A constitutive framework for tension-compression failure asymmetry in soft materials

TL;DR

This paper introduces a Lode-invariant-based hyperelastic softening model that captures tension-compression failure asymmetry in soft materials, validated with agarose hydrogels, and capable of predicting behavior across different deformation modes.

Contribution

It develops a novel, thermodynamically consistent constitutive model incorporating deformation-mode dependence without internal damage variables, extending previous energy-limiting approaches.

Findings

Accurately reproduces uniaxial tension and compression responses.

Predicts pure shear behavior from calibrated parameters.

Confirms stable energy landscape across deformation modes.

Abstract

Soft materials often exhibit pronounced tension-compression asymmetry (TCA) in their softening and failure behavior, a feature that conventional hyperelastic and continuum-damage formulations fail to capture within a unified framework. This work presents a Lode-invariant-based hyperelastic softening model that explicitly incorporates deformation-mode dependence through a bi-failure construction with distinct tensile and compressive energy limiters. The proposed model extends Volokh's classical energy-limiting approach by embedding a Lode-angle-dependent weighting function, which ensures a smooth and thermodynamically consistent transition of failure behavior across distortion modes, achieved directly within the constitutive description of the bulk response, without introducing internal damage variables. Agarose hydrogels (1, 2, and 3% w/v) serve as the model system for validation. The framework accurately reproduces experimental stress-stretch responses in uniaxial tension and compression, capturing concentration-dependent stiffness and failure energetics. Using parameters calibrated solely from combined uniaxial data, the model predicts pure shear behavior, including softening and failure, demonstrating strong cross-mode generalizability. To further assess thermodynamic stability and deformation-mode sensitivity, the model's energy landscape was analyzed across the Lode-invariant space, confirming stable behavior under diverse loading conditions. Parameter evolution with concentration follows power-law scaling, enabling interpolation and predictive validation at intermediate concentrations (2.5% w/v). By establishing a physically interpretable damage framework over the Lode invariant space, this work provides a unified framework for tension-compression-asymmetric softening and lays the foundation for distortional-mode-sensitive, three-dimensional failure mapping of soft materials.