Calculus of Variations and Geometric Measure Theory

S. Krömer - M. Kruzik - M. Morandotti - E. Zappale

Measure structured deformations

created by morandott on 22 Feb 2024
modified on 26 Feb 2024


Submitted Paper

Inserted: 22 feb 2024
Last Updated: 26 feb 2024

Year: 2024

ArXiv: 2402.14790 PDF


Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via relaxation departing either from energies associated with classical deformations or from energies associated with structured deformations. A concise integral representation of the energy functional is provided both in the unconstrained case and under Dirichlet conditions on a part of the boundary.

Keywords: relaxation, Integral representation, energy minimization, Structured deformations, functionals depending on measures