International Journal for Numerical Methods in Engineering

Huerta, Antonio; Angeloski, Aleksandar; Roca, Xevi; Peraire, Jaime

doi: 10.1002/nme.4547pmid: N/A

To evaluate the computational performance of high‐order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear versus high‐order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution. Continuous and discontinuous Galerkin methods are considered in two‐dimensional and three‐dimensional domains for simplices and parallelotopes. Moreover, both element‐wise and global operations arising from different Galerkin approaches are studied. The operation count estimates show, that for implicit solvers, high‐order methods are more efficient than linear ones. Copyright © 2013 John Wiley & Sons, Ltd.

Cao, T.‐S.; Montmitonnet, P.; Bouchard, P.‐O.

doi: 10.1002/nme.4571pmid: N/A

In an effort to implement Gurson‐type models into a mixed velocity–pressure finite element formulation with the MINI‐element P1 +  ∕ P1, the algorithm proposed by Aravas (IJNME, 1987) to integrate the pressure dependent plasticity as well as the formulations of consistent tangent moduli have been analyzed. This work firstly reviews and clarifies the mathematical basis of the formulations used by Aravas (IJNME, 1987) and demonstrates the equality of the tangent moduli formulations proposed by Govindarajan and Aravas (CNME, 1995) and Zhang (CMAME, 1995), which are widely used in the literature. A unified formulation to calculate the tangent moduli is proven, and its accuracy is also investigated by the finite difference method. The implementation of the Gurson–Tvergaard–Needleman model is then detailed for the mixed velocity–pressure finite element formulation, which employs the MINI‐element P1 +  ∕ P1. Due to the particularity of this element, one needs to calculate two tangent moduli instead of one. The formulas for calculating the ‘linear tangent modulus’ and the ‘bubble tangent modulus’ are then detailed. Finally, comparison tests are carried out with ABAQUS (Dassault System, Simulia Corp., Providence, RI, USA) in order to validate the present implementation for both homogeneous and heterogeneous deformations. Copyright © 2013 John Wiley & Sons, Ltd.

Visseq, Vincent; Alart, Pierre; Dureisseix, David

doi: 10.1002/nme.4578pmid: N/A

We investigate two algorithms for solving large‐scale granular problems using DD methods. These numerical schemes can be connected to classical DDs, with and without overlapping, developed in continuum mechanics. The two algorithms are compared in terms of implementation and parallel performance. We focus the numerical study on communication procedures between processors, load balancing, and scalability, topics particularly crucial in nonlinear evolutive problems. Copyright © 2013 John Wiley & Sons, Ltd.