Implicit finite element formulation of multiresolution continuum theory

Hao Qin; Lars Erik Lindgren; Wing Kam Liu; Jacob Smith

doi:10.1016/j.cma.2015.04.009

Implicit finite element formulation of multiresolution continuum theory

Hao Qin^*, Lars Erik Lindgren, Wing Kam Liu, Jacob Smith

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The multiresolution continuum theory is a higher order continuum theory where additional kinematic variables account for microstructural inhomogeneities at several distinct length scales. This can be particularly important for localization problems. The strength of this theory is that it can account for details in the microstructure of a material without using an extremely fine mesh. The present paper describes the implementation and verification of a 3D elastic-plastic multiresolution element based on an implicit time stepping algorithm. It is implemented in the general purpose finite element program FEAP. The mesh independency associated with the length scale parameter is examined and the convergence rate of the element is also evaluated.

Original language	English (US)
Pages (from-to)	114-130
Number of pages	17
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	293
DOIs	https://doi.org/10.1016/j.cma.2015.04.009
State	Published - Aug 5 2015

Keywords

Damage
Finite element method
Localization
Multiresolution continuum theory

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2015.04.009

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title = "Implicit finite element formulation of multiresolution continuum theory",

abstract = "The multiresolution continuum theory is a higher order continuum theory where additional kinematic variables account for microstructural inhomogeneities at several distinct length scales. This can be particularly important for localization problems. The strength of this theory is that it can account for details in the microstructure of a material without using an extremely fine mesh. The present paper describes the implementation and verification of a 3D elastic-plastic multiresolution element based on an implicit time stepping algorithm. It is implemented in the general purpose finite element program FEAP. The mesh independency associated with the length scale parameter is examined and the convergence rate of the element is also evaluated.",

keywords = "Damage, Finite element method, Localization, Multiresolution continuum theory",

author = "Hao Qin and Lindgren, {Lars Erik} and Liu, {Wing Kam} and Jacob Smith",

note = "Funding Information: The authors gratefully acknowledge the support of CHS (Center of High Performance Steels) of Lule{\aa} University of Technology and Swedish Steel Research Program. This work was also performed under the following financial assistance award 70NANB14H012 from U.S. Department of Commerce, National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD). Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

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doi = "10.1016/j.cma.2015.04.009",

language = "English (US)",

volume = "293",

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journal = "Computer Methods in Applied Mechanics and Engineering",

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T1 - Implicit finite element formulation of multiresolution continuum theory

AU - Qin, Hao

AU - Lindgren, Lars Erik

AU - Liu, Wing Kam

AU - Smith, Jacob

N1 - Funding Information: The authors gratefully acknowledge the support of CHS (Center of High Performance Steels) of Luleå University of Technology and Swedish Steel Research Program. This work was also performed under the following financial assistance award 70NANB14H012 from U.S. Department of Commerce, National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD). Publisher Copyright: © 2015 Elsevier B.V.

PY - 2015/8/5

Y1 - 2015/8/5

N2 - The multiresolution continuum theory is a higher order continuum theory where additional kinematic variables account for microstructural inhomogeneities at several distinct length scales. This can be particularly important for localization problems. The strength of this theory is that it can account for details in the microstructure of a material without using an extremely fine mesh. The present paper describes the implementation and verification of a 3D elastic-plastic multiresolution element based on an implicit time stepping algorithm. It is implemented in the general purpose finite element program FEAP. The mesh independency associated with the length scale parameter is examined and the convergence rate of the element is also evaluated.

AB - The multiresolution continuum theory is a higher order continuum theory where additional kinematic variables account for microstructural inhomogeneities at several distinct length scales. This can be particularly important for localization problems. The strength of this theory is that it can account for details in the microstructure of a material without using an extremely fine mesh. The present paper describes the implementation and verification of a 3D elastic-plastic multiresolution element based on an implicit time stepping algorithm. It is implemented in the general purpose finite element program FEAP. The mesh independency associated with the length scale parameter is examined and the convergence rate of the element is also evaluated.

KW - Damage

KW - Finite element method

KW - Localization

KW - Multiresolution continuum theory

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DO - 10.1016/j.cma.2015.04.009

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SN - 0045-7825

VL - 293

SP - 114

EP - 130

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

Implicit finite element formulation of multiresolution continuum theory

Abstract

Keywords

ASJC Scopus subject areas

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