On fibre bundle approach to a damage analysis

In this paper the geometric structure of a damaged state in the medium is i nvestigated based on the fibre bundle technique. The damage (a failure) in some region of the medium under loads is regarded as breakdown of the holon omicity in this region. A measure of reduction of load carrying area elemen ts caused by the development of microcracks or microvoids in the damaged me dium is identified with the damage tensor. Multiplicative representations o f the damage tensor formulated both on the tangent bundle with an affine co nnection and a fibre bundle with a non-linear connection over the damaged m edium are obtained. In the former case the generalization of the damage ten sor to the tangent bundle rests on the technique of prolonging the deformat ion vector to-include not only the independent variables and dependent vari ables appearing in the damage tensor, but also the derivatives of the depen dent variables. The so-called lifting technique is used to express the dama ge tensor by initial, additional and direct (deformation-induced) damages o r by direct and transferred ones. In the latter one the higher-order contac t geometry approach identified with the Finslerian geometry is employed to analyze the influences of elastic, inelastic, direct, transferred and initi al damages on the total damage tensor. Time-dependent relationships of the damage tensor are then presented. (C) 1998 Elsevier Science Ltd. All rights reserved.