arXiv subjects

Stefanie Reese

Publications and source records attributed to Stefanie Reese.

At least 37 records · Page 2Linked to original sources

arXiv2023

Mechanical Comparison of Arrangement Strategies for Topological Interlocking Assemblies

Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the literature several blocks are introduced that can be arranged into different interlocking assemblies. In this study we investigate the influence of arrangement on the overall structural behaviour of the resulting interlocking assemblies. This is performed using the Versatile Block, as it can be arranged in three different doubly periodic ways given by wallpaper symmetries. Our focus lies on the load transfer mechanisms from the assembly onto the frame. For fast a priori evaluation of the assemblies we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection. The results of the finite element analysis are in very good agreement with the predictions of the Interlocking Flow model. Our source code, data and examples are available under https://doi.org/10.5281/zenodo.10246034.

cs.CE↗

arXiv2023

Discrete Empirical Interpolation Method for nonlinear softening problems involving damage and plasticity

Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties lead to a significant increase in computational effort. Model order reduction aims to implement efficient methods for accelerating the simulation process while preserving a high degree of accuracy. Numerous studies have already demonstrated the benefits of this method for linear elastic material modeling. However, in the present work, we investigate a two-surface gradient-extended damage-plasticity model. We conducted complex simulations with this model, demonstrating both damage behavior and softening. The POD-based discrete empirical interpolation method (DEIM) is introduced and implemented. To accomplish simulations with DEIM and softening behaviour, we propose the implementation of a reduced form of the arc-length method. Existing research on calculating models with both damage and softening behavior using the DEIM and arc-length method is limited. To validate the methods, two numerical examples are thoroughly investigated in this study: a plate with a hole and an asymmetrically notched specimen. The results show that the proposed methods can create a reduced order model with high accuracy and a significant speedup of the simulation. For both examples, the analysis is conducted in three steps: first, plasticity without damage is examined, followed by damage without plasticity, and finally, the combination of plasticity and damage is investigated.

cs.CE↗

arXiv2023

A comparative study of micromorphic gradient-extensions for anisotropic damage at finite strains

Modern inelastic material model formulations rely on the use of tensor-valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the tensor-valued internal variables is essential to obtain physically correct results. Here, we focus on the regularization of anisotropic damage at finite strains. Thus, a flexible anisotropic damage model with isotropic, kinematic, and distortional hardening is equipped with three gradient-extensions using a full and two reduced regularizations of the damage tensor. Theoretical and numerical comparisons of the three gradient-extensions yield excellent agreement between the full and the reduced regularization based on a volumetric-deviatoric regularization using only two nonlocal degrees of freedom.

cs.CE↗

arXiv2023

Theory and implementation of inelastic Constitutive Artificial Neural Networks

Nature has always been our inspiration in the research, design and development of materials and has driven us to gain a deep understanding of the mechanisms that characterize anisotropy and inelastic behavior. All this knowledge has been accumulated in the principles of thermodynamics. Deduced from these principles, the multiplicative decomposition combined with pseudo potentials are powerful and universal concepts. Simultaneously, the tremendous increase in computational performance enabled us to investigate and rethink our history-dependent material models to make the most of our predictions. Today, we have reached a point where materials and their models are becoming increasingly sophisticated. This raises the question: How do we find the best model that includes all inelastic effects to explain our complex data? Constitutive Artificial Neural Networks (CANN) may answer this question. Here, we extend the CANNs to inelastic materials (iCANN). Rigorous considerations of objectivity, rigid motion of the reference configuration, multiplicative decomposition and its inherent non-uniqueness, restrictions of energy and pseudo potential, and consistent evolution guide us towards the architecture of the iCANN satisfying thermodynamics per design. We combine feed-forward networks of the free energy and pseudo potential with a recurrent neural network approach to take time dependencies into account. We demonstrate that the iCANN is capable of autonomously discovering models for artificially generated data, the response of polymers for cyclic loading and the relaxation behavior of muscle data. As the design of the network is not limited to visco-elasticity, our vision is that the iCANN will reveal to us new ways to find the various inelastic phenomena hidden in the data and to understand their interaction. Our source code, data, and examples are available at doi.org/10.5281/zenodo.10066805

cs.LG↗

arXiv2023

Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have shown that when designing loss functions for many engineering problems, using first-order derivatives and combining equations from both strong and weak forms can lead to much better accuracy, especially when there are heterogeneity and variable jumps in the domain. This new approach is called the mixed formulation for PINNs, which takes ideas from the mixed finite element method. In this method, the PDE is reformulated as a system of equations where the primary unknowns are the fluxes or gradients of the solution, and the secondary unknowns are the solution itself. In this work, we propose applying the mixed formulation to solve multi-physical problems, specifically a stationary thermo-mechanically coupled system of equations. Additionally, we discuss both sequential and fully coupled unsupervised training and compare their accuracy and computational cost. To improve the accuracy of the network, we incorporate hard boundary constraints to ensure valid predictions. We then investigate how different optimizers and architectures affect accuracy and efficiency. Finally, we introduce a simple approach for parametric learning that is similar to transfer learning. This approach combines data and physics to address the limitations of PINNs regarding computational cost and improves the network's ability to predict the response of the system for unseen cases. The outcomes of this work will be useful for many other engineering applications where deep learning is employed on multiple coupled systems of equations for fast and reliable computations.

cs.CE↗

arXiv2023

Computational modeling of in-stent restenosis: Pharmacokinetic and pharmacodynamic evaluation

Persistence of the pathology of in-stent restenosis even with the advent of drug-eluting stents warrants the development of highly resolved in silico models. These computational models assist in gaining insights into the transient biochemical and cellular mechanisms involved and thereby optimize the stent implantation parameters. Within this work, an already established fully-coupled Lagrangian finite element framework for modeling the restenotic growth is enhanced with the incorporation of endothelium-mediated effects and pharmacological influences of rapamycin-based drugs embedded in the polymeric layers of the current generation drug-eluting stents. The continuum mechanical description of growth is further justified in the context of thermodynamic consistency. Qualitative inferences are drawn from the model developed herein regarding the efficacy of the level of drug embedment within the struts as well as the release profiles adopted. The framework is then intended to serve as a tool for clinicians to tune the interventional procedures patient-specifically.

cs.CE↗

arXiv2023

Mechanical modeling of the maturation process for tissue-engineered implants: application to biohybrid heart valves

The development of tissue-engineered cardiovascular implants can improve the lives of large segments of our society who suffer from cardiovascular diseases. Regenerative tissues are fabricated using a process called tissue maturation. Furthermore, it is highly challenging to produce cardiovascular regenerative implants with sufficient mechanical strength to withstand the loading conditions within the human body. Therefore, biohybrid implants for which the regenerative tissue is reinforced by standard reinforcement material (e.g. textile or 3d printed scaffold) can be an interesting solution. In silico models can significantly contribute to characterizing, designing, and optimizing biohybrid implants. The first step towards this goal is to develop a computational model for the maturation process of tissue-engineered implants. This paper focuses on the mechanical modeling of textile-reinforced tissue-engineered cardiovascular implants. First, we propose an energy-based approach to compute the collagen evolution during the maturation process. Then, we apply the concept of structural tensors to model the anisotropic behavior of the extracellular matrix and the textile scaffold. Next, the newly developed material model is embedded into a special solid-shell finite element formulation with reduced integration. Finally, we use our framework to compute two structural problems: a pressurized shell construct and a tubular-shaped heart valve. The results show the ability of the model to predict collagen growth in response to the boundary conditions applied during the maturation process. Consequently, we can predict the implant's mechanical response, such as the deformation and stresses of the implant.

cs.CE↗

arXiv2022

Model-Free Data-Driven Inference in Computational Mechanics

We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a constitutive relation. We specifically assume that the material likelihood measure is known only through an empirical point-data set in material or phase space. The state of the solid or structure is additionally subject to compatibility and equilibrium constraints. The problem is then to infer the likelihood of a given structural outcome of interest. In this work, we present a Data-Driven method of inference that determines likelihoods of outcomes from the empirical material data and that requires no material or prior modeling. In particular, the computation of expectations is reduced to explicit sums over local material data sets and to quadratures over admissible states, i. e., states satisfying compatibility and equilibrium. The complexity of the material data-set sums is linear in the number of data points and in the number of members in the structure. Efficient population annealing procedures and fast search algorithms for accelerating the calculations are presented. The scope, cost and convergence properties of the method are assessed with the aid selected applications and benchmark tests.

cs.CE↗

arXiv2022

A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering problems. The main contribution of the current work is to promote using the spatial gradient of the primary variable as an output from separated neural networks. Later on, the strong form which has a higher order of derivatives is applied to the spatial gradients of the primary variable as the physical constraint. In addition, the so-called energy form of the problem is applied to the primary variable as an additional constraint for training. The proposed approach only required up to first-order derivatives to construct the physical loss functions. We discuss why this point is beneficial through various comparisons between different models. The mixed formulation-based PINNs and FE methods share some similarities. While the former minimizes the PDE and its energy form at given collocation points utilizing a complex nonlinear interpolation through a neural network, the latter does the same at element nodes with the help of shape functions. We focus on heterogeneous solids to show the capability of deep learning for predicting the solution in a complex environment under different boundary conditions. The performance of the proposed PINN model is checked against the solution from FEM on two prototype problems: elasticity and the Poisson equation (steady-state diffusion problem). We concluded that by properly designing the network architecture in PINN, the deep learning model has the potential to solve the unknowns in a heterogeneous domain without any available initial data from other sources. Finally, discussions are provided on the combination of PINN and FEM for a fast and accurate design of composite materials in future developments.

cs.CE↗

arXiv2022

A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation

Development of in silico models are intrinsic in understanding disease progression in soft biological tissues. Within this work, we propose a fully-coupled Lagrangian finite element framework which replicates the process of in-stent restenosis observed post stent implantation in a coronary artery. Coupled advection-reaction-diffusion reactions are set up that track the evolution of the concentrations of the platelet-derived growth factor, the transforming growth factor-$β$, the extracellular matrix, and the density of the smooth muscle cells. A continuum mechanical description of growth incorporating the evolution of arterial wall constituents is developed, and a suitable finite element implementation discussed. Qualitative validation of the computational model are presented by emulating a stented artery. Patient-specific data can be integrated into the model to predict the risk of restenosis and thereby assist in tuning of stent implantation parameters to mitigate the risk.

cs.CE↗

arXiv2022

Modeling moving boundary value problems in electrochemical machining

This work presents a new approach to efficiently model the cathode in the moving boundary value problem of electrochemical machining. Until recently, the process simulation with finite elements had the drawback of remeshing required by the changing surface geometries. This disadvantage was overcome by a novel model formulation for the anodic dissolution that utilizes effective material parameters as well as the dissolution level as an internal variable and, thereby, does not require remeshing. Now, we extend this concept to model arbitrarily shaped and moving cathodes. Two methodologies are investigated to describe the time varying position of the cathode. In the first approach, we change the electric conductivity of elements within the cathode and, in a second approach, we apply Dirichlet boundary conditions on the nodes of corresponding elements. For both methods, elements on the cathode's surface are treated with effective material parameters. This procedure allows for the efficient simulation of industrially relevant, complex geometries without mesh adaptation. The model's performance is validated by means of analytical, numerical and experimental results from the literature. The short computation times make the approach interesting for industrial applications.

cs.CE↗

arXiv2021

An anisotropic cohesive fracture model: advantages and limitations of length-scale insensitive phase-field damage models

The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the idea introduced in \cite{REZAEI2021a} for direction-dependent fracture energy and also anisotropic PF damage models based on structural tensors. The cohesive PF damage formulation used in the current contribution is motivated by the works of \cite{LORENTZ201120, wu2018, GEELEN2019}. The results of the latter models are shown to be insensitive with respect to the length scale parameter for the isotropic case. This is because they manage to formulate the fracture energy as a function of diffuse displacement jumps in the localized damaged zone. In the present paper, we discuss numerical examples and details on finite element implementations where the fracture energy, as well as the material strength, are introduced as an arbitrary function of the crack direction. Using the current formulation for anisotropic cohesive fracture, the obtained results are almost insensitive with respect to the length scale parameter. The latter is achieved by including the direction-dependent strength of the material in addition to its fracture energy. Utilizing the current formulation, one can increase the mesh size which reduces the computational time significantly without any severe change in the predicted crack path and overall obtained load-displacement curves. We also argue that these models still lack to capture mode-dependent fracture properties. Open issues and possible remedies for future developments are finally discussed as well.

cs.CE↗

arXiv2021

A geometrically adapted reduced set of frequencies for a FFT-based microstructure simulation

We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al. [2019]), which is based on solving the Lippmann-Schwinger equation in Fourier space by a reduced set of frequencies. Crucial for the accuracy of this MOR technique is on the one hand the amount of used frequencies and on the other hand the choice of frequencies used within the simulation. Kochmann et al. [2019] defined the reduced set of frequencies by using a fixed sampling pattern, which is most general but leads to poor microstructural results when considering only a few frequencies. Consequently, a reconstruction algorithm based on the TV1-algorithm [Candes et al., 2006] was used in a post-processing step to generate highly resolved micromechanical fields. The present work deals with a modified sampling pattern generation for this MOR technique. Based on the idea, that the micromechanical material response strongly depends on the phase-wise material behavior, we propose the usage of sampling patterns adapted to the spatial arrangement of the individual phases. This leads to significantly improved microscopic and overall results. Hence, the time-consuming reconstruction in the post-processing step that was necessary in the earlier work is no longer required. To show the adaptability and robustness of this new choice of sampling patterns, several two dimensional examples are investigated. In addition, also the 3D extension of the algorithm is presented.

cs.CE↗

arXiv2021

A novel approach for the efficient modeling of material dissolution in electrochemical machining

This work presents a novel approach to efficiently model anodic dissolution in electrochemical machining. Earlier modeling approaches employ a strict space discretization of the anodic surface that is associated with a remeshing procedure at every time step. Besides that, the presented model is formulated by means of effective material parameters. Thereby, it allows to use a constant mesh for the entire simulation and, thus, decreases the computational costs. Based on Faraday's law of electrolysis, an effective dissolution level is introduced, which describes the ratio of a dissolved volume and its corresponding reference volume. This inner variable allows the modeling of the complex dissolution process without the necessity of computationally expensive remeshing by controlling the effective material parameters. Additionally, full coupling of the thermoelectric problem is considered and its linearization and numerical implementation are presented. The model shows good agreement with analytical and experimental validation examples by yielding realistic results. Furthermore, simulations of a pulsed electrochemical machining process yield a process signature of the surface roughness related to the specific accumulated electric charge. The numerical examples confirm the simulation's computational efficiency and accurate modeling qualities.

cs.CE↗

arXiv2020

Finite element modelling of in-stent restenosis

From the perspective of coronary heart disease, the development of stents has come significantly far in reducing the associated mortality rate, drug-eluting stents being the epitome of innovative and effective solutions. Within this work, the intricate process of in-stent restenosis is modelled considering one of the significant growth factors and its effect on constituents of the arterial wall. A multiphysical modelling approach is adopted in this regard. Experimental investigations from the literature have been used to hypothesize the governing equations and the corresponding parameters. A staggered solution strategy is utilised to capture the transport phenomena as well as the growth and remodeling that follows stent implantation. The model herein developed serves as a tool to predict in-stent restenosis depending on the endothelial injury sustained and the protuberance of stents into the lumen of the arteries. Keywords: in-stent restenosis, smooth mucsle cells, platelet-derived growth factor, extracellular matrix, growth

cs.CE↗

arXiv2020

Efficient Data Structures for Model-free Data-Driven Computational Mechanics

The data-driven computing paradigm initially introduced by Kirchdoerfer and Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data set. In this study, we compare and develop several possible data structures for solving the nearest-neighbor problem. We show that approximate nearest-neighbor (ANN) algorithms can accelerate material data searches by several orders of magnitude relative to exact searching algorithms. The approximations are suggested by--and adapted to--the structure of the data-driven iterative solver and result in no significant loss of solution accuracy. We assess the performance of the ANN algorithm with respect to material data set size with the aid of a 3D elasticity test case. We show that computations on a single processor with up to one billion material data points are feasible within a few seconds execution time with a speedup of more than 106 with respect to exact k-d trees.

cs.CE↗

arXiv2020

Model-free Data-Driven Computational Mechanics Enhanced by Tensor Voting

The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent spaces are constructed by means of the tensor voting method introduced by Mordohai & Medioni (2010) which improves the learning of the underlying structure of a data set. Tensor voting is an instance-based machine learning technique which accumulates votes from the nearest neighbors to build up second-order tensors encoding tangents and normals to the underlying data structure. The here proposed second-order data-driven paradigm is a plug-in method for distance-minimizing as well as entropy-maximizing data-driven schemes. Like its predecessor, the resulting method aims to minimize a suitably defined free energy over phase space subject to compatibility and equilibrium constraints. The method's implementation is straightforward and numerically efficient since the data structure analysis is performed in an offline step. Selected numerical examples are presented that establish the higher-order convergence properties of the data-driven solvers enhanced by tensor voting for ideal and noisy data sets.

cs.CE↗

arXiv2019

Proper orthogonal decomposition (POD) combined with hierarchical tensor approximation (HTA) in the context of uncertain parameters

The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the proper orthogonal decomposition. When only a few quantities are of interest an approximative mapping from the high-dimensional parameter space onto each quantity of interest is sufficient. Appropriate methods for this task are for instance the polynomial chaos expansion or low-rank tensor approximations. In this work we focus on a non-linear neo-hookean deformation problem with the maximal deformation as our quantity of interest. POD and adaptive POD models of this problem are constructed and compared with respect to approximation quality and construction cost. Additionally, the adapative proper orthogonal decomposition (APOD) is introduced and compared to the regular POD. Building upon that, several hierarchical Tucker approximations (HTAs) are constructed from the reduced and unreduced models. A simple Monte Carlo method in combination with HTA and (A)POD is used to estimate the mean and variance of our quantity of interest. Furthermore, the HTA of the unreduced model is employed to find feasible snapshots for (A)POD.

math.NA↗