New concepts in nonlocal mechanics and analogies with quantum mechanics

Author. A new theoretical framework for nonlocal mechanics is defined, based on the concept of influence functions between material points within the continuum. The traditional ideas of a fixed and isotropic representative volume is completely abandoned and the nonlocality is introduced via some influence function, which set up a nonlocal interaction between material points. The general framework developed is exemplified by the description of damages as an internal dissipative phenomenon: the local damage rate at a given point can be expressed as a path 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 stationarity of the internal entropy production with respect to the path. An implicit equation which defines the representative volume is formulated. Finally, a comparison between nonlocal mechanics, quantum mechanics and general relativity is performed