Coarse-Graining Inelasticity of Non-Local Lattices

Lattice systems are regular structures composed of interacting nodes whose overall mechanical response is profoundly affected by the presence of inelastic phenomena such as plasticity, damage, viscosity, and friction. These mechanisms introduce irreversible deformations, energy dissipation, and path-dependent behavior. Despite advances in numerical methods for solving large sparse systems, element-by-element simulation of inelastic lattice systems remains computationally prohibitive in realistic applications, where full-scale structures and a large number of defect configurations must be considered.

Continuum models provide an effective alternative for the predictive design of lattice materials, as they avoid the need to explicitly resolve each discrete element. The transition from the microscopic to the macroscopic scale is typically achieved through homogenization techniques, which allow one to derive equivalent continuum models from the underlying discrete description.

For lattice systems with local or weakly nonlocal interactions, accurate and computationally efficient inelastic continuum theories are available. In contrast, for strongly nonlocal lattice systems—where interactions extend over significant distances—a reliable continuum description is still lacking, and one must resort to direct simulations of the discrete model. In particular, the behavior of these systems in the continuum limit, in the presence of dissipation, remains largely unexplored.

This project aims to fill this gap. The working hypothesis is that microscopic length scales and interaction rules leave a measurable imprint on the macroscopic response, leading to a new class of inelastic models that cannot be reduced to existing ones. To test this hypothesis, an integrated approach will be adopted, combining experiments on 3D-printed samples, discrete modeling, homogenization techniques, and continuum simulations. If confirmed, this hypothesis would enable the design of nonlocal lattice materials with tailored mechanical properties and establish new paradigms in the multiscale modeling of large-deformation inelastic phenomena.

Principal investigator
Emilio Barchiesi

Call
Bando FIS 3 (starting grant)

Project duration:
60 months

Main ERC field:
PE - Physical Sciences and Engineering

ERC subfields
PE11_13 Metamaterials engineering 
PE11_14 Computational methods for materials engineering
PE11_8 Engineering of alternative established or emergent materials

Keywords
Continuum mechanics, Lattice dynamics, Mathematical modeling of complex systems, Mechanics of materials, Metamaterials, Coarse-graining approaches, Inelasticity mechanics, Generalized continuum theories