Design of a specimen to train path-dependent deep learning material models from a single uniaxial test: eliciting strain diversity via automatically differentiable elastoplastic topology optimization

TL;DR

This paper introduces a novel specimen design method using differentiable topology optimization to generate diverse stress-strain data from a single uniaxial test, enabling efficient training of neural network material models.

Contribution

It presents a new automatically differentiable elastoplastic topology optimization technique to create specimens that produce varied stress-strain responses from a single test.

Findings

Neural networks can be trained with data from a single optimized specimen.

The method reduces the need for multiple experiments or complex tests.

Topology-optimized specimens effectively generate diverse stress-strain trajectories.

Abstract

Artificial neural networks accurately learn nonlinear, path-dependent material behavior. However, training them typically requires large, diverse datasets, often created via synthetic unit cell simulations. This hinders practical adoption because physical experiments on standardized specimens with simple geometries fail to generate sufficiently diverse stress-strain trajectories. Consequently, an unreasonably large number of experiments or complex multi-axial tests would be needed. This work shows that such networks can be trained from a single specimen subjected to simple uniaxial loading, by designing the specimen using a novel automatically differentiable elastoplastic topology optimization method. Our strategy diversifies the stress-strain states observed in a single test involving plastic deformation. We then employ the automatically differentiable model updating (ADiMU) method to train the neural network surrogates. This work demonstrates that topology-optimized specimens under simple loading can train large neural networks, thereby substantially reducing the experimental burden associated with data-driven material modeling.