Some Developments for Mathematical Theory of Modern Mechanics

Abstract

Classical development and the formation of some new modern branches in mechanics require continuous improvement and modification of mathematical models and methods to solve the model problems. In this article we consider some developments in mechanics and mathematical models for the description of the mechanical state and different material behaviour and perspectives of fractional calculus for the use in mechanics, and describe the conjugate biophysical and biomechanical problems, the mathematical models of material deformation taking into account their complex heterogeneous structure.

Keywords

• mechanical and mathematical models of fractional order
• generalized model of maxwell
• kelvin-voigt
• zener
• models of viscoelasticity
• heterogeneous environments