Work

The energy scaling behaviour of singular perturbation models of staircase type in linearized elasticity for higher order laminates

Year: 2026

Type: article

Abstract: We investigate the scaling behaviour of a singular perturbation model within the geometrically linearized theory of elasticity involving data of higher lamination order. We study boundary data which are of staircase type and show rather general lower scaling bounds, both in the setting of prescribed Dirichlet data and for periodic configurations with a mean value constraint. In contrast to the setting without gauge invariances, these lower scaling bounds depend on two parameters – the order of lamination of the boundary data as well as the number of involved (non-)degenerate symmetrized rank-one directions. By discussing upper bounds in specific geometries and for a specific constellation of wells, we give evidence of the sharpness of these lower bound estimates. Hence, it is necessary to keep track of the outlined two parameters in deducing scaling laws within the geometrically linearized theory of elasticity.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-026-02228-x

Authors: Lennart Machill, Angkana Rüland

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: $3,090

Funder: Deutsche Forschungsgemeinschaft

Awards: G7072843018, G8669908120