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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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 198; no. 30; pp. 2286 - 2296
Main Authors: Tu, Xuxin, Andrade, José E., Chen, Qiushi
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.06.2009
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2009.02.014