Gradient constitutive relations: numerical aspects and application to gradient damage

The description of localisation and structural failure through local strain-softening constitutive laws leads to ill-posed problems. To retrieve a well-posed problem, the material state is described through the gradients of internal variables in addition to the strain and the internal variables them...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2005-12, Vol.194 (50-52), p.5191-5220
Main Authors: Lorentz, E., Benallal, A.
Format: Article
Language:English
Subjects:
Augmented Lagrangian
Computational techniques
Damage
Engineering Sciences
Exact sciences and technology
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
Gradient constitutive laws
Mathematical methods in physics
Mechanics
Physics
Solid mechanics
Strain-softening
Structural and continuum mechanics
Structural mechanics
Variational formulation
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Summary:The description of localisation and structural failure through local strain-softening constitutive laws leads to ill-posed problems. To retrieve a well-posed problem, the material state is described through the gradients of internal variables in addition to the strain and the internal variables themselves. Under some assumptions, it is shown that these gradient laws can be cast into a variational formulation. After time discretisation, the evolution of the internal variable field is characterised by a minimum principle. A specific algorithm is proposed to perform the minimisation in the context of finite elements. Finally, it is applied to a gradient brittle damage model.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2004.12.016