High-order quasi-static finite element computations in space and time with application to finite strain viscoelasticity

Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p‐version finite elements

“…The numerical simulation can provide some insight into the experimental behavior. Due to its applicability and efficiency in the context of hyper-elastic materials, as demonstrated by [40] and [14], we choose the p-version of the finite element method. For details of p-FEM based on integrated Legendre-polynomials, see [55] and [12], and for a bio-mechanical application [59].…”

“…For details of p-FEM based on integrated Legendre-polynomials, see [55] and [12], and for a bio-mechanical application [59]. In particular, [40] compare classical h-element formulations (linear and quadratic shape functions for hexahedral and tetrahedral elements on the basis of Lagrange-polynomials), a mixed element formulation (linear and quadratic ansatz functions with constant and linear approaches for the dilatational and pressure degree of freedom based on the proposal of [51] or [52]) and p-version finite elements. It is shown that for a particular error measure, the specific quadratic, mixed elements are comparable with higherorder elements (which cannot be generalized to include other mixed element formulations).…”