Mixed linear/linear simplicial elements for incompressible elasticity and plasticity

By Miguel Cervera, Michele Chiumenti, Quino Valverde, Carlos Agelet de Saracibar. 2003

122 citations recorded by the source corpus.

This paper exploits the concept of orthogonal sub-grid scales to stabilize the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible or nearly incompressible situations. Both incompressible elastic and J2-plastic constitutive behaviours have been considered. The different assumptions and approximations used to derive the method are exposed. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the elements derived are free of volumetric locking and spurious oscillations of the pressure, and that the results obtained compare favourably with those obtained with the Q1P0 quadrilateral.

Subfields: Biomedical Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/e63a075adc1b75879572b937695fb6760aa10707

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Miguel Cervera
2. Michele Chiumenti
3. Carlos Agelet de Saracibar

In Computational Mechanics

1. Miguel Cervera
2. Michele Chiumenti
3. Eugenio Oñate
4. Carlos Agelet de Saracibar
5. Robert Taylor
6. J. Rojek
7. O. C. Zienkiewicz
8. Ramon Codina

Citations in the corpus

• Finite calculus formulation for incompressible solids using linear triangles and tetrahedra (2004, background): “[34] for non-linear analysis of incompressible problems using linear triangles.”
• Mixed stabilized finite element methods in nonlinear solid mechanics: Part II: Strain localization (2010, methodology): “In previous works, the authors have applied stabilized mixed displacementpressure methods ([16], [17], [18], [19], [20], [21] and [1]) to the solution of J2 elasto-plastic and damage problems with simplicial elements.”
• Continuum damage model for orthotropic materials: Application to masonry (2011, background): “The interested reader is referred to [68-73] for details.”
• Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity (2004, methodology): “It is here proposed to regularize the elasto-plastic constitutive model with an artificial viscosity defined in terms of the normal proyection of the residual of the momentum equation onto the finite element space (see Reference [27]), in the form”
• Numerical modeling of friction stir welding processes (2013, unknown): “[5], [17], [21], [22]).”
• An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems (2013, unknown): “[22], Saracibar et al.”