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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| Published in: | Computer methods in applied mechanics and engineering Vol. 199; no. 37-40; pp. 2571 - 2589 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Kidlington
Elsevier
01.08.2010
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| ISSN: | 0045-7825 |
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| Abstract | 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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| AbstractList | 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. |
| Author | CHIUMENTI, M CERVERA, M CODINA, R |
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| Keywords | 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 |
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| Snippet | This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local... |
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| SubjectTerms | 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 |
| Title | Mixed stabilized finite element methods in nonlinear solid mechanics Part II: Strain localization |
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