Stress softening damage in strongly nonlinear viscoelastic soft materials: A physics-informed data-driven constitutive model with time–temperature coupling

Document Type

Article

Publication Date

2-1-2026

Abstract

This work introduces a constitutive modeling framework based on a physics-informed Temporal Convolutional Network (TCN) for capturing the extremely nonlinear thermoviscoelastic behavior of soft materials, including large cyclic elongations up to 200%, temperature-dependent viscoelasticity, and Mullins-type damage. In contrast to conventional Mullins or thermo-viscoelastic models—which require specifying hard-coded functional forms and calibrating numerous parameters across 8–12 experiments—the proposed framework defines a new evolution law for stress, damage, and reduced-time temperature effects through a causal temporal architecture. Time–temperature superposition is embedded directly via the Williams–Landel–Ferry (WLF) shift factor, making temperature an intrinsic driver for reduced time rather than an externally appended parameter. This allows the model to learn temperature–rate–damage coupling sequentially, without predefined analytical evolution equations. As a result, the framework requires only three experimental tests for training yet generalizes to six entirely unseen tests that span different temperatures, strain rates, cycle counts, and elongation levels. The model successfully extrapolates to regimes far outside the training domain, including temperatures not used in training, strain rates 2.5 × higher, elongations 50% greater, and significantly longer cyclic histories. Thermodynamic admissibility is promoted by softly enforcing the Clausius–Duhem inequality in the loss function, while damage evolution is constrained by physical principles. The resulting surrogate constitutes a new constitutive model expressed through physics-embedded sequence learning rather than traditional closed-form equations. The trained model is directly implementable in finite element solvers through a VUMAT subroutine, enabling predictive simulations under complex geometries and loading conditions. Its robustness to experimental uncertainty is demonstrated through accurate predictions under 20% Gaussian stress noise. Validation includes three training cases, six independent experimental tests, and a geometry-dependent deployment example involving cyclic Mullins damage in an open-hole specimen, all showing close agreement. These results demonstrate that embedding reduced-time physics into a TCN framework not only accelerates training and improves predictive accuracy but also establishes a fundamentally new, thermodynamically anchored constitutive formulation that surpasses the capabilities of traditional phenomenological models and existing ML-based surrogates.

Publication Source (Journal or Book title)

International Journal of Plasticity

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