A Mixed Finite Element Approach for Large-Deformation Inelasticity with Reduced Remeshing-Induced Internal Variable Diffusion

  • Rossi, Nestor (IMDEA Materials)
  • Romero, Ignacio (IMDEA Materials)

Please login to view abstract download link

It is well known that large-deformation processes in solids can compromise the predictive capability of the finite element method when the computational mesh becomes excessively distorted. A common remedy is remeshing of the deformed body. In inelastic problems, however, this procedure leads to diffusion of internal variables due to their remapping from the quadrature points of the discarded mesh to those of the new one. The main objective of this work is to assess the effectiveness of a mixed finite element formulation in reducing the diffusion of internal variables induced by remeshing. Building on the ideas of [1] in the context of linear elasticity, we develop a variational framework for a saddle-point problem tailored to large-deformation kinematics, together with its finite element discretization based on tetrahedral meshes. The resulting formulation behaves as a nodally integrated finite element method, equivalent to the one proposed by [2], originally introduced to alleviate locking phenomena. A key advantage of this approach is that the material history is stored at the nodes, thereby mitigating the diffusion associated with remapping. Quantitative measures to assess internal variable diffusion are introduced and evaluated through numerical examples in large-strain elasto-plasticity. [1] Lamichhane B.P., From the Hu–Washizu formulation to the average nodal strain formulation, Computer Methods in Applied Mechanics and Engineering, 198(49-52), 3957–3961, 2009. [2] Puso M., Solberg J., A stabilized nodally integrated tetrahedral, International Journal for Numerical Methods in Engineering, 67(6), 841–867, 2006.