Mixed stabilized finite element methods in nonlinear solid mechanics Part II: Strain localization

This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local isotropic Rankine damage model with strain-softening is used as exemplary constitutive model. Both the irreducible and mixed forms of the problem are...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 199; no. 37-40; pp. 2571 - 2589
Main Authors: CERVERA, M, CHIUMENTI, M, CODINA, R
Format: Journal Article
Language:English
Published: Kidlington Elsevier 01.08.2010
Subjects:
Constitutive relationships
Discretization
Exact sciences and technology
Finite element method
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
Inelasticity (thermoplasticity, viscoplasticity...)
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Nonlinearity
Numerical analysis. Scientific computation
Physics
Sciences and techniques of general use
Softening
Solid mechanics
Strain localization
Structural and continuum mechanics
Deformation band
Constitutive equation
Solid mechanics
Mesh dependence
High strain
Non linear material
Tracking
Strain localization
Strain softening
Stress strain relation
Stabilization
Displacement(deformation)
Modeling
Mixed method
Finite element method
Inelasticity
Mixed problem
Localization
Local damage models
Solvability
Damaging
Mixed finite elements
ISSN:0045-7825
Online Access:Get full text
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Summary:This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local isotropic Rankine damage model with strain-softening is used as exemplary constitutive model. Both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed. Lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated. From this analysis, the issue of local discretization error in the pre-localization regime is deemed as the main difficulty to be overcome in the discrete problem. Focus is placed on low order finite elements with continuous strain and displacement fields (triangular P1P1 and quadrilateral Q1Q1), although the presented approach is very general. Numerical examples show that the resulting procedure is remarkably robust: it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh-bias dependence.
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ISSN:0045-7825
DOI:10.1016/j.cma.2010.04.005