Anisotropic mesh adaptation for crack propagation induced by a thermal shock in 2D

Ferro, Nicola; Micheletti, Stefano; Perotto, Simona

doi:10.1016/j.cma.2017.11.024

Cited by 31 publications

(12 citation statements)

References 28 publications

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“…Anisotropic remeshing led to significant computational time savings in comparison to isotropic remeshing. Similar results were obtained in [6], where the problem was extended to thermally induced fracture, and in [7], where the brittle fracture was studied extensively. In [8] a predictor-corrector scheme for mesh adaptivity was used, while in [9] a residual type a posteriori error estimator was presented, and in both works, quadrangle meshes with hanging nodes were used.…”

Section: Introductionsupporting

confidence: 78%

“…The main features of the algorithm are simplicity, easy implementation, and low computational costs. The algorithm relies on simple splitting and merging operations with mesh quality preservation, similarly as in [14] and in contrast to work as [5][6][7], where mesh rebuilding process is more complex. Such an approach leads to less computational effort in remeshing, and a remapping of both nodal and integration point data that is easier and less prone to error.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Phase-Field Modeling of Brittle Fracture

Jukić

Jarak

Seleš

et al. 2021

Lecture Notes in Civil Engineering

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The phase-field method for brittle fracture is a powerful and versatile method, but it suffers from high computational costs due to high mesh density requirement. This problem can be tackled by the development of adaptive remeshing procedures. In this paper, a simple and easily implementable adaptive remeshing scheme for a phase-field model of brittle fracture is presented. The mesh refinement scheme is based on the splitting of triangle elements into two new elements, resulting in conforming meshes. A simple mesh hierarchy is utilized for mesh coarsening. Remeshing criteria are based on physical quantities such as the deformation energy density and the gradient of phase-field. The phase-field model is solved using a staggered algorithm and the remeshing procedure is performed after every two iterations of the algorithm. The AT2 model is utilized, together with the spectral energy split. Generated results such as crack paths and force-displacement diagrams are compared to the results from the literature. It is shown that the utilization of adaptive remeshing leads to significant time savings without compromising the solution accuracy.

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Section: Introductionsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Adaptive Phase-Field Modeling of Brittle Fracture

Jukić

Jarak

Seleš

et al. 2021

Lecture Notes in Civil Engineering

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“…Standard isotropic adapted meshes allow us to improve the solution accuracy (for a certain mesh cardinality) or to contain the number of elements (for a user-defined tolerance on the numerical approximation) by optimizing the element size. These improvements can be further enhanced by resorting to anisotropic grids, which tune the size, the shape, and the orientation of the mesh triangles in order to track the directional features of the modeled phenomena, such as steep boundary and internal layers, discontinuities, sharp fronts, shocks in compressible flows, more in general areas where the problem exhibits strong gradients (Formaggia and Perotto 2001;Dompierre et al 2002;Formaggia et al 2002;Belhamadia et al 2014;Porta et al 2012;Ferro et al 2018). The generation of anisotropic grids deserves more technicalities when compared with an isotropic context.…”

Section: The Simpaty Algorithmmentioning

confidence: 99%

Design of cellular materials for multiscale topology optimization: application to patient-specific orthopedic devices

Ferro

Perotto

Bianchi

et al. 2022

Struct Multidisc Optim

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A flexible problem-specific multiscale topology optimization is introduced to associate different areas of the design domain with diverse microstructures extracted from a dictionary of optimized unit cells. The generation of the dictionary is carried out by exploiting micro-SIMP with AnisoTropic mesh adaptivitY (microSIMPATY) algorithm, which promotes the design of free-form layouts. The proposed methodology is particularized in a proof-of-concept setting for the design of orthotic devices for the treatment of foot diseases. Different patient-specific settings drive the prototyping of customized insoles, which are numerically verified and successively validated in terms of mechanical performances and manufacturability.

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“…It has been also proved for a few years that using an adjoint is efficient for improving by a correction the accuracy of the evaluation of a quantity of interest ( [17]). As GO mesh adaptation is concerned, a remarkable quantity of papers deals with a posteriori goal-based error formulation to drive adaptivity, using adjoint formulations or gradients (see for example [19,18]). Our group is investigating GO formulations for steady and unsteady problems in an a priori context.…”

Section: The Goal-oriented Formulationmentioning

confidence: 99%

<i>A priori</i> error-based mesh adaptation in CFD

Gauci

Belme

Carabias

et al. 2019

Methods and Applications of Analysis

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The main purpose of Computational Mechanics research is not to obtain more efficient computational methods on existing cases (or more accurate, which is somewhat equivalent). This purpose is to perform new computations which were not affordable before. Future researchers will hopefully be able to face the many challenges of the century (global change, health, energy). This remark holds (to a lesser extend) for mesh adaptation research. The purpose is to be able to compute new phenomena and also to master the numerical uncertainties which have been up to now unsufficiently controlled.Many phenomena in continuum mechanics real world involve multiple scales or/and singularities and cannot computed with uniform meshes. Designing non uniform meshes will become so complex that automatic adaptation will be mandatory.

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Anisotropic mesh adaptation for crack propagation induced by a thermal shock in 2D

Cited by 31 publications

References 28 publications

Adaptive Phase-Field Modeling of Brittle Fracture

Adaptive Phase-Field Modeling of Brittle Fracture

Design of cellular materials for multiscale topology optimization: application to patient-specific orthopedic devices

<i>A priori</i> error-based mesh adaptation in CFD

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