A Micromechanics-Based Softening Hyperelastic Model for Granular Materials: Multiscale Insights into Strain Localization and Softening
Chenxi Xiu1,2,*, Xihua Chu2, Ao Mei1, Liangfei Gong1
1 School of Civil Engineering, Chongqing Jiaotong University, Chongqing, 400074, China
2 School of Civil Engineering, Wuhan University, Wuhan, 430072, China
* Corresponding Author: Chenxi Xiu. Email: 
Computers, Materials & Continua https://doi.org/10.32604/cmc.2025.073193
Received 12 September 2025; Accepted 29 October 2025; Published online 21 November 2025
Abstract
Granular materials exhibit complex macroscopic mechanical behaviors closely related to their micro-scale microstructural features. Traditional macroscopic phenomenological elasto-plastic models, however, usually have complex formulations and lack explicit relations to these microstructural features. To avoid these limitations, this study proposes a micromechanics-based softening hyperelastic model for granular materials, integrating softening hyperelasticity with microstructural insights to capture strain softening, critical state, and strain localization behaviors. The model has two key advantages: (1) a clear conceptualization, straightforward formulation, and ease of numerical implementation (via Abaqus UMAT subroutine in this study); (2) explicit incorporation of micro-scale features (e.g., contact stiffness, particle size, porosity) to reveal their influences on macroscopic responses. An isotropic directional distribution density of contacts and three specific microstructures are considered, and their softening hyperelastic constitutive modulus tensors are explicitly derived. By introducing a softening factor and critical failure energy density, the model can describe geomaterial behaviors, simulating residual strength, X-shaped shear bands, and strain localization evolution. Numerical validations in comparison with the macro-scale hyperelastic model, Abaqus Drucker-Prager model, and the experiment confirm its accuracy. Parametric studies reveal critical dependencies: a normal to tangential contact stiffness ratio of 2–8 (depending on stiffness magnitude), an internal length of 2–4 mm to ensure shear band formation, and a critical failure energy density (≤10 kJ/m
3) to trigger strain softening and localization. Influences of the specific microstructures on strain localization and softening are investigated. The model also shows mesh independence due to the introduction of an internal length. The model’s applicability is further demonstrated by slope stability analysis, capturing slip surface evolution, and load-displacement characteristics. This study develops a robust microstructure-aware hyperelastic framework to describe the mechanical behaviors of granular materials, providing multiscale insights for geotechnical engineering applications.
Keywords
Granular materials; hyperelasticity; micromechanics; strain softening and localization; critical state; microstructure
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