Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

We present a machine learning approach that integrates geometric deep learning and
Sobolev training to generate a family of finite strain anisotropic hyperelastic models that …

We present a new neural-network architecture, called the Cholesky-factored symmetric
positive definite neural network (SPD-NN), for modeling constitutive relations in …

This paper examines the frame-invariance (and the lack thereof) exhibited in simulated
anisotropic elasto-plastic responses generated from supervised machine learning of …

The commercial finite element (FE) code Abaqus is coupled with the deep neural network
(DNN) model, namely Abaqus-DNN mechanics system, to learn the constitutive law of the …

Neural networks with physical governing equations as constraints have recently created a
new trend in machine learning research. In this context, a review of related research is first …

Artificial neural network (ANN) models are used to learn the nonlinear constitutive laws
based on indirectly measurable data. The real input and output of the ANN model are …

This paper presents a finite element (FE) coupled positive definite deep neural networks
mechanics system (FE-PDNN). The proposed approach enables neural networks to learn …

Real-world fabrics, composed of threads and yarns, often display complex stress-strain
relationships, making their homogenization a challenging task for fast simulation by …

A general‐purpose computational homogenization framework is proposed for the nonlinear
dynamic analysis of membranes exhibiting complex microscale and/or mesoscale …