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Constitutive models play a crucial role in materials science as they describe the behavior of the materials in mathematical forms. Over the last few decades, the rapid development of manufacturing technologies have led to the discovery of…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose…

We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…

In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies…

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation.…

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the…

In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using…

We propose a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations. We formulate the problem of inferring constitutive relations from experiments as an indirect inverse…

Data-driven methods are becoming an essential part of computational mechanics due to their unique advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of…

The accuracy and fidelity of deformation simulations are highly dependent upon the underlying constitutive material model. Commonly used linear or nonlinear constitutive material models only cover a tiny part of possible material behavior.…

Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized…

There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during…

We develop a new neural network architecture that strictly enforces constitutive constraints such as polyconvexity, frame-indifference, and the symmetry of the stress and material stiffness. Additionally, we show that the accuracy of the…

We introduce inverse transport networks as a learning architecture for inverse rendering problems where, given input image measurements, we seek to infer physical scene parameters such as shape, material, and illumination. During training,…