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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…

In recent years, various artificial intelligence-based surrogate models have been proposed to provide rapid manufacturability predictions of material forming processes. However, traditional AI-based surrogate models, typically built with…

As a surrogate for computationally intensive meso-scale simulation of woven composites, this article presents Recurrent Neural Network (RNN) models. Leveraging the power of transfer learning, the initialization challenges and sparse data…

Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties.…

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

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…

We present a method whereby the finite element method is used to train physics-informed neural networks that are suitable for surrogate modeling. The method is based on a custom convolutional operation called stencil convolution which…

Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. Traditionally, these surrogates have been…

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…

Artificial Neural Networks (NNWs) are appealing functions to substitute high dimensional and non-linear history-dependent problems in computational mechanics since they offer the possibility to drastically reduce the computational time.…

This study presents an integrated computational framework that, given synthesis parameters, predicts the resulting microstructural morphology and mechanical response of ceramic aerogel porous materials by combining physics-based simulations…

The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential.…

We propose a surrogate model for two-scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macro-energy density.…

The purpose of this work is the development of an artificial neural network (ANN) for surrogate modeling of the mechanical response of viscoplastic grain microstructures. To this end, a U-Net-based convolutional neural network (CNN) is…

Accurate modeling of Short Fiber Reinforced Composites (SFRCs) remains computationally expensive for full-field simulations. Data-driven surrogate models using Artificial Neural Networks (ANNs) have been proposed as an efficient alternative…

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…

The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…

We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure and…

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…