Strain- and stress-based continuum damage models—II. Computational aspects

Simo, J. C.; Ju, J. W.

doi:10.1016/0895-7177(89)90118-0

Cited by 59 publications

(97 citation statements)

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“…where the operators LOE and BOE are linear partial differential operators on the domain and on the boundary @ , describing the governing equation and boundary conditions, respectively. Collocating the interpolation formula (18) at N distinct locations known as test points, x j , coinciding with the trial centres j , leads to a system of equations which is fully populated and nonsymmetric. In principle, the set of functional centres i need not coincide with the set of test points x i ; however, in the present work, the two sets are always of equal size 443 and are placed at identical locations, leading to a single set of 'collocation centres'.…”

Section: Rbf-fc Methods For Poroelasticitymentioning

confidence: 99%

“…Using the appropriate RBF reconstruction formula, that is, equation (18) or equation (25), the approximate value of the field variable u.x/ (or a component thereof in the case of elasticity) may be computed for any x within the support domain of system k. Expressing this computation as a vector product, we have…”

Section: Rbf-fc Methods For Poroelasticitymentioning

confidence: 99%

“…Because the RBFs, , are known (equation (17)), their derivatives may be computed analytically. For a general partial differential operator Q, the equivalent RBF reconstruction formula (18) would become…”

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confidence: 99%

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A high‐resolution local RBF collocation method for steady‐state poroelasticity and hydromechanical damage analysis

Stevens

Power

Polanco

et al. 2014

Num Anal Meth Geomechanics

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International audiencen this work, we describe a meshless numerical method based on local collocation with RBFs for the solution of the poroelasticity equation. The RBF finite collocation approach forms a series of overlapping nodal stencils, over which an RBF collocation is performed. These local collocation systems enforce the governing PDE operator throughout their interior, with the intersystem communication occurring via the collocation of field variables at the stencil periphery. The method does not rely on a generalised finite differencing approach, whereby the governing partial differential operator is reconstructed at the global level to drive the solution of the PDE. Instead, the PDE governing and boundary operators are enforced directly within the local RBF collocation systems, and the sparse global assembly is formed by reconstructing the value of the field variables at the centrepoint of the local stencils. In this way, the solution of the PDE is driven entirely by the local RBF collocation, and the method more closely resembles the approach of the full-domain RBF collocation method. By formulating the problem in this fashion, high rates of convergence may be attained without the computational cost and numerical ill-conditioning issues that are associated with the full-domain RBF collocation approach. An analytical solution is formulated for a 2D poroelastic fluid injection scenario and is used to verify the proposed implementation of the method. Highly accurate solutions are produced, and convergence rates in excess of sixth order are observed for each field variable (i.e. pressure and displacement) and field-variable derivative (i.e. pressure gradients and stresses). The stress and displacement fields resulting from the solution of the poroelasticity equation are then used to describe the formation and propagation of microfractures and microfissures, which may form in the presence of large shear strain, in terms of a continuous damage variable which modifies the mechanical and hydraulic properties of the porous medium. The formation of such hydromechanical damage, and the resulting increase in hydraulic conductivity, is investigated for a pressurised injection into sandstone. Copyright © 2014 John Wiley & Sons, Lt

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Section: Rbf-fc Methods For Poroelasticitymentioning

confidence: 99%

Section: Rbf-fc Methods For Poroelasticitymentioning

confidence: 99%

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A high‐resolution local RBF collocation method for steady‐state poroelasticity and hydromechanical damage analysis

Stevens

Power

Polanco

et al. 2014

Num Anal Meth Geomechanics

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“…In the example, three different meshes were used to study the damage and failure behaviour of bars under uniaxial tension. An isotropic damage constitutive law proposed by Simo and Ju [32] is applied to model them. The numbers of the mesh are 33, 90 and 550, respectively, and all the other conditions are the same.…”

Section: Gradient-enhanced Damage Modelmentioning

confidence: 99%

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Weiyuan

Zhao

Liu

et al. 2002

Num Anal Meth Geomechanics

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SUMMARYStrain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a microcrack-based anisotropic damage model for rock-like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well-known meshsensitivity problem in FEM. In the computation, elements with C 1 continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D-non-linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented.

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“…Theoretical aspects (plasticity with damage models) and numerical aspects have been widely developed for many years, and more or less efficient tools have been proposed (see References [1][2][3][4][5][6][7][8][9] and references given there). Concerning geometrical aspects, the 2D or 3D object representation, as well as the initial finite element discretization, has also given rise to many development efforts (see References [10,11] for a synthesis).…”

Section: Introductionmentioning

confidence: 99%

Adaptive remeshing in large plastic strain with damage

Borouchaki

Laug

Cherouat

et al. 2005

Int. J. Numer. Meth. Engng

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SUMMARYThe analysis of mechanical structures using the finite element method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during the computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behaviour of the solution as the plastic strain or the damage fields. This paper gives the necessary steps to remesh a mechanical structure during large elasto-plastic deformations with damage. An important part of this process concerns the geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. After recalling the formulation of the elasto-plastic problem with damage, four types of applications using the proposed adaptive remeshing are given: orthogonal cutting, sidepressing of an infinite cylinder, blanking and backward extrusion with drilling.

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Strain- and stress-based continuum damage models—II. Computational aspects

Cited by 59 publications

References 0 publications

A high‐resolution local RBF collocation method for steady‐state poroelasticity and hydromechanical damage analysis

A high‐resolution local RBF collocation method for steady‐state poroelasticity and hydromechanical damage analysis

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Adaptive remeshing in large plastic strain with damage

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