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 |
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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
Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame. / Areias, P.; Mota Soares, C. A.; Rabczuk, Timon.
In: Finite Elements in Analysis and Design, Vol. 108, 01.01.2016, p. 96-109.Research output: Contribution to journal › Article
}
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
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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 -