Work

Geometric non-locality in multi-scale models of manifold-valued microstructures

Year: 2025

Type: article

Abstract: We develop a geometric framework for representing spatial non-locality in two-scale continuum descriptions of microstructured bodies. Starting with continua endowed with spin-type microstructures, we construct approximation formulas for response functionals that involve microstructural descriptor fields taking values on geodesically complete Riemannian manifolds. This setting provides a mathematically rigorous and physically motivated approach to overcome, in terms of the derived approximations, some foundational problems that arise when considering non-local interactions in finitely extended bodies. The results generalize Coleman and Noll’s theorems on the approximation of constitutive functionals.

Source: Zeitschrift für angewandte Mathematik und Physik

DOI: 10.1007/s00033-025-02606-7

Author: Paolo Maria Mariano

Institution: University of Florence

Language: English

Topic: Nonlocal and gradient elasticity in micro/nano structures

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funders: Scuola Normale Superiore, Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Firenze, Gruppo Nazionale per la Fisica Matematica