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- Title
Quasi-quadratic elements for nonlinear compressible and incompressible elasticity.
- Authors
Quaglino, A.; Favino, M.; Krause, R.
- Abstract
This work deals with novel triangular and tetrahedral elements for nonlinear elasticity. While it is well-known that linear and quadratic elements perform, respectively, poorly and accurately in this context, their cost is very different. We construct an approximation that falls in-between these two cases, which we refer to as quasi-quadratic. We seek to satisfy the following: (1) absence of locking and pressure oscillations in the incompressible limit, (2) an exact equivalence to quadratic elements on linear problems, and (3) a computational cost comparable to linear elements on nonlinear problems. Our construction is formally based on the Hellinger-Reissner principle, where strains and displacement are interpolated linearly on nested meshes, but it can be recast in a pure displacement form via static condensation. We show that (1) and (2) are fulfilled via numerical studies on a series of benchmarks and analyze the cost of quadrature in order to show (3).
- Subjects
NONLINEAR elastic fracture; COMPRESSIBLE flow; INCOMPRESSIBLE flow; DEFORMATIONS (Mechanics); STRAINS &; stresses (Mechanics)
- Publication
Computational Mechanics, 2018, Vol 62, Issue 2, p213
- ISSN
0178-7675
- Publication type
Article
- DOI
10.1007/s00466-017-1494-0