An improved strain gradient plasticity formulation with energetic interfaces: theory and a fully implicit finite element formulation

A fully implicit backward-Euler implementation of a higher order strain gradient plasticity theory is presented. A tangent operator consistent with the numerical update procedure is given. The implemented theory is a dissipative bulk formulation with energetic contribution from internal interface to...

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Bibliographic Details
Published in:Computational mechanics Vol. 51; no. 5; pp. 641 - 659
Main Authors: Dahlberg, Carl F. O., Faleskog, Jonas
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.05.2013
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Backward-Euler algorithm
Boundaries
Boundary conditions
Classical and Continuum Physics
Computational Science and Engineering
Dislocations
Dissipation
Engineering
Finite element method
Interface modeling
Mathematical analysis
Mathematical models
Mixed order FE-elements
Original Paper
Plastic deformation
Plastic flow
Plastic properties
Plastic strain
Plasticity
Strain
Strain gradient plasticity
Theoretical and Applied Mechanics
Toy industry
Interface modeling
Strain gradient plasticity
Backward-Euler algorithm
Mixed order FE-elements
ISSN:0178-7675, 1432-0924, 1432-0924
Online Access:Get full text
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Summary:A fully implicit backward-Euler implementation of a higher order strain gradient plasticity theory is presented. A tangent operator consistent with the numerical update procedure is given. The implemented theory is a dissipative bulk formulation with energetic contribution from internal interface to model the behavior of material interfaces at small length scales. The implementation is tested by solving some examples that specifically highlight the numerics and the effect of using the energetic interfaces as higher order boundary conditions. Specifically, it is demonstrated that the energetic interface formulation is able to mimic a wide range of plastic strain conditions at internal boundaries. It is also shown that delayed micro-hard conditions may arise under certain circumstances such that an interface at first offers little constraints on plastic flow, but with increasing plastic deformation will develop and become a barrier to dislocation motion.
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ISSN:0178-7675
1432-0924
1432-0924
DOI:10.1007/s00466-012-0743-5