On universal relations in continuum mechanics: A discussion centred on shearing motions

Abstract

A local universal relation is an equation between the stress components and the position vector components which holds for any material in an assigned constitutive family. Although universal relations may be of great help to modellers in characterizing the material behaviour, they are often ignored. In this paper we briefly discuss the valuable insights that universal relations may offer in solid mechanics and determine novel universal relations associated with shearing motions in nonlinearly elastic and nonlinearly viscoelastic materials of differential type.

Keywords

• Universal relations
• Universal solutions
• Shearing motions
• Nonlinear elasticity
• Nonlinear viscoelastic materials