A Generalized Variable Formulation for Gradient Dependent Softening Plasticity

Comi, Claudia; Perego, U.

doi:10.1002/(sici)1097-0207(19961115)39:21<3731::aid-nme24>3.0.co;2-z

Cited by 57 publications

(47 citation statements)

References 31 publications

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“…The example consists of a rod subjected to uniaxial tensile load by displacement control [3] as show Fig. 1.…”

Section: One-dimensional Examplementioning

confidence: 99%

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Applications of the Finite Points Method in the Strain-Gradient Plasticity

Rodrıguez¹,

Pozo²

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. In this paper, the meshless Finite Points Method (FPM) is used for numerical simulation of one and two-dimensional elastoplastic problems, which develop a softening response after to exceed the elastic range. In such problems, a pathological behaviour of the solutions is induced by the ill-conditioning of the partial differential equations after reaching the yield limit, producing the localization of deformations.Specifically, this work presents the implementation of a regularization technique through the enrichment of the constitutive equations using strain gradients, with a characteristic length based on a non-local plastic strain formulation in order to maintain the ellipticity of the differential equations.The strain localization phenomenon is replicated objectively in the computational simulation considering an isotropic Von Mises (J2) softening model. This localization phenomenon is induced weakening a region of the material and also developing problems with geometrical discontinuities.The FPM performs the domain's discretization in a finite number of points in each of which the punctual collocation of the equations is performed. For these reasons the FPM applies the strong formulation, allowing the use of high-order differentiability shape functions (C2 class or higher). This features can improve the computational cost because of the same shape functions are used in order to approximate non-local strain and the displacement nodal fields. Both fields are obtained by using the iterative Newton-Raphson method. To ensure convergence of the iterative method, the algorithmic tangent operator is obtained by Perturbation Method.The theory is developed for one-dimensional geometries, being extended to two and three-dimensional problems.In order to validate the proposal, a benchmarking is developed with typical problems extracted from literature.

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“…The example consists of a rod subjected to uniaxial tensile load by displacement control [3] as show Fig. 1.…”

Section: One-dimensional Examplementioning

confidence: 99%

“…To treat this behaviour in problems of mechanical damage or softening, traditionally techniques of fracture energy regularization ( [11,23,27]) or enrichment approach of the constitutive equations with strain gradients ( [3,6,7,22,31]) has used.…”

Section: Introductionmentioning

confidence: 99%

Applications of the Finite Points Method in the Strain-Gradient Plasticity

Rodrıguez¹,

Pozo²

2014

Proceedings of 10th World Congress on Computational Mechanics

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“…44, permits one to regard Eq. (44) as a natural boundary condition and to achieve a generalized, gradient-plasticity version of the cell constitutive laws without the explicit presence of that boundary condition, but with the addition in the yield criterion, Eq.…”

Section: Materials Instabilitiesmentioning

confidence: 99%

Symmetric Galerkin Boundary Element Method

Bonnet

Maier²,

Polizzotto³

2008

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This review concerns a methodology for solving numerically, to engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form; the discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager's sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions, some quadratic forms have a clear energy meaning, variational properties characterize the solutions and other results, invalid in traditional boundary element methods, enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, computer implementations. Areas and aspects which at present require further research are identified and comparative assessments are attempted with respect to traditional boundary integral-element methods.

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“…This phase, which requires the solution of nonlinear equations (item 5 in Box 1), in classical local plasticity can be efficiently performed at each Gauss point separately. On the contrary, when nonlocality is considered the loading-unloading conditions are coupled and this can require another nested iteration process or ad hoc numerical formulations (see e.g [8,34]). This is not the case for the choice here proposed of the total deformation gradient as nonlocal variable.…”

Section: Algorithmic Aspectsmentioning

confidence: 99%

On nonlocal regularization in one dimensional finite strain elasticity and plasticity

2005

Self Cite

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The purpose of this article is to explore in details the theoretical and numerical aspects of the behavior of spatial trusses, undergoing large elastic and/ or elastoplastic strains. Two nonlocal formulations are proposed in order to regularize the problem, avoiding the mesh dependence of the numerical response. The classical example of a simple bar in tension is chosen to explore the various features of the proposed models and to highlight the interplay between material and geometrical nonlinearity in the localization.

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A Generalized Variable Formulation for Gradient Dependent Softening Plasticity

Cited by 57 publications

References 31 publications

Applications of the Finite Points Method in the Strain-Gradient Plasticity

Applications of the Finite Points Method in the Strain-Gradient Plasticity

Symmetric Galerkin Boundary Element Method

On nonlocal regularization in one dimensional finite strain elasticity and plasticity

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