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Variational modeling of microstructures in plasticity

Hackl, Klaus and Hoppe, Ulrich and Kochmann, Dennis M. (2014) Variational modeling of microstructures in plasticity. In: Plasticity and Beyond: Microstructures, Crystal-Plasticity and Phase Transitions. CISM International Centre for Mechanical Sciences. No.550. Springer , Vienna, pp. 65-129. ISBN 978-3-7091-1624-1. https://resolver.caltech.edu/CaltechAUTHORS:20170622-130748872

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Abstract

The analysis and simulation of microstructures in solids has gained crucial importance, virtue of the influence of all microstructural characteristics on a material’s macroscopic, mechanical behavior. In particular, the arrangement of dislocations and other lattice defects to particular structures and patterns on the microscale as well as the resultant inhomogeneous distribution of localized strain results in a highly altered stress-strain response. Energetic models predicting the mechanical properties are commonly based on thermodynamic variational principles. Modeling the material response in finite-strain crystal plasticity very often results in a nonconvex variational problem so that the minimizing deformation fields are no longer continuous but exhibit small-scale fluctuations related to probability distributions of deformation gradients to be calculated via energy relaxation. This results in fine structures which can be interpreted as the observed microstructures. This manuscript is supposed to give an overview of the available methods and results in this field. We start by discussing the underlying variational principles for inelastic materials, derive evolution equations for internal variables, and introduce the concept of condensed energy. As a mathematical prerequisite we review the variational calculus of nonconvex potentials and the notion of relaxation. We use these instruments in order to study the initiation of plastic microstructures. Here we focus on a model of single-slip crystal plasticity. Afterward we move on to model the evolution of microstructures. We introduce the concept of essential microstructures and the corresponding relaxed energies and dissipation potentials, and derive evolution equations for microstructure parameters. We then present a numerical scheme by means of which the microstructure development can be computed, and show numerical results for particular examples in single- and double-slip plasticity. We discuss the influence of hardening and of slip system orientations in the present model.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/ 10.1007/978-3-7091-1625-8_2DOIArticle
https://link.springer.com/chapter/10.1007%2F978-3-7091-1625-8_2PublisherArticle
ORCID:
AuthorORCID
Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2014 CISM, Udine.
Series Name:CISM International Centre for Mechanical Sciences
Issue or Number:550
Record Number:CaltechAUTHORS:20170622-130748872
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170622-130748872
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78467
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:22 Jun 2017 20:24
Last Modified:03 Oct 2019 18:09

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