Calculus of Variations and Geometric Measure Theory

V. Goldshtein - P. M. Mariano - D. Mucci - R. Segev

Continuum Kinematics with Incompatible-Compatible Decomposition

created by mucci on 10 Mar 2023
modified on 28 Sep 2023


Accepted Paper

Inserted: 10 mar 2023
Last Updated: 28 sep 2023

Journal: Philosophical Transactions A
Year: 2023

ArXiv: 2301.08450 PDF


Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points, changes. The setting we propose may be relevant to phenomena such as plasticity, fracture, discontinuities, and non-injectivity of the deformations. In this framework, we construct an unambiguous decomposition into incompatible and compatible factors which includes the standard elastic-plastic decomposition in plasticity.