Internally balanced hyperelastic constitutive model in terms of principal stretches

Abstract

Internal variables are included in material constitutive models to capture realistic mechanical effects such as viscosity. Recent work for compressible hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition of the deformation gradient. Strain energy function is expressed in terms of principal invariants of the deformation gradient decomposed counterparts. The present work permits the use of strain energy function in terms principal stretches of the deformation gradient multiplicatively decomposed counterparts directly. This simplifies significantly the expression of second Piola–Kirchhoff stress and internal balance tensor.