Adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements

► Parameter identification for inhomogeneous states of stresses. ► Incompressible elastic materials with stabilized mixed finite elements of low order. ► Goal oriented adaptive remeshing. ► Local element-wise, higher-order approximation on recovered gradients. This work is concerned with the identification of material parameters for isotropic, incompressible hyperelastic material models. Besides the principal stretch-based strain–energy function by Ogden an invariant-based strain–energy function by Rivlin/Saunders is considered for which parameter sensitivities are derived. The identification is formulated as a least-squares minimization problem based on the finite element method to account for inhomogeneous states of stresses and strains in the experimental data which is obtained by optical measurements. For the finite element method low-order tetrahedral elements in a mixed displacement–pressure formulation with stabilization are considered. Special attention is payed to an adaptive mesh-refinement based on a goal-oriented a posteriori error indicator to gain reliable material parameters. To approximate error terms an element-wise recovery technique based on enhanced gradients is introduced.