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Abstract

The Arbitrary Lagrangian Eulerian (ALE) formulation is applied to materials with memory, namely, non-linear path-dependent materials.
This report details 2 distinct strategies, borrowed from the fluid dynamic experience: a Lax-Wendroff scheme based on nodal averaging and smoothing of the stress gradients, and a Godunov scheme inspired by methods often used for conservation laws in finite volumes. Both techniques are implemented in 2-dimensional quadrilateral finite elements using single-point as well as multiple-point spatial numerical integration.
Several applications are presented showing that, if adequate stress updating techniques are implemented, the ALE formulation can be much more competitive than classical Lagrangian computations. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate meshes are employed, with obvious benefits both on the accuracy and (for explicit time integration stencils) on the efficiency of the numerical solutions.
The numerical examples shown range from a purely academic test to more realistic engineering simulations. They show the effective applicability of the ALE formulation to non-linear solid mechanics and, in particular, to impact, coining or forming analyses. s.

Additional information

Authors: CASADEI F, Universitat Politècnica de Catalunya, Departamento de Matemática Aplicada III, Barcelona (ES);DONEA J, Universitat Politècnica de Catalunya, Departamento de Matemática Aplicada III, Barcelona (ES);HUERTA A, Universitat Politècnica de Catalunya, Departamento de Matemática Aplicada III, Barcelona (ES)
Bibliographic Reference: EUR 16327 EN (1995) 155pp., FS
Availability: Available from the Public Relations and Publications Unit, JRC Ispra, I-21020 Ispra (IT)
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