Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame - Areias, P.; Mota Soares, C.A.; Rabczuk, T. (Finite elements in analysis and design, 2016)
Two novelties are introduced: (i) a finite-strain semi-implicit integration algorithm compatible with current element technologies and (ii) the application to assumed-strain hexahedra. The Löwdin algorithm is adopted to obtain evolving frames applicable to finite strain anisotropy and a weighted least-squares algorithm is used to determine the mixed strain. Löwdin frames are very convenient to model anisotropic materials. Weighted least-squares circumvent the use of internal degrees-of-freedom. Heterogeneity of element technologies introduce apparently incompatible constitutive requirements. Assumed-strain and enhanced strain elements can be either formulated in terms of the deformation gradient or the Green–Lagrange strain, many of the high-performance shell formulations are corotational and constitutive constraints (such as incompressibility, plane stress and zero normal stress in shells) also depend on specific element formulations. We propose a unified integration algorithm compatible with possibly all element technologies. To assess its validity, a least-squares based hexahedral element is implemented and tested in depth. Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy. •(First time) Use of least-square based strains in an 8 node (assumed-strain) hexahedron. Full finite strain formulation.•(First time in a Hexahedron) Use of Löwdin frames and rotation based on these frames in a semi-implicit form.•Analysis of null-space under satisfaction of constraints (Kirchhoff–Love and incompressibility).•Semi-implicit constitutive integration.•Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy.