The Conservation Law Related to Path Independent Integral and Expression of Crack Energy Density by Path Independent Integral

Abstract

The conservation laws related to path independent integrals are discussed based on the conservation of energy and the principle of virtual work, and the equality of these laws is proved. Through the discussion of the conservation laws, it is also shown that the concept of energy momentum tensor which can be applied when limited constitutive equations are assumed can be extended to the useful concept which has no limitation on constitutive equation. Secondly, an expression of crack energy density by path independent integral is given based on the above conservation laws and the relations to other known path independent integrals (J-integral and J^^- -integral) are discussed. The concept of crack energy density was previously proposed by the author as a fundamental parameter in fracture mechanics and it is the purpose of the present paper to obtain a path independent expression of crack energy density for evaluating its value.