Work

Commutativity and Non-commutativity of Limits in the Nonlinear Bending Theory for Prestrained Microheterogeneous Plates

Year: 2026

Type: article

Abstract: In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional nonlinear elasticity via homogenization and dimension reduction. We compare effective models obtained by either simultaneously or consecutively passing to the $$\Gamma $$ Γ -limits as the thickness $$h\ll 1$$ h ≪ 1 and the size of the material microstructure $$\epsilon \ll 1$$ ϵ ≪ 1 vanish. In the regime $$\epsilon \ll h$$ ϵ ≪ h we show that the consecutive and simultaneous limit are equivalent, and also analyze the rate of convergence. In contrast, we observe that there are several different limit models in the case $$h\ll \epsilon $$ h ≪ ϵ .

Source: Journal of Nonlinear Science

DOI: 10.1007/s00332-026-10240-4

Authors: Klaus Böhnlein, Lucas Bouck, Stefan Neukamm, David Padilla-Garza, Kai Richter

Institutions: Technische Universität Dresden, Carnegie Mellon University, Hebrew University of Jerusalem

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Hebrew University of Jerusalem