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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Vydané v:	Computational mechanics Ročník 51; číslo 5; s. 641 - 659
Hlavní autori:	Dahlberg, Carl F. O., Faleskog, Jonas
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer-Verlag 01.05.2013 Springer Springer Nature B.V
Predmet:	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
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Abstract	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.
AbstractList	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. 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. Keywords Strain gradient plasticity * Interface modeling * Mixed order FE-elements * Backward-Euler algorithm
Audience	Academic
Author	Dahlberg, Carl F. O. Faleskog, Jonas
Author_xml	– sequence: 1 givenname: Carl F. O. surname: Dahlberg fullname: Dahlberg, Carl F. O. email: carl@hallf.kth.se organization: Department of Solid Mechanics, Royal Institute of Technology – sequence: 2 givenname: Jonas surname: Faleskog fullname: Faleskog, Jonas organization: Department of Solid Mechanics, Royal Institute of Technology
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SubjectTerms	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
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Title	An improved strain gradient plasticity formulation with energetic interfaces: theory and a fully implicit finite element formulation
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