Automated discovery of generalized standard material models with EUCLID

We extend the scope of our approach for unsupervised automated discovery of material laws (EUCLID) to the case of a material belonging to an unknown class of behavior. To this end, we leverage the theory of generalized standard materials, which encompasses a plethora of important constitutive classes. We show that, based only on full-field kinematic measurements and net reaction forces, EUCLID is able to automatically discover the two scalar thermodynamic potentials, namely, the Helmholtz free energy and the dissipation potential, which completely define the behavior of generalized standard materials. The a priori enforced constraint of convexity on these potentials guarantees by construction stability and thermodynamic consistency of the discovered model; balance of linear momentum acts as a fundamental constraint to replace the availability of stress-strain labeled pairs; sparsity promoting regularization enables the automatic selection of a small subset from a possibly large number of candidate model features and thus leads to a parsimonious, i.e., simple and interpretable, model. Importantly, since model features go hand in hand with the correspondingly active internal variables, sparse regression automatically induces a parsimonious selection of the few internal variables needed for an accurate but simple description of the material behavior. A fully automatic procedure leads to the selection of the hyperparameter controlling the weight of the sparsity promoting regularization term, in order to strike a user-defined balance between model accuracy and simplicity. By testing the method on synthetic data including artificial noise, we demonstrate that EUCLID is able to automatically discover the true hidden material model from a large catalog of constitutive classes, including elasticity, viscoelasticity, elastoplasticity, viscoplasticity, isotropic and kinematic hardening

A comparative study on different neural network architectures to model inelasticity

The mathematical formulation of constitutive models to describe the path-dependent, i.e., inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased efforts to facilitate or automate this task through data-driven techniques, impelled in particular by the recent revival of neural networks (NNs) in computational mechanics. However, it seems questionable to simply not consider fundamental findings of constitutive modeling originating from the last decades research within NN-based approaches. Herein, we propose a comparative study on different feedforward and recurrent neural network architectures to model inelasticity. Within this study, we divide the models into three basic classes: black box NNs, NNs enforcing physics in a weak form, and NNs enforcing physics in a strong form. Thereby, the first class of networks can learn constitutive relations from data while the underlying physics are completely ignored, whereas the latter two are constructed such that they can account for fundamental physics, where special attention is paid to the second law of thermodynamics in this work. Conventional linear and nonlinear viscoelastic as well as elastoplastic models are used for training data generation and, later on, as reference. After training with random walk time sequences containing information on stress, strain, and, for some models, internal variables, the NN-based models are compared to the reference solution, whereby interpolation and extrapolation are considered. Besides the quality of the stress prediction, the related free energy and dissipation rate are analyzed to evaluate the models. Overall, the presented study enables a clear recording of the advantages and disadvantages of different NN architectures to model inelasticity and gives guidance on how to train and apply these models

Determining kernels in linear viscoelasticity

In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal viscoelastic wave equation. To this end, we minimize a tracking-type data misfit function under this PDE constraint. We perform the well-posedness analysis of the state and adjoint problems and, using these results, rigorously derive the first-order sensitivities. Numerical experiments in a three-dimensional setting illustrate the method

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.10066805Comment: 54 pages, 14 figures, 14 table

Bridging spatiotemporal scales in biomechanical models for living tissues : from the contracting Esophagus to cardiac growth

Appropriate functioning of our body is determined by the mechanical behavior of our organs. An improved understanding of the biomechanical functioning of the soft tissues making up these organs is therefore crucial for the choice for, and development of, efficient clinical treatment strategies focused on patient-specific pathophysiology. This doctoral dissertation describes the passive and active biomechanical behavior of gastrointestinal and cardiovascular tissue, both in the short and long term, through computer models that bridge the cell, tissue and organ scale. Using histological characterization, mechanical testing and medical imaging techniques, virtual esophagus and heart models are developed that simulate the patient-specific biomechanical organ behavior as accurately as possible. In addition to the diagnostic value of these models, the developed modeling technology also allows us to predict the acute and chronic effect of various treatment techniques, through e.g. drugs, surgery and/or medical equipment. Consequently, this dissertation offers insights that will have an unmistakable impact on the personalized medicine of the future.Het correct functioneren van ons lichaam wordt bepaald door het mechanisch gedrag van onze organen. Een verbeterd inzicht in het biomechanisch functioneren van deze zachte weefsels is daarom van cruciale waarde voor de keuze voor, en ontwikkeling van, efficiënte klinische behandelingsstrategieën gefocust op de patiënt-specifieke pathofysiologie. Deze doctoraatsthesis brengt het passieve en actieve biomechanisch gedrag van gastro-intestinaal en cardiovasculair weefsel, zowel op korte als lange termijn, in kaart via computermodellen die een brug vormen tussen cel-, weefsel- en orgaanniveau. Aan de hand van histologische karakterisering, mechanische testen en medische beeldvormingstechnieken worden virtuele slokdarm- en hartmodellen ontwikkeld die het patiënt-specifieke orgaangedrag zo accuraat mogelijk simuleren. Naast de diagnostische waarde van deze modellen, laat de ontwikkelde modelleringstechnologie ook toe om het effect van verschillende behandelingstechnieken, via medicatie, chirurgie en/of medische apparatuur bijvoorbeeld, acuut en chronisch te voorspellen. Bijgevolg biedt deze doctoraatsthesis inzichten die een onmiskenbare impact zullen hebben op de gepersonaliseerde geneeskunde van de toekomst

Continuum Mechanical Models for Design and Characterization of Soft Robots

The emergence of ``soft'' robots, whose bodies are made from stretchable materials, has fundamentally changed the way we design and construct robotic systems. Demonstrations and research show that soft robotic systems can be useful in rehabilitation, medical devices, agriculture, manufacturing and home assistance. Increasing need for collaborative, safe robotic devices have combined with technological advances to create a compelling development landscape for soft robots. However, soft robots are not yet present in medical and rehabilitative devices, agriculture, our homes, and many other human-collaborative and human-interactive applications. This gap between promise and practical implementation exists because foundational theories and techniques that exist in rigid robotics have not yet been developed for soft robots. Theories in traditional robotics rely on rigid body displacements via discrete joints and discrete actuators, while in soft robots, kinematic and actuation functions are blended, leading to nonlinear, continuous deformations rather than rigid body motion. This dissertation addresses the need for foundational techniques using continuum mechanics. Three core questions regarding the use of continuum mechanical models in soft robotics are explored: (1) whether or not continuum mechanical models can describe existing soft actuators, (2) which physical phenomena need to be incorporated into continuum mechanical models for their use in a soft robotics context, and (3) how understanding on continuum mechanical phenomena may form bases for novel soft robot architectures. Theoretical modeling, experimentation, and design prototyping tools are used to explore Fiber-Reinforced Elastomeric Enclosures (FREEs), an often-used soft actuator, and to develop novel soft robot architectures based on auxetic behavior. This dissertation develops a continuum mechanical model for end loading on FREEs. This model connects a FREE’s actuation pressure and kinematic configuration to its end loads by considering stiffness of its elastomer and fiber reinforcement. The model is validated against a large experimental data set and compared to other FREE models used by roboticists. It is shown that the model can describe the FREE’s loading in a generalizable manner, but that it is bounded in its peak performance. Such a model can provide the novel function of evaluating the performance of FREE designs under high loading without the costs of building and testing prototypes. This dissertation further explores the influence viscoelasticity, an inherent property of soft polymers, on end loading of FREEs. The viscoelastic model developed can inform soft roboticists wishing to exploit or avoid hysteresis and force reversal. The final section of the dissertations explores two contrasting styles of auxetic metamaterials for their uses in soft robotic actuation. The first metamaterial architecture is composed of beams with distributed compliance, which are placed antagonistic configurations on a variety of surfaces, giving ride to shape morphing behavior. The second metamaterial architecture studied is a ``kirigami’’ sheet with an orthogonal cut pattern, utilizing lumped compliance and strain hardening to permanently deploy from a compact shape to a functional one. This dissertation lays the foundation for design of soft robots by robust physical models, reducing the need for physical prototypes and trial-and-error approaches. The work presented provides tools for systematic exploration of FREEs under loading in a wide range of configurations. The work further develops new concepts for soft actuators based on continuum mechanical modeling of auxetic metamaterials. The work presented expands the available tools for design and development of soft robotic systems, and the available architectures for soft robot actuation.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163236/1/asedal_1.pd

NN-EVP: A physics informed neural network-based elasto-viscoplastic framework for predictions of grain size-aware flow response under large deformations

We propose a physics informed, neural network-based elasto-viscoplasticity (NN-EVP) constitutive modeling framework for predicting the flow response in metals as a function of underlying grain size. The developed NN-EVP algorithm is based on input convex neural networks as a means to strictly enforce thermodynamic consistency, while allowing high expressivity towards model discovery from limited data. It utilizes state-of-the-art machine learning tools within PyTorch's high-performance library providing a flexible tool for data-driven, automated constitutive modeling. To test the performance of the framework, we generate synthetic stress-strain curves using a power law-based model with phenomenological hardening at small strains and test the trained model for strain amplitudes beyond the training data. Next, experimentally measured flow responses obtained from uniaxial deformations are used to train the framework under large plastic deformations. Ultimately, the Hall-Petch relationship corresponding to grain size strengthening is discovered by training flow response as a function of grain size, also leading to efficient extrapolation. The present work demonstrates a successful integration of neural networks into elasto-viscoplastic constitutive laws, providing a robust automated framework for constitutive model discovery that can efficiently generalize, while also providing insights into predictions of flow response and grain size-property relationships in metals and metallic alloys under large plastic deformations