Work

Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case

Year: 2025

Type: book-chapter

Abstract: We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint $$\det (\nabla u)=1$$ det ( ∇ u ) = 1 . We show that the ’usual’ homogenized integral functional $$\int W_{\textrm{hom}}(\nabla u)\,dx$$ ∫ W hom ( ∇ u ) d x , where $$W_{\textrm{hom}}$$ W hom is the standard multicell-formula of non-convex homogenization restricted to volume preserving deformations, yields an upper bound for the $$\Gamma $$ Γ -limit as the scale of periodicity tends to zero.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-03177-1

Authors: Matthias Ruf, Mathias Schäffner

Institutions: University of Augsburg, Martin Luther University Halle-Wittenberg

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: $3,190

Funder: Deutsche Forschungsgemeinschaft