### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Finite Elements in Analysis and Design*,

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

**Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame.** / Areias, P.; Mota Soares, C. A.; Rabczuk, Timon.

Research output: Contribution to journal › Article

*Finite Elements in Analysis and Design*, vol. 108, pp. 96-109. https://doi.org/10.1016/j.finel.2015.09.010

}

TY - JOUR

T1 - Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame

AU - Areias, P.

AU - Mota Soares, C. A.

AU - Rabczuk, Timon

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Assumed-strain hexahedron

KW - Constitutiveintegration

KW - Finite strains

KW - Löwdin frame

UR - http://www.scopus.com/inward/record.url?scp=84945588842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945588842&partnerID=8YFLogxK

U2 - 10.1016/j.finel.2015.09.010

DO - 10.1016/j.finel.2015.09.010

M3 - Article

AN - SCOPUS:84945588842

VL - 108

SP - 96

EP - 109

JO - Finite Elements in Analysis and Design

JF - Finite Elements in Analysis and Design

SN - 0168-874X

ER -