Analytical bounds for damage induced planar anisotropy

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:60-61

Article

Vannucci, P.^1,2  Desmorat, B.^1,3,4 

[1] Univ Paris Saclay, UPSAy, Paris, France

[2] UVSQ, UMR CNRS 8100, Lab Math Versailles, F-78035 Versailles, France

[3] Univ Paris 11, Orsay, France

[4] Univ Paris 06, CNRS UMR 7190, Inst Jean Le Rond dAlembert, F-75252 Paris, France

关键词: Planar elasticity;    Damage;    Anisotropy;    Polar method;    Tensor invariants;    Explicit bounds;   

DOI  :  10.1016/j.ijsolstr.2015.02.017

来源: Elsevier

【 摘 要 】

The damage of a planar, elastic and initially isotropic material is considered in the framework of a classical approach where the damaged elasticity tensor is ruled by a fourth-rank symmetric damage tensor. The analysis is completely carried on using the so-called polar method for the invariant representation of tensors in R-2. The final elastic behavior, induced by damage, can be anisotropic: all the possible situations of elastic symmetries are considered, and for each one an analytical expression for the bounds on the invariants of the damaged elastic tensor and of the damage tensor is given. An admissible domain for the damage invariants and for the damaged elastic invariants is so provided, the convexity of these domains is also proved. (C) 2015 Elsevier Ltd. All rights reserved.

【 授权许可】

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