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Elastoplasticity with linear tetrahedral elements: A variational multiscale method

Publication ,  Journal Article
Abboud, N; Scovazzi, G
Published in: International Journal for Numerical Methods in Engineering
August 24, 2018

We present a computational framework for the simulation of J2-elastic/plastic materials in complex geometries based on simple piecewise linear finite elements on tetrahedral grids. We avoid spurious numerical instabilities by means of a specific stabilization method of the variational multiscale kind. Specifically, we introduce the concept of subgrid-scale displacements, velocities, and pressures, approximated as functions of the governing equation residuals. The subgrid-scale displacements/velocities are scaled using an effective (tangent) elastoplastic shear modulus, and we demonstrate the beneficial effects of introducing a subgrid-scale pressure in the plastic regime. We provide proofs of stability and convergence of the proposed algorithms. These methods are initially presented in the context of static computations and then extended to the case of dynamics, where we demonstrate that, in general, naïve extensions of stabilized methods developed initially for static computations seem not effective. We conclude by proposing a dynamic version of the stabilizing mechanisms, which obviates this problematic issue. In its final form, the proposed approach is simple and efficient, as it requires only minimal additional computational and storage cost with respect to a standard finite element relying on a piecewise linear approximation of the displacement field.

Duke Scholars

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

August 24, 2018

Volume

115

Issue

8

Start / End Page

913 / 955

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering
 

Citation

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Abboud, N., & Scovazzi, G. (2018). Elastoplasticity with linear tetrahedral elements: A variational multiscale method. International Journal for Numerical Methods in Engineering, 115(8), 913–955. https://doi.org/10.1002/nme.5831
Abboud, N., and G. Scovazzi. “Elastoplasticity with linear tetrahedral elements: A variational multiscale method.” International Journal for Numerical Methods in Engineering 115, no. 8 (August 24, 2018): 913–55. https://doi.org/10.1002/nme.5831.
Abboud N, Scovazzi G. Elastoplasticity with linear tetrahedral elements: A variational multiscale method. International Journal for Numerical Methods in Engineering. 2018 Aug 24;115(8):913–55.
Abboud, N., and G. Scovazzi. “Elastoplasticity with linear tetrahedral elements: A variational multiscale method.” International Journal for Numerical Methods in Engineering, vol. 115, no. 8, Aug. 2018, pp. 913–55. Scopus, doi:10.1002/nme.5831.
Abboud N, Scovazzi G. Elastoplasticity with linear tetrahedral elements: A variational multiscale method. International Journal for Numerical Methods in Engineering. 2018 Aug 24;115(8):913–955.
Journal cover image

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

August 24, 2018

Volume

115

Issue

8

Start / End Page

913 / 955

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering