Continuum kinematics with incompatible–compatible decomposition

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 that includes the standard elastic– plastic decomposition in plasticity. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.