On Nonlocal Plasticity, Strain Softening and Localization
(1994) In TVSM- Abstract
- Plasticity theory represents a fundamental continuum approach to the study of great variety of phenomena in the mechanics of inelastic solids. Basic to the theory is the appearance of permanent deformation and its association with the phenomenological concept of plastic deformation. The origin of plastic deformation in a solid may be looked upon as the result of a complex interference of its microstructure with its macrastructure. In a crystalline material it is the defects in its structure which cause the permanent deformation, and especially, as far as metals are concerned, it is dislocations which acts as carriers of plastic deformation. Thus, in a general phenomenological approach there must be an interplay between microstructural and... (More)
- Plasticity theory represents a fundamental continuum approach to the study of great variety of phenomena in the mechanics of inelastic solids. Basic to the theory is the appearance of permanent deformation and its association with the phenomenological concept of plastic deformation. The origin of plastic deformation in a solid may be looked upon as the result of a complex interference of its microstructure with its macrastructure. In a crystalline material it is the defects in its structure which cause the permanent deformation, and especially, as far as metals are concerned, it is dislocations which acts as carriers of plastic deformation. Thus, in a general phenomenological approach there must be an interplay between microstructural and macrostructural scales. This leads us to the conclusion that plastic deformation is nonlocal in character and hence a general theory of plasticity should be nonlocal.
The present work on nonlocal plasticity is based on a strain space formulation where plastic strain is regarded as a primitive variable, characterized by an appropriate constitutive equation for its rate. Nonlocal constitutive variables are constructed from a set of basic state functions, constituted by total (kinematical) strain, plastic strain and a scalar measure of strain hardening. A rate-independent theory is formulated where stress is assumed to be a function of the nonlocal variables.
A yield function in strain space is introduced, where the same set of independent variables occurs as in the case of the stress response function. This is fundamental for the theory. We recall that in classical plasticity the yield condition implies that whether a state is elastic or plastic depends only on the plastic strain at the actual stress point and not on plastic strain at neighbouring points, hence excluding any dependence on gradients of plastic strain. From a physical view, however, it is hard to find any support for rejecting long-range interactions in the yield criterion, keeping in mind the complex interplay between microstructure and macrostructure with regard to plastic deformation.
Yield criteria, flow rules, and loading conditiona are formulated. The loading conditions in strain space give rise to associated conditions in stress space of quite different form (constrasting with local theory). This difference between stress space and strain space is seen to favour the choice of strains over stresses as primary variables in nonlocal plasticity.
Numerical techniques are developed for integrating the rate equations, subject to the constraints implied by the consistency condition, in nonlocal plasticity, being represented by an integral equation defined throughout the region of plastic loading.
A strain softening problem is investigated by fintite element analysis. Solutions are obtained which converge properly and also show computational objectivity. (Less)
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- author
- Nilsson, Christer
- supervisor
- organization
- publishing date
- 1994-11
- type
- Thesis
- publication status
- published
- subject
- keywords
- Nonlocal plasticity, Plastic dissipation, Strain softening, Loalization, Integration of elastic-plastic equations, finite element analysis
- in
- TVSM
- issue
- 1007
- edition
- 1
- pages
- 166 pages
- publisher
- Division of Structural Mechanics, LTH
- language
- English
- LU publication?
- no
- id
- 6dd437f9-6366-4dd7-aac4-37ca10333526
- date added to LUP
- 2023-08-09 17:08:42
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- 2024-04-03 08:48:30
@phdthesis{6dd437f9-6366-4dd7-aac4-37ca10333526,
abstract = {{Plasticity theory represents a fundamental continuum approach to the study of great variety of phenomena in the mechanics of inelastic solids. Basic to the theory is the appearance of permanent deformation and its association with the phenomenological concept of plastic deformation. The origin of plastic deformation in a solid may be looked upon as the result of a complex interference of its microstructure with its macrastructure. In a crystalline material it is the defects in its structure which cause the permanent deformation, and especially, as far as metals are concerned, it is dislocations which acts as carriers of plastic deformation. Thus, in a general phenomenological approach there must be an interplay between microstructural and macrostructural scales. This leads us to the conclusion that plastic deformation is nonlocal in character and hence a general theory of plasticity should be nonlocal.<br/><br/>The present work on nonlocal plasticity is based on a strain space formulation where plastic strain is regarded as a primitive variable, characterized by an appropriate constitutive equation for its rate. Nonlocal constitutive variables are constructed from a set of basic state functions, constituted by total (kinematical) strain, plastic strain and a scalar measure of strain hardening. A rate-independent theory is formulated where stress is assumed to be a function of the nonlocal variables.<br/><br/>A yield function in strain space is introduced, where the same set of independent variables occurs as in the case of the stress response function. This is fundamental for the theory. We recall that in classical plasticity the yield condition implies that whether a state is elastic or plastic depends only on the plastic strain at the actual stress point and not on plastic strain at neighbouring points, hence excluding any dependence on gradients of plastic strain. From a physical view, however, it is hard to find any support for rejecting long-range interactions in the yield criterion, keeping in mind the complex interplay between microstructure and macrostructure with regard to plastic deformation.<br/><br/>Yield criteria, flow rules, and loading conditiona are formulated. The loading conditions in strain space give rise to associated conditions in stress space of quite different form (constrasting with local theory). This difference between stress space and strain space is seen to favour the choice of strains over stresses as primary variables in nonlocal plasticity.<br/><br/>Numerical techniques are developed for integrating the rate equations, subject to the constraints implied by the consistency condition, in nonlocal plasticity, being represented by an integral equation defined throughout the region of plastic loading.<br/><br/>A strain softening problem is investigated by fintite element analysis. Solutions are obtained which converge properly and also show computational objectivity.}},
author = {{Nilsson, Christer}},
keywords = {{Nonlocal plasticity; Plastic dissipation; Strain softening; Loalization; Integration of elastic-plastic equations; finite element analysis}},
language = {{eng}},
number = {{1007}},
publisher = {{Division of Structural Mechanics, LTH}},
series = {{TVSM}},
title = {{On Nonlocal Plasticity, Strain Softening and Localization}},
url = {{https://lup.lub.lu.se/search/files/178515568/web1007.pdf}},
year = {{1994}},
}