2016
DOI: 10.1016/j.cma.2016.07.015
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Implicit finite incompressible elastodynamics with linear finite elements: A stabilized method in rate form

Abstract: We propose a stabilization method for linear tetrahedral finite elements, suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics. In particular, we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models. In this sense the presented development can be considered an important extension and complement to the stabilization approac… Show more

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Cited by 70 publications
(98 citation statements)
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References 127 publications
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“…For this reason, this method was named the “dynamic variational multiscale method” (D‐VMS). This work was extended in the work of Rossi et al to a broad class of implicit time integrators and in the work of Zeng et al to viscoelastic material models.…”
Section: Overview Of Recent Work On Tetrahedral Finite Elementsmentioning
confidence: 98%
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“…For this reason, this method was named the “dynamic variational multiscale method” (D‐VMS). This work was extended in the work of Rossi et al to a broad class of implicit time integrators and in the work of Zeng et al to viscoelastic material models.…”
Section: Overview Of Recent Work On Tetrahedral Finite Elementsmentioning
confidence: 98%
“…The VMS approach consists in decomposing the exact solution bold-italicY=false{uT,pfalse}TscriptS=S-2ptκ×S-2ptp of the problem as Y = Y h + Y ′ , where YhS-2pth=scriptS-2ptκ-2pth×scriptS-2ptp-2pth is the coarse‐scale or finite element solution, and YS-2pt is the subgrid‐ or fine‐scale solution, with scriptS=S-2pthS-2pt. Using this decomposition of the displacement and pressure variables, we obtain bold-italicu=uh+u, p=ph+p.1.5pt We proceed here in a very similar manner to the approach presented in the works of Rossi et al, Scovazzi et al, and Zeng et al Applying the decomposition (32) to (30), integrating by parts the terms involving gradients of the fine‐scale fields, and neglecting inter‐element boundary terms yield the following coarse‐scale variational equations:
Find uhscriptS-2ptκ-2pth, uscriptS-2ptκ-2pt, phscriptS-2ptp-2pth, pscriptS-2ptp...
…”
Section: Small‐strain J2‐elastoplasticitymentioning
confidence: 99%
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“…Alternatively, if a Variational Multi-Scale (VMS) approach [2][3][4][5][45][46][47][48] is followed, the stabilised first Piola-Kirchhoff stress tensor P st is obtained as a function of the extended set of stabilised strains, namely P st := P (F st , H st , J st ) [2][3][4][5], with {F st , H st , J st } defined as…”
Section: Remarkmentioning
confidence: 99%