Calculus of Variations and Geometric Measure Theory

M. Santilli - B. Schmidt

Two phase models for elastic membranes with soft inclusions

created by santilli on 14 Jun 2021
modified on 22 Aug 2023


Accepted Paper

Inserted: 14 jun 2021
Last Updated: 22 aug 2023

Journal: Rendiconti Lincei Matematica e Applicazioni
Year: 2021

ArXiv: 2106.01120 PDF


We derive an effective membrane theory in the thin film limit within a two phase material model for a specimen consisting of an elastic matrix and soft inclusions. The soft inclusions may lead to the formation of cracks within the elastic matrix and the corresponding limiting models are described by Griffith type fracture energy functionals. We also provide simplified proofs of relaxation results for bulk materials