Non-local Solutions to Direct and Inverse Problems in Mechanics: A Fractional Calculus Approach

Abstract

In this paper we present a new non-local model of continuum mechanics based on fractional calculus. The model encompasses in a single unified framework both classical continuum mechanics and non-local theories for continua with discontinuities and long range forces. Our theoretical framework can be used to solve both direct and inverse problems of importance in practical applications. We present results to two direct mechanical problems: (1) the deformation of an infinite bar subjected to a self-equilibrated load distribution, and (2) the propagation of longitudinal waves in a thin finite bar. We also show results to the inverse problem of magnetic resonance elastography using our proposed model.