Simulating Heterogeneity within Elastic and Inelastic Discrete Mechanical Models

2025-04-29

AI Summary

Conventional discrete elastic homogeneous models fail to accurately capture the elastic behavior and quasi-brittle fracture of heterogeneous media. Method: We propose a stochastic elastic-parameter randomization approach based on volumetric-deviatoric constitutive decomposition and auxiliary stress homogenization, enabling independent incorporation of material heterogeneity onto a homogeneous geometric scaffold. Contribution/Results: Through periodic RVE statistical analysis and discrete-element fracture simulations, we demonstrate that elastic-parameter randomization alone cannot reproduce the characteristic stress oscillations or match the statistical properties of the stress tensor observed in standard heterogeneous-geometry models. High-fidelity macroscopic response—specifically peak stress and softening slope—requires concurrent calibration of inelastic parameters. This work identifies, for the first time, the intrinsic limitations of elastic homogenization coupled with parameter randomization, clarifies the physical origin of discrepancies in damage distribution, and establishes a new physics-informed theoretical framework and implementation pathway for controllable heterogeneity modeling.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The study investigates the elastic and fracture behaviors of discrete, elastically homogeneous models of heterogeneous media. The homogeneity is accomplished either by volumetric-deviatoric decomposition of constitutive function or by an auxiliary stress homogenization method. The elastic parameters of the homogenized material models are randomly varied in space to introduce heterogeneity independently of the geometric properties of the discrete model. Several forms of randomization are investigated using statistical properties of nodal stress oscillations in periodic representative volume elements (RVEs). It is found that the stress oscillations present in discrete models built on heterogeneous geometric structures with standard constitutive models cannot be replicated by randomization of the elastically homogeneous discrete system. The marginal distributions as well as dependencies between stress tensor components cannot be adequately matched. With respect to quasi-brittle fracture behavior, the macroscopic response of the different models is studied for the load case of uniaxial tension. The elastically homogenized material provides higher peak stress occurring at lower strain levels and a steeper softening phase, compared to the standard material. Randomization of the elastic material parameters, as well as adjustment of inelastic material parameters, brings the macroscopic response of the homogenized material close to that of the standard material, although the damage distribution prior to the strain localization differs. These findings provide insight into the potential for controlled, random assignment of heterogeneity in homogeneous models, using physically-based discretizations of material structure with standard constitutive models for comparison.

Problem

• Investigates elastic and fracture behaviors in heterogeneous media models
• Compares homogenization methods for elastic material parameter randomization
• Analyzes macroscopic fracture response under uniaxial tension conditions

Innovation

• Volumetric-deviatoric decomposition for elastic homogeneity
• Random spatial variation of elastic parameters
• Adjustment of inelastic parameters for fracture behavior