Work

Non-interpenetration of rods derived by Γ-limits

Year: 2024

Type: article

Abstract: Ensuring non-interpenetration of matter is a fundamental prerequisite when modeling the deformation response of solid materials. In this contribution, we thoroughly examine how this requirement, equivalent to the injectivity of deformations within bulk structures, manifests itself in dimensional-reduction problems. Specifically, we focus on the case of rods embedded in a two-dimensional plane. Our results focus on [Formula: see text]-limits of energy functionals that enforce an admissible deformation to be a homeomorphism. These [Formula: see text]-limits are evaluated along a passage from the bulk configuration to the rod arrangement. The proofs rely on the equivalence between the weak and strong closures of the set of homeomorphisms from [Formula: see text] to [Formula: see text], a result that is of independent interest and that we establish in this paper, too.

Source: Mathematical Models and Methods in Applied Sciences

DOI: 10.1142/s0218202525500010

Authors: Barbora Benešová, Daniel Campbell, Stanislav Hencl, Martin Kružík

Institutions: Charles University, Czech Academy of Sciences, Czech Academy of Sciences, Institute of Information Theory and Automation, Czech Technical University in Prague

Language: English

Topic: Nonlocal and gradient elasticity in micro/nano structures

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: green

Funder: Grantová Agentura České Republiky

Awards: Variational approaches to dynamical problems in continuum mechanics, Geometric and Harmonic Analysis 2