Mixed linear/linear simplicial elements for incompressible elasticity and plasticity

Cervera, Miguel; Chiumenti, Michele; Valverde, Quino; Saracibar, C. Agelet de

doi:10.1016/j.cma.2003.07.007

Cited by 94 publications

(75 citation statements)

References 27 publications

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“…The examples involve both compressible and incompressible plasticity using the Drucker-Prager model with exponential softening. Results obtained for the incompressible cases are compared with those obtained with the previously developed stabilized mixed pressure/displacement formulation ( [4,5,6,7,8] and [9]). …”

Section: Numerical Examplesmentioning

confidence: 99%

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Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Cervera

Chiumenti

Benedetti

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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This paper presents the application of a stabilized mixed strain/displacement …nite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order interpolations in a consistent way. Such formulation presents two advantages when compared to the standard, displacement based, irreducible formulation: (a) it provides enhanced rate of convergence for the strain (and stress) …eld and (b) it is able to deal with incompressible situations. The …rst advantage also applies to the comparison with the mixed pressure/displacement formulation. The paper investigates the e¤ect of the improved strain and stress …elds in problems involving strain softening and localization leading to failure, using low order …nite elements with continuous strain and displacement …elds (P 1P 1 triangles or tetrahedra and Q1Q1 quadrilaterals, hexahedra, and triangular prisms) in conjunction with an associative frictional Drucker-Prager plastic model. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to a previously proposed pressure/displacement formulation. 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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Section: Numerical Examplesmentioning

confidence: 99%

“…In previous works, the authors have applied stabilized mixed displacement-pressure methods ( [4,5,6,7,8] and [9]) to the solution of J 2 elasto-plastic problems with simplicial elements. In J 2 dependent problems, the plastic ‡ow is isochoric and the main challenge for the discrete formulation is the incompressibility constraint.…”

Section: Introductionmentioning

confidence: 99%

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Cervera

Chiumenti

Benedetti

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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“…Initially, Cervera et al [30,31] proved that avoiding global pressure locking in J2 softening material (both with plasticity and isotropic damage constitutive laws) with the introduction of a proper mixed displacement/pressure u−p formulation leads to mesh-bias independent results for quasi-incompressible localization problems. Then, Cervera et al [32,33] generalized such concept with the introduction of the strain/displacement ε − u formulation.…”

Section: Introductionmentioning

confidence: 99%

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

Benedetti

Cervera

Chiumenti

2017

Engineering Fracture Mechanics

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The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle materials. In this work, the application of the mixed strain displacement ε − u finite element formulation to three examples involving skew notched beams is presented. The use of this FE technology is effective in problems involving localization of strains in softening materials.The objectives of the paper are: (i) to test the mixed formulation in mode III and mixed mode failure and (ii) to present an enhancement in terms of computational time given by the kinematic compatibility between irreducible displacement-based and the mixed strain-displacement elements.Three tests of skew-notched beams are presented: firstly, a three point bending test of a PolyMethyl MethaAcrylate beam; secondly, a torsion test of a plain concrete prismatic beam with square base; finally, a torsion test of a cylindrical beam made of plain concrete as well. To describe the mechanical behavior of the material in the inelastic range, Rankine and Drucker-Prager failure criteria are used in both plasticity and isotropic continuum damage formats.The proposed mixed formulation is capable of yielding results close to the experimental ones in terms of fracture surface, peak load and global loss of carrying capability. In addition, the symmetric secant formulation and the compatibility condition between the standard irreducible method and the strain-displacement one is exploited, resulting in a significant speedup of the computational procedure.

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“…This fact has been identified by Cervera et al [34] for non-linear analysis of incompressible problems using linear triangles.…”

Section: About the Computation Of The Intrinsic Time Parameter For Nomentioning

confidence: 89%

Finite calculus formulation for incompressible solids using linear triangles and tetrahedra

Oñate

Rojek

Taylor

et al. 2004

Numerical Meth Engineering

112

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SUMMARYMany finite elements exhibit the so-called 'volumetric locking' in the analysis of incompressible or quasi-incompressible problems. In this paper, a new approach is taken to overcome this undesirable effect. The starting point is a new setting of the governing differential equations using a finite calculus (FIC) formulation. The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem. The FIC approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective-diffusive and fluid flow problems. The same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to linear static problems as well as to the semi-implicit and explicit 2D and 3D non-linear transient dynamic analysis of an impact problem and a bulk forming process are presented.

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Mixed linear/linear simplicial elements for incompressible elasticity and plasticity

Cited by 94 publications

References 27 publications

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

Finite calculus formulation for incompressible solids using linear triangles and tetrahedra

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