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Goal‐oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis
Author(s) -
Ju X.,
Mahnken R.
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5541
Subject(s) - a priori and a posteriori , discretization , finite element method , degrees of freedom (physics and chemistry) , estimator , computation , mathematics , mathematical optimization , linear elasticity , duality (order theory) , elasticity (physics) , computer science , consistency (knowledge bases) , algorithm , mathematical analysis , geometry , physics , philosophy , quantum mechanics , discrete mathematics , thermodynamics , statistics , epistemology
Summary Microscopic considerations are drawing increasing attention for modern simulation techniques. Micromorphic continuum theories, considering micro degrees of freedom, are usually adopted for simulation of localization effects like shear bands. The increased number of degrees of freedom 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. Copyright © 2017 John Wiley & Sons, Ltd.