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Return mapping for nonsmooth and multiscale elastoplasticity Xuxin Tu, Jose E. Andrade

Summary: Return mapping for nonsmooth and multiscale elastoplasticity
Xuxin Tu, Jos´e E. Andrade
, and Qiushi Chen
Theoretical & Applied Mechanics, Northwestern University, Evanston, IL 60208, USA
We present a semi-implicit return mapping algorithm for integrating generic nonsmooth elasto-
plastic 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 (C0) 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.


Source: Andrade, Jose - Department of Civil and Environmental Engineering, Northwestern University


Collections: Engineering