Inelastic response of solids described by implicit constitutive relations with nonlinear small strain elastic response

•The model does not require the notion of a yield surface or a purely elastic response.•A novel implicit model to describe inelastic response is developed.•The model takes into account non-linear response in the small strain range.•A variety of inelastic response is described.

We develop a model to describe the inelastic response of bodies that exhibit non-linear response even in the small strain regime. We introduce a new approach to modeling the inelastic response of materials by gainfully exploiting the discontinuity of the functions that appear in the constitutive relations to describe a plethora of inelastic responses that have been observed. The model that has been developed and its generalizations can be used to describe the response of geomaterials such as clay and rocks, traditional materials such as Aluminum and several polymeric solids, as well as modern intermetallic alloys.