Two-scale hyperelastic model of a material with prestress at cellular level

Abstract

We propose the two-scale hyperelastic model of a material defined at micro-scale. The microstructure, motivated by the arrangement of soft tissues at the cellular level, is formed by an incompressible inclusion and linear elastic elements. The prestress of such structure is maintained by the assumption of constant volume of the inclusion. In the continuum limit, the prestressed microstructure is considered as a single material particle governed by the macroscopic deformation gradient. Thus the strain-energy is obtained as a function of both macro-deformation and micro-prestress. Although we have no analytical formula, an approximation is found using assumptions that hold for soft tissues. It shows clearly the ability of the model to control the overall mechanical behaviour by setting the prestress at micro-scale (the prestress-induced stiffening).

Keywords

• Multi-scale modelling
• Prestress
• Soft tissue