Model adaptivity on effective elastic properties coupled with adaptive FEM

Ju, Xiaozhe; Mahnken, Rolf

doi:10.1016/j.cma.2017.04.013

Cited by 15 publications

(13 citation statements)

References 48 publications

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“…The error estimate

{\overset{E}{true}}^{i}

appears to somewhat underestimate the actual error

{\overset{E}{true}}^{i}

and is able to mimic the decreasing trend of the actual error

{\overset{E}{true}}^{i}

. These observations are quite similar to those obtained from our previous work for a different model hierarchy, where a more detailed discussion on the error estimator was given. Finally, Figures M to O show several model distributions obtained by the adaptive approach for different error levels.…”

Section: Numerical Examplessupporting

confidence: 86%

“…To this end, we first briefly recall the general goal-oriented adaptive approach developed in our previous work. 63 Then, we propose a novel model hierarchy, including the aspects of mean-field and full-field homogenization methods as well as unit cell size.…”

Section: Goal-oriented Adaptivity On the Macroscalementioning

confidence: 99%

“…Here, z h is the FE solution of the approximate dual problem (C2), which is not directly useful for the error representation (44) due to the Galerkin orthogonality. For this reason, we use, in this work, a patch recovery approach developed in our previous works 61,63 to construct an approximate solution of…”

Section: B4 Interaction Direct Derivativementioning

confidence: 99%

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Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Mahnken

2019

Numerical Meth Engineering

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Summary Homogenization methods are drawing increasing attention for simulation of heterogeneous materials like composites. For balancing the accuracy and the numerical efficiency of such strategies, we deal with both model and discretization errors of the finite element method (FEM) on a macroscale. Within a framework of goal‐oriented adaptivity, we consider linear elastic heterogeneous materials, for which first‐order homogenization schemes apply. A novel model hierarchy is proposed based on mean‐field and full‐field homogenization methods. For the former, we consider several well‐established schemes like Mori‐Tanaka or self‐consistent as basic models, and for the latter, as superior models, unit cell problems are solved via the FEM under an a priori chosen boundary condition. For a further stage of the model hierarchy, we consider hierarchical unit cells within the frame of the FEM toward an adaptive selection of the unit cell size. By means of several numerical examples, we illustrate the effectiveness of the proposed adaptive approach.

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“…The error estimate

{\overset{E}{true}}^{i}

appears to somewhat underestimate the actual error

{\overset{E}{true}}^{i}

and is able to mimic the decreasing trend of the actual error

{\overset{E}{true}}^{i}

Section: Numerical Examplessupporting

confidence: 86%

Section: Goal-oriented Adaptivity On the Macroscalementioning

confidence: 99%

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Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Mahnken

2019

Numerical Meth Engineering

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“…For a more detailed comparison of the proposed recovery technique w.r.t. model adaptivity of multiscale problems, we refer to our recent work .…”

Section: Introductionmentioning

confidence: 99%

Goal‐oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis

Mahnken

2017

Numerical Meth Engineering

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SUMMARYMicroscopic considerations are drawing increasing attention for modern simulation techniques. Micromorphic continuum theories, considering micro degrees of freedom (DoFs), are usually adopted for simulation of localization effects like shear bands. The increased number of DoFs clearly motivates an application of adaptive methods. In this work, the adaptive FEM is tailored for micromorphic elasticity. The proposed adaptive procedure is driven by a goal-oriented a posteriori error estimator based on duality techniques. For efficient computation of the dual solution, a patch-based recovery technique is proposed and compared to a reference approach. In order to theoretically ensure optimal convergence order of the proposed adaptive procedure, adjoint consistency of the FE-discretized solution for the linear elastic micromorphic continua is shown. For illustration, numerical examples are provided.

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“…For a more detailed comparison of the proposed recovery technique w.r.t. model adaptivity of multiscale problems, we refer to our recent work [37].…”

Section: Introductionmentioning

confidence: 99%

Goal‐oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis

Ju¹,

Mahnken²

2018

Numerical Meth Engineering

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Model adaptivity on effective elastic properties coupled with adaptive FEM

Cited by 15 publications

References 48 publications

Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Goal‐oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis

Goal‐oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis

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