Mixed stabilized finite element methods in nonlinear solid mechanics

Cervera, Miguel; Chiumenti, Michele; Codina, Ramon

doi:10.1016/j.cma.2010.04.006

Cited by 132 publications

(147 citation statements)

References 41 publications

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“…As a remark we observe that as shown in previous works [7,8,15], where the static case was explored, the explicit mixed formulation is always (independently on the τ ε ) more accurate than the irreducible formulation on a given mesh.…”

Section: Dynamic Cantilever Beam Small Deformations Casesupporting

confidence: 69%

“…For simplicity, in the case of constant meshes it is customary to take a constant value of the stabilization parameter [8] [15]. In this work typical values, in the range 0.1-0.5, were considered in all the examples.…”

Section: Stabilized Finite Element Methodsmentioning

confidence: 99%

“…The idea is to combine different primary variables, in our case displacements and strains, following the concept described in [7]. This approach was proved to show better mesh independence properties while providing the formal guarantee of a strain field converging at the same rate as the displacement one, which manifests in enhanced stress/analysis accuracy in both linear and non-linear analyses [8]. Following the ideas in [9,10,11,12,13,14], a stabilization technique is needed to allow the use of the same order of interpolation for the two primary variables of interest.…”

Section: Introductionmentioning

confidence: 99%

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Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

et al. 2015

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Computational mechanics. Although appealing for their simplicity, low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff behaviour when dealing with complex problems. A recent proposal to address such limitations is the adoption of mixed displacement-strain technologies which were shown to satisfactorily address both problems. Unfortunately, although appealing, the use of such element technology puts a large burden on the linear algebra, as the solution of larger linear systems is needed. In this paper, the use of an explicit time integration scheme for the solution of the mixed strain-displacement problem is explored as an alternative. An algorithm is devised to allow the effective time integration of the mixed problem. The developed method retains second order accuracy in time and is competitive in terms of computational cost with the standard irreducible formulation.

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Section: Dynamic Cantilever Beam Small Deformations Casesupporting

confidence: 69%

Section: Stabilized Finite Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

et al. 2015

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“…Some technical details may be omitted by considering that the subscale enhancements behave as bubble functions, vanishing on the elements boundaries. They can be viewed as a "high frequency" perturbation of the finite element field, which cannot be resolved in V h [12,21].…”

Section: Variational Multiscale Stabilizationmentioning

confidence: 99%

“…In these works, deviatoric strains are calculated by differentiation of the displacement field; hence, the rate of convergence for the angular distortions is the same as in the irreducible formulation. More recently, Cervera et al [12,13,14] introduced a mixed ε− u strain/ displacement FE formulation and have applied it to address problems of strain localization using compressible and incompressible plasticity models [2,10]. The objective of such formulation is to achieve a discrete scheme with enhanced stress accuracy.…”

Section: Introductionmentioning

confidence: 99%

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

et al. 2016

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K: explicit mixed finite elements, stabilization, incompressibility, plasticity, strain softening, strain localization, mesh independence. AbstractThis paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P 1P 1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.

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Finite Element Approach to the Sintering Process at the Grain Scale

Bruchon¹,

Muñoz²

2014

Thermomechanical Industrial Processes

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Mixed stabilized finite element methods in nonlinear solid mechanics

Cited by 132 publications

References 41 publications

Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

Finite Element Approach to the Sintering Process at the Grain Scale

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