連続体損傷力学における異方損傷状態の数学的モデル化

概要

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A fictitious equivalent undamaged configuration B^*_t of an element of a damaged material is first introduced into a three-dimensional Riemannian manifold by excluding the irrelevant rigid rotation of the element. Then a new symmetric damage tensor for three-dimensional anisotropic damage is developed in terms of Finger's tensor of a fictitious deformation gradient from the current damaged configuration B_t to the equivalent undamaged configuration B^*_t. The damage tensor components are expressed in terms of the metric tensor components of the convective coordinate systems of B_t and B^*_t. Furthermore, the effective stress tensor of damage mechanics is defined by the equality of stress vectors acting on the damaged and equivalent undamaged plane elements, and the mechanical interpretation of the effective stress tensor and its symmetry condition are discussed. The symmetry condition is also formulated by means of a commutator tensor formed by the tensor pairs : damage tensor-Cauchy stress tensor and damage tensor-reversible gradient. Finally, the symmetrized effective stress tensor is introduced and interpreted.
一般社団法人日本機械学会の論文
1994-12-25