New concepts in nonlocal continuum mechanics and new materials obeying a generalised continuum behaviour

Abstract

A new theoretical framework in nonlocal mechanics has been defined, relying on the concept of a propagation of interactions between material points within the continuum along certain paths. The general framework developed is exemplified by the description of damage as a scalar internal variable: the local damage rate at a given point is expressed as a path integral involving the influence functions and the values of the local rate of the damage transported along each path. The paths that do effectively contribute to the interaction are selected from an extremal argument that pertain to irreversible thermodynamics. The strength of the nonlocal interaction is further incorporated into the space geometry, so that a metric characteristic of a Riemanian space emerges, which is further coupled to the internal variables distribution. It appears that the curvature characterises the strength of the nonlocal interaction. In the second part of this work, a more material oriented perspective of nonlocal mechanics is provided: textile are shown to be good candidates to obey a micropolar hyperelastic model. The combination of discrete models with statistical approaches is lastly mentioned as a promising opening of nonlocal mechanics.