Analysis of the Driving Forces for Multiple Cracks in an Infinite Nonhomogeneous Plate, Part I: Theoretical Analysis

A general methodology is constructed for the fundamental solution of an arbitrarily oriented crack embedded in an infinite nonhomogeneous plate in which the shear modulus varies exponentially with one coordinate. The stress is evaluated as a summation of two states of stresses; one is associated with a local coordinate system in an infinite plate, while the other is associated with the boundaries of a finite plate defined in a structural coordinate system. The fundamental solution is used to generate stress intensity factors and strain energy release rates for fully interactive multiple crack problems. Part I of this paper focuses on the analytical development of the solution. In Part II, the numerical technique used in solving singular integral equations obtained in Part I is presented, along with a parametric study.