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Title: Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame
Authors: Areias, P.
MotaSoares b, C.A.
Rabczuk, T.
Issue Date: 1-Jan-2016
Publisher: John Dolbow
Abstract: 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.
Type: article
Appears in Collections:FIS - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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