
%@ 2296-4185
%A Linka, K.
%A Reiter, N.
%A Würges, J.
%A Schicht, M.
%A Bräuer, L.
%A Cyron, C.
%A Paulsen, F.
%A Budday, S.
%D 2021
%J Frontiers in Bioengineering and Biotechnology
%N 2665
%P 704738
%R doi:10.3389/fbioe.2021.704738
%T Unraveling the Local Relation Between Tissue Composition and Human Brain Mechanics Through Machine Learning
%U https://dx.doi.org/10.3389/fbioe.2021.704738
%X The regional mechanical properties of brain tissue are not only key in the context of brain injury and its vulnerability towards mechanical loads, but also affect the behavior and functionality of brain cells. Due to the extremely soft nature of brain tissue, its mechanical characterization is challenging. The response to loading depends on length and time scales and is characterized by nonlinearity, compression-tension asymmetry, conditioning, and stress relaxation. In addition, the regional heterogeneity–both in mechanics and microstructure–complicates the comprehensive understanding of local tissue properties and its relation to the underlying microstructure. Here, we combine large-strain biomechanical tests with enzyme-linked immunosorbent assays (ELISA) and develop an extended type of constitutive artificial neural networks (CANNs) that can account for viscoelastic effects. We show that our viscoelastic constitutive artificial neural network is able to describe the tissue response in different brain regions and quantify the relevance of different cellular and extracellular components for time-independent (nonlinearity, compression-tension-asymmetry) and time-dependent (hysteresis, conditioning, stress relaxation) tissue mechanics, respectively. Our results suggest that the content of the extracellular matrix protein fibronectin is highly relevant for both the quasi-elastic behavior and viscoelastic effects of brain tissue. While the quasi-elastic response seems to be largely controlled by extracellular matrix proteins from the basement membrane, cellular components have a higher relevance for the viscoelastic response. Our findings advance our understanding of microstructure - mechanics relations in human brain tissue and are valuable to further advance predictive material models for finite element simulations or to design biomaterials for tissue engineering and 3D printing applications.
%0 Artikel
%@ 1617-7061
%A Abdolazizi, K.
%A Linka, K.
%A Sprenger, J.
%A Neidhardt, M.
%A Schlaefer, A.
%A Cyron, C.
%D 2021
%J PAMM: Proceedings in Applied Mathematics and Mechanics
%N 1874
%P e202000284
%R doi:10.1002/pamm.202000284
%T Concentration-Specific Constitutive Modeling of Gelatin Based on Artificial Neural Networks
%U https://dx.doi.org/10.1002/pamm.202000284
1
%X Gelatin phantoms are frequently used in the development of surgical devices and medical imaging techniques. They exhibit mechanical properties similar to soft biological tissues [1] but can be handled at a much lower cost. Moreover, they enable a better reproducibility of experiments. Accurate constitutive models for gelatin are therefore of great interest for biomedical engineering. In particular it is important to capture the dependence of mechanical properties of gelatin on its concentration. Herein we propose a simple machine learning approach to this end. It uses artificial neural networks (ANN) for learning from indentation data the relation between the concentration of ballistic gelatin and the resulting mechanical properties.
%0 Artikel
%@ 1742-7061
%A Eichinger, J.F.
%A Paukner, D.
%A Aydin, R.C.
%A Wall, W.A.
%A Humphrey, J.D.
%A Cyron, C.J.
%D 2021
%J Acta Biomaterialia
%N 2256
%P 348 - 356
%R doi:10.1016/j.actbio.2021.07.054
%T What do cells regulate in soft tissues on short time scales?
%U https://dx.doi.org/10.1016/j.actbio.2021.07.054
%X Cells within living soft biological tissues seem to promote the maintenance of a mechanical state within a defined range near a so-called set-point. This mechanobiological process is often referred to as mechanical homeostasis. During this process, cells interact with the fibers of the surrounding extracellular matrix (ECM). It remains poorly understood, however, what individual cells actually regulate during these interactions, and how these micromechanical regulations are translated to the tissue-level to lead to what we observe as biomaterial properties. Herein, we examine this question by a combination of experiments, theoretical analysis, and computational modeling. We demonstrate that on short time scales (hours) - during which deposition and degradation of ECM fibers can largely be neglected - cells appear to not regulate the stress / strain in the ECM or their own shape, but rather only the contractile forces that they exert on the surrounding ECM.
%0 Artikel
%@ 0893-6080
%A Schiessler, E.
%A Aydin, R.
%A Linka, K.
%A Cyron, C.
%D 2021
%J Neural networks
%N 1812
%P 384 - 393
%R doi:10.1016/j.neunet.2021.08.034
%T Neural network surgery: Combining training with topology optimization
%U https://dx.doi.org/10.1016/j.neunet.2021.08.034
%X With ever increasing computational capacities, neural networks become more and more proficient at solving complex tasks. However, picking a sufficiently good network topology usually relies on expert human knowledge. Neural architecture search aims to reduce the extent of expertise that is needed. Modern architecture search techniques often rely on immense computational power, or apply trained meta-controllers for decision making. We develop a framework for a genetic algorithm that is both computationally cheap and makes decisions based on mathematical criteria rather than trained parameters. It is a hybrid approach that fuses training and topology optimization together into one process. Structural modifications that are performed include adding or removing layers of neurons, with some re-training applied to make up for any incurred change in input–output behaviour. Our ansatz is tested on several benchmark datasets with limited computational overhead compared to training only the baseline. This algorithm can achieve a significant increase in accuracy (as compared to a fully trained baseline), rescue insufficient topologies that in their current state are only able to learn to a limited extent, and dynamically reduce network size without loss in achieved accuracy. On standard ML datasets, accuracy improvements compared to baseline performance can range from 20% for well performing starting topologies to more than 40% in case of insufficient baselines, or reduce network size by almost 15%.
%0 Artikel
%@ 2057-3960
%A Schiessler, E.
%A Würger, T.
%A Lamaka, S.
%A Meißner, R.
%A Cyron, C.
%A Zheludkevich, M.
%A Feiler, C.
%A Aydin, R.
%D 2021
%J npj Computational Materials
%N 3030
%P 193
%R doi:10.1038/s41524-021-00658-7
%T Predicting the inhibition efficiencies of magnesium dissolution modulators using sparse machine learning models
%U https://dx.doi.org/10.1038/s41524-021-00658-7
1
%X The degradation behaviour of magnesium and its alloys can be tuned by small organic molecules. However, an automatic identification of effective organic additives within the vast chemical space of potential compounds needs sophisticated tools. Herein, we propose two systematic approaches of sparse feature selection for identifying molecular descriptors that are most relevant for the corrosion inhibition efficiency of chemical compounds. One is based on the classical statistical tool of analysis of variance, the other one based on random forests. We demonstrate how both can—when combined with deep neural networks—help to predict the corrosion inhibition efficiencies of chemical compounds for the magnesium alloy ZE41. In particular, we demonstrate that this framework outperforms predictions relying on a random selection of molecular descriptors. Finally, we point out how autoencoders could be used in the future to enable even more accurate automated predictions of corrosion inhibition efficiencies.
%0 Artikel
%@ 0264-1275
%A Ganesan, H.
%A Scheider, I.
%A Cyron, C.
%D 2021
%J Materials & Design
%N 2008
%P 110282
%R doi:10.1016/j.matdes.2021.110282
%T Understanding creep in TiAl alloys on the nanosecond scale by molecular dynamics simulations
%U https://dx.doi.org/10.1016/j.matdes.2021.110282
%X Molecular dynamics (MD) simulations of creep generally face the problem that the creep most often evolves on time scales hard to capture with MD due to their typically short time step size. Consequently, MD studies of creep often use unrealistically high temperatures and stresses and simplified atomistic models to make creep-like processes happen on computationally accessible time scales. Apparently, this compromises the physical reliability of such studies. To alleviate this problem, we designed an MD model of titanium aluminide (TiAl) with a microstructure matching at least many of the key parameters of experimentally observed microstructures. We applied this MD model with stresses much lower than the ones used in most previous creep studies (well below yield stress) and in the temperature range , with melting temperature . Compared to typical previous MD studies, this much more realistic setup produces creep rates more than three orders of magnitude smaller and thus much closer to reality. We identified the driving mechanisms of primary creep on the nanosecond scale that agree very well with recent experimental observations, thus contributing towards the overarching goal of bridging the gap between atomistic creep simulations and continuum-scale creep simulations for engineering applications.
%0 Artikel
%@ 2375-2548
%A Giuntini, D.
%A Zhao, S.
%A Krekeler, T.
%A Li, M.
%A Blankenburg, M.
%A Bor, B.
%A Schaan, G.
%A Domènech, B.
%A Müller, M.
%A Scheider, I.
%A Ritter, M.
%A Schneider, G.A.
%D 2021
%J Science Advances
%N 2650
%P eabb6063
%R doi:10.1126/sciadv.abb6063
%T Defects and plasticity in ultrastrong supercrystalline nanocomposites
%U https://dx.doi.org/10.1126/sciadv.abb6063
2
%X Supercrystalline nanocomposites are nanoarchitected materials with a growing range of applications but unexplored in their structural behavior. They typically consist of organically functionalized inorganic nanoparticles arranged into periodic structures analogous to crystalline lattices, including superlattice imperfections induced by processing or mechanical loading. Although featuring a variety of promising functional properties, their lack of mechanical robustness and unknown deformation mechanisms hamper their implementation into devices. We show that supercrystalline materials react to indentation with the same deformation patterns encountered in single crystals. Supercrystals accommodate plastic deformation in the form of pile-ups, dislocations, and slip bands. These phenomena occur, at least partially, also after cross-linking of the organic ligands, which leads to a multifold strengthening of the nanocomposites. The classic shear theories of crystalline materials are found to describe well the behavior of supercrystalline nanocomposites, which result to feature an elastoplastic behavior, accompanied by compaction.
%0 Artikel
%@ 2213-9567
%A Tang, W.
%A Lee, J.
%A Wang, H.
%A Steglich, D.
%A Li, D.
%A Peng, Y.
%A Wu, P.
%D 2021
%J Journal of Magnesium and Alloys
%N 2523
%P 927 - 936
%R doi:10.1016/j.jma.2020.02.023
%T Unloading behaviors of the rare-earth magnesium alloy ZE10 sheet
%U https://dx.doi.org/10.1016/j.jma.2020.02.023
3
%X Due to their low symmetry in crystal structure, low elastic modulus (∼45 GPa) and low yielding stress, magnesium (Mg) alloys exhibit strong inelastic behaviors during unloading. As more and more Mg alloys are developed, their unloading behaviors were less investigated, especially for rare-earth (RE) Mg alloys. In the current work, the unloading behaviors of the RE Mg alloy ZE10 sheet is carefully studied by both mechanical tests and crystal plasticity modeling. In terms of the stress–strain curves, the inelastic strain, the chord modulus, and the active deformation mechanisms, the substantial anisotropy and the loading path dependency of the unloading behaviors of ZE10 sheets are characterized. The inelastic strains are generally larger under compressive Loading–UnLoading (L–UL) than under tensile L–UL, along the transverse direction (TD) than along the rolling direction (RD) under tensile L–UL, and along RD than along TD under compressive L–UL. The basal slip, twinning and de-twinning are found to be responsible for the unloading behaviors of ZE10 sheets.