### 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.

Original language | English |
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Pages (from-to) | 96-109 |

Number of pages | 14 |

Journal | Finite Elements in Analysis and Design |

Volume | 108 |

DOIs | |

Publication status | Published - 2016 Jan 1 |

Externally published | Yes |

### Keywords

- Assumed-strain hexahedron
- Constitutiveintegration
- Finite strains
- Löwdin frame

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Engineering(all)
- Computer Graphics and Computer-Aided Design

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## Cite this

*Finite Elements in Analysis and Design*,

*108*, 96-109. https://doi.org/10.1016/j.finel.2015.09.010