On the role of the microstructure in the deformation of porous solids

TL;DR

This paper investigates how microstructure influences the macroscopic response of porous elastic materials and introduces a fractional calculus-based nonlocal continuum theory to model complex spatial effects accurately.

Contribution

It develops a novel variable-order fractional calculus model to capture microstructure-dependent nonlocal effects in porous solids, improving accuracy over classical methods.

Findings

Fractional model accurately predicts nonlinear thermoelastic response.

Model outperforms classical approaches based on average porosity.

Simulation demonstrates robustness and efficiency of the fractional approach.

Abstract

This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the configuration of the microstructure. Then, a nonlocal continuum theory based on variable-order fractional calculus is developed in order to accurately capture the complex spatially distributed nonlocal response. The remarkable potential of the fractional approach is illustrated by simulating the nonlinear thermoelastic response of porous beams. The performance, evaluated both in terms of accuracy and computational efficiency, is directly contrasted with high-fidelity finite element models that fully resolve the pores' geometry. Results indicate that the reduced-order representation of the porous microstructure, captured by the synthetic variable-order parameter, offers a robust and accurate representation of the multiscale material architecture that largely outperforms classical approaches based on the concept of average porosity.