Return mapping for nonsmooth and multiscale elastoplasticity

We present a semi-implicit return mapping algorithm for integrating generic nonsmooth elastoplastic models. The semi-implicit nature of the algorithm stems from “freezing” the plastic internal variables at their previous state, followed by implicitly integrating the stresses and plastic multiplier....

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Vydáno v:	Computer methods in applied mechanics and engineering Ročník 198; číslo 30; s. 2286 - 2296
Hlavní autoři:	Tu, Xuxin, Andrade, José E., Chen, Qiushi
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier B.V 01.06.2009 Elsevier
Témata:	Computational techniques Elastoplasticity Exact sciences and technology Fundamental areas of phenomenology (including applications) Inelasticity (thermoplasticity, viscoplasticity...) Mathematical methods in physics Micromechanics Multiscale Nonsmooth Physics Semi-implicit Solid mechanics Stress integration Structural and continuum mechanics Nonsmooth Micromechanics Semi-implicit Stress integration Elastoplasticity Multiscale Constitutive equation Modeling Freezing Return mapping Continuum Inelasticity Multiscale method Plasticity Internal variable material Microstructure Freeze
ISSN:	0045-7825, 1879-2138
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Popis
Shrnutí:	We present a semi-implicit return mapping algorithm for integrating generic nonsmooth elastoplastic models. The semi-implicit nature of the algorithm stems from “freezing” the plastic internal variables at their previous state, followed by implicitly integrating the stresses and plastic multiplier. The plastic internal variables are incrementally updated once convergence is achieved ( a posteriori). Locally, the algorithm behaves as a classic return mapping for perfect plasticity and, hence, inherits the stability of implicit integrators. However, it differs from purely implicit integrators by keeping the plastic internal variables locally constant. This feature affords the method the ability to integrate nonsmooth ( C 0 ) evolution laws that may not be integrable using implicit methods. As a result, we propose and use the algorithm as the backbone of a semi-concurrent multiscale framework, in which nonsmooth constitutive relationships can be directly extracted from the underlying micromechanical processes and faithfully incorporated into elastoplastic continuum models. Though accuracy of the proposed algorithm is step size-dependent, its simplicity and its remarkable ability to handle nonsmooth relations make the method promising and computationally appealing.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0045-7825 1879-2138
DOI:	10.1016/j.cma.2009.02.014