Damage assessment for 2D multicracked materials/structures by using M_c-integral

An efficient method is presented to characterize the damage state for two-dimensional multicracked elastic solids. This method is based on the concept of a path-independent M_c-integral, through which the surface energy associated with creation of all the cracks is evaluated. On one hand, when the cracked media are homogeneously stressed, the correspondence relation between the effective material moduli and MM_c is established. On the other hand, when the cracked solids are nonhomogeneously stressed, the effective structural stiffness is determined by using the result of MM_c. Through proper use of MM_c, the damage state of the cracked structure can be assessed both qualitatively and quantitatively.