Influence of Heterogeneity on the Response of Architected Metamaterials

TL;DR

This paper introduces a stochastic continuum model for architected metamaterials that captures how microstructural heterogeneity influences their mechanical response, including phase transitions and localization.

Contribution

It extends a gradient-enhanced nonlocal formulation to incorporate Gaussian random fields, allowing independent control of heterogeneity amplitude and correlation, and links microstructural variability to mechanical behavior.

Findings

Heterogeneity alters phase nucleation and localization morphology.

Material fluctuations influence macroscopic response and stability.

The framework enables modeling at the limit of random or correlated microstructures.

Abstract

Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in their microstructure often caused through manufacturing processes. In this study we extend a gradient-enhanced, nonlocal continuum formulation to incorporate stochastic material heterogeneity through Gaussian random fields imposed on selected constitutive parameters. The framework enables independent control of both the amplitude and spatial correlation of material fluctuations while preserving thermodynamic consistency and regularization of localization. It also introduces a characteristic lengthscale ratio between the nonlocal and correlation lengthscales, that enables modeling at the limit of random or spatially correlated microstructures. Finite element simulations of confined compression and indentation show that heterogeneity fundamentally alters phase nucleation, localization morphology, and macroscopic response. Overall, the proposed framework provides a unified approach for linking stochastic material variability to instability-driven mechanics in architected metamaterials, enabling improved understanding of imperfection sensitivity, stability and design. It showcases how heterogeneity alone can influence characteristic features of the response, such as stability, slope of the plateau region, and elimination of the initial elastic regime.