A new framework in nonlocal mechanics

A new theoretical framework in nonlocal mechanics is defined, based on the concept of influence functions between material points within the continuum . The traditional idea of a fixed and isotropic representative volume is ab andoned and the nonlocality is introduced via an influence function, which defines a nonlocal interaction between material points. The general framewo rk developed is exemplified by the description of damage as a scalar intern al variable: the local damage rate at a given point can be expressed as a p ath integral involving the influence functions and the values of the local rate of damage transported along each path. The properties satisfied by the influence function are first evidenced and the influence function is given an explicit expression, using a path integration technique. The concept of a representative volume is further defined as an outcome of the stationari ty of the internal entropy production with respect to the path. An implicit equation which defines the representative volume is formulated. A numerica l implementation of the proposed concepts is performed in the case of inter facial damage. The strength of the nonlocal interaction is further incorpor ated into the space geometry, so that a metric characteristic of a Riemania n space is coupled to the internal variable distribution. It appears that t he curvature characterises the strength of the nonlocal interaction. (C) 20 00 Elsevier Science Ltd. All rights reserved.