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Multisurface plasticity for Cosserat materials: Plate element implementation and validation
Author(s) -
Godio Michele,
Stefanou Ioannis,
Sab Karam,
Sulem Jean
Publication year - 2016
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.5219
Subject(s) - plasticity , finite element method , hardening (computing) , softening , mathematics , quadratic equation , projection (relational algebra) , mathematical analysis , computer science , structural engineering , algorithm , geometry , materials science , engineering , composite material , statistics , layer (electronics)
Summary The macroscopic behavior of materials is affected by their inner micro‐structure. Elementary considerations based on the arrangement, and the physical and mechanical features of the micro‐structure may lead to the formulation of elastoplastic constitutive laws, involving hardening/softening mechanisms and non‐associative properties. In order to model the non‐linear behavior of micro‐structured materials, the classical theory of time‐independent multisurface plasticity is herein extended to Cosserat continua. The account for plastic relative strains and curvatures is made by means of a robust quadratic‐convergent projection algorithm, specifically formulated for non‐associative and hardening/softening plasticity. Some important limitations of the classical implementation of the algorithm for multisurface plasticity prevent its application for any plastic surfaces and loading conditions. These limitations are addressed in this paper, and a robust solution strategy based on the singular value decomposition technique is proposed. The projection algorithm is then implemented into a finite element formulation for Cosserat continua. A specific finite element is considered, developed for micropolar plates. The element is validated through illustrative examples and applications, showing able performance. Copyright © 2016 John Wiley & Sons, Ltd.