Biaxial characterization of soft elastomers: experiments and data-adaptive configurational forces for fracture

Abstract

Understanding the fracture mechanics of soft solids remains a fundamental challenge due to their complex, nonlinear responses under large deformations. While multiaxial loading is key to probing their mechanical behavior, the role of such loading in fracture processes is still poorly understood. Here, we present a combined experimental-computational framework to investigate fracture in soft elastomers under equi-biaxial loading. We report original equi-biaxial quasi-static experiments on five elastomeric materials, revealing a spectrum of material and fracture behavior, from brittle-like to highly deformable response with crack tip strains exceeding 150 %. Motivated by these observations, we develop a hybrid computational testbed that mirrors the experimental setup and enables virtual biaxial tests. Central to this framework are two components: a data-adaptive formulation of hyperelastic energy functions that flexibly captures material behavior, and a post-processing implementation of the Configurational Force Method, providing a computationally efficient estimate of the J-integral at the crack tip. Our data-adaptive framework for hyperelastic energy functions proves versatility to capture with high accuracy the hyperelastic behavior observed in the biaxial experiments. This is important because accurately capturing the constitutive behaviour of soft solids is key for a reliable application of the Configurational Force Method to soft solids. In the limit of crack onset, a critical value of the crack tip configurational force allows for a criterion of fracture toughness. Together, our experimental, theoretical, and computational contributions offer a new paradigm for characterizing and designing soft materials with tailored fracture properties.