Finite Element Models of Hyperelastic Materials Based on a New Strain Measure

To construct constitutive equations for hyperelastic materials, one increasingly often proposes new strain measures, which result in significant simplifications and error reduction in experimental data processing. One such strain measure is based on the upper triangular (QR) decomposition of the deformation gradient. We describe a finite element method for solving nonlinear elasticity problems in the framework of finite strains for the case in which the constitutive equations are written with the use of the QR-decomposition of the deformation gradient. The method permits developing an efficient, easy-to-implement tool for modeling the stress–strain state of any hyperelastic material.