A critical comparison of nonlocal and gradient-enhanced softening continua

Peerlings, Rhj Ron; Geers, Mgd Marc; Borst, de R René; Brekelmans, Wam Marcel

doi:10.1016/s0020-7683(01)00087-7

Cited by 565 publications

(432 citation statements)

References 40 publications

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“…The last important problem arises from the well known loss of ellipticity of the damage problem. Developing a model that overcomes localization problems, such as those carried out by Kuhl and Ramm (1999), Steinmann (1999), Peerlings et al (2001) or Peña (2011) will subject for future work.…”

Section: Discussionmentioning

confidence: 99%

Anisotropic microsphere-based approach to damage in soft fibered tissue

Saéz

Alastrué²,

Peña

et al. 2011

Biomech Model Mechanobiol

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An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi scale scheme and focusing on the directionally-dependent behavior of these materials. For this purpose, a microstructural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and

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Section: Discussionmentioning

confidence: 99%

Anisotropic microsphere-based approach to damage in soft fibered tissue

Saéz

Alastrué²,

Peña

et al. 2011

Biomech Model Mechanobiol

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“…In implicit gradient models [5] the nonlocal state variable Y is the solution of a partial differential equation with the local state variable Y as the source term. Various studies [18,17] show that the second-order implicit gradient enhancement provides the best approximation to the integral-type nonlocal model. For this reason, we have chosen this particular gradient approach to facilitate our comparative analysis.…”

Section: Gradient Nonlocal Damage Modelsmentioning

confidence: 99%

A New Damage Model based on Nonlocal Displacements

Rodríguez-Ferran¹,

Morata²,

Huerta³

Civil-Comp Proceedings

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A. RODRÍGUEZ-FERRAN, I. MORATA AND A. HUERTA quantities. In fact, a number of proposals can be found in the literature. For integral-type regularization, some examples are the use of a nonlocal damage parameter [3], nonlocal strains [7] or nonlocal strain invariants [8]. These and other existing approaches are compared in [9] by means of a simple 1D numerical test (bar under uniaxial tension). Various approaches are also possible for gradient regularization. In [10], for instance, the loading function depends on the Laplacian of the damage parameter. Note that all these strategies involve Gauss-point based quantities.A new proposal is made here: to use nonlocal displacements to regularize the problem. The two versions are proposed, discussed and compared: integral-type (nonlocal displacements obtained as the weighted average of standard, local displacements), see [11], and gradienttype (nonlocal displacements obtained as the solution of a second-order PDE). As discussed and illustrated by means of numerical examples, the regularization capabilities of this new model are very similar to that of the standard model. In addition, it is very attractive from a computational viewpoint, especially regarding (1) the computation of the consistent tangent matrix and (2) the simple and straightforward upgrade of a nonlinear FE code to account for nonlocality.An outline of this paper follows. The basic features of standard nonlocal damage models are reviewed in Section 2. The new model based on nonlocal displacements is presented in Section 3. The integral-type and gradient versions are discussed in Sections 3.1 and 3.2 respectively. The regularization capabilities are illustrated by means of a uniaxial tension test. Section 4 deals with the consistent linearization of the nonlinear equilibrium equation. It is shown how the consistent tangent matrix is much simpler to compute for the new model than for the standard models, both in the integral-type (Section 4.1) and the gradient (Section 4.2) cases. Quadratic convergence is shown for the uniaxial tension test. Section 5 shows how nonlocal displacements can be used to incorporate nonlocality into a FE code in a very simple and efficient manner, especially if the gradient regularization is chosen. The concluding remarks of Section 6 close the paper.Standard notation is used. Vector fields in the continuum are represented by slanted boldface type (u u: displacement field). Nodal vectors associated to FE discretization are denoted by upright boldface type (u: nodal displacements). OVERVIEW OF DAMAGE MODELSFor simplicity, only elastic-scalar damage models are considered here. However, the concept of nonlocal displacements can be extended to more complex damage models exhibiting, for instance, anisotropy or plasticity [4,12]. Local damage modelsA generic local damage model consists of the following equations, summarized in table I:• A relation between Cauchy stresses σ σ and small strains ε ε -i.e. the symmetrized gradient of displacements u u, Equation (2)-, where the loss of sti...

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“…Several techniques to overcome this drawback have been developed and published in the literature. Peerlings et al [4] compare the different averaging techniques with different weight functions with the gradient enhance method. In the present work, the simplest method has been chosen: The parameters for damage evolution have simple been optimized for mesh sizes between 5-10 mm.…”

Section: Localisationmentioning

confidence: 99%

Craters in concrete slabs due to detonation – drawbacks of material models with a Mohr-Coulomb yield surface

Conrad

2015

EPJ Web of Conferences

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Abstract. Numerical simulations have been performed with a commercial distributed explicit FE-solver and the results have been compared with experiments. High explosive was placed in front of different concrete slabs with the dimension 100 × 100 × 16 cm. Some of the results of the simulations, in particular the profile of the craters, are not in agreement with the test results. Therefore the key characteristics of the constitutive equation based on Mohr-Coulomb yield surfaces and a damage evolution linked to the plastic strain has been reviewed.

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A critical comparison of nonlocal and gradient-enhanced softening continua

Cited by 565 publications

References 40 publications

Anisotropic microsphere-based approach to damage in soft fibered tissue

Anisotropic microsphere-based approach to damage in soft fibered tissue

A New Damage Model based on Nonlocal Displacements

Craters in concrete slabs due to detonation – drawbacks of material models with a Mohr-Coulomb yield surface

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