A regularized XFEM model for the transition from continuous to discontinuous displacements

Benvenuti, Elena; Tralli, Antonio; Ventura, Giulio

doi:10.1002/nme.2196

Cited by 58 publications

(58 citation statements)

References 39 publications

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“…In the framework of the regularized step function approach introduced by Patzak and Jirasek [83], Benvenuti et al [17] proposed a different mechanical model where the bulk strain field and the localized strain field are assumed to govern distinct mechanically uncoupled mechanisms. A bounded spring-like model is assumed for the localized constitutive law, so that its mechanical work converges to the traction−separation work when the regularization parameter vanishes, i.e.…”

Section: Localization Damage and Transition To Fracturementioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

1,198

695

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Abstract.The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

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Section: Localization Damage and Transition To Fracturementioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

1,198

695

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“…Munjiza [27] developed a combined finite-discrete element method (FDEM), in which elasticity calculations are based on continuum finite element methods, and discontinuous behavior is represented by a discrete method. Whereas the transition from continuous to discontinuous behavior needs proper attention [5], [29], [30], [34], FDEM capably simulates both elasticity and failure processes of geomaterials, as demonstrated through comparisons with theory and laboratory studies [26], [24]. Munjiza et al [28] cover several methods that describe physical systems using discrete entities.…”

Section: Introductionmentioning

confidence: 99%

Simulating the Poisson effect in lattice models of elastic continua

Asahina

Ito

Houseworth

et al. 2015

Computers and Geotechnics

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Lattice models provide discontinuous approximations of the displacement field over the computational domain, which facilitates the modeling of fracture and other discontinuous phenomena. By discretizing the domain with two-node elements, however, ordinary lattice models cannot simulate the Poisson effect in a local (intra-element) sense, which is problematic for some types of analyses.Furthermore, such methods are limited in the range of Poisson ratio values that can be simulated. We present a new approach to remedy such known, yet underappreciated, shortcomings of lattice models. In this approach, the Poisson effect is modeled through the introduction of fictitious stresses into a regular lattice. Capabilities of the new approach are demonstrated through compressive test simulations of homogeneous and heterogeneous materials. The simulation results are compared with theory and those of continuum finite element models. The comparisons show good agreement for arbitrary Poisson ratios (including ν ⩾ 1/3) with respect to nodal displacement, intra-element stress, and nodal stress. This form of discrete method, supplemented by the proposed fictitious measures of stress, retains the simplicity of collections of two-node elements.

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“…For example, in case of two integrands, we have: fn(1).h = @integrand1; and fn (2).h = @integrand2;, where integrand1.m and integrand2.m are MATLAB functions defined as R n → R.…”

Section: A Matlab Code For the Adaptive Integration Schemementioning

confidence: 99%

Efficient adaptive integration of functions with sharp gradients and cusps in n‐dimensional parallelepipeds

Mousavi

Pask

Sukumar

2012

Numerical Meth Engineering

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In this paper, we study the efficient numerical integration of functions with sharp gradients and cusps. An adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions. The algorithm is based on a divide and conquer strategy and is independent of the location of the sharp gradient or cusp. The error analysis reveals that for a C 0 function (derivative-discontinuity at a point), a rate of convergence of n + 1 is obtained in R n . Two applications of the adaptive integration scheme are studied. First, we use the adaptive quadratures for the integration of the regularized Heaviside function-a strongly localized function that is used for modeling sharp gradients. Then, the adaptive quadratures are employed in the enriched finite element solution of the all-electron Coulomb problem in crystalline diamond. The source term and enrichment functions of this problem have sharp gradients and cusps at the nuclei. We show that the optimal rate of convergence is obtained with only a marginal increase in the number of integration points with respect to the pure finite element solution with the same number of elements. The adaptive integration scheme is simple, robust, and directly applicable to any generalized finite element method employing enrichments with sharp local variations or cusps in n-dimensional parallelepiped elements.

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A regularized XFEM model for the transition from continuous to discontinuous displacements

Cited by 58 publications

References 39 publications

The extended/generalized finite element method: An overview of the method and its applications

The extended/generalized finite element method: An overview of the method and its applications

Simulating the Poisson effect in lattice models of elastic continua

Efficient adaptive integration of functions with sharp gradients and cusps in n‐dimensional parallelepipeds

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