SMEARED-TIP SUPERPOSITION METHOD FOR NONLINEAR AND TIME-DEPENDENT FRACTURE

A crack with bridging stresses is treated as a superposition of many cracks whose tips are continuously distributed (smeared) along the crack line. The solution is reduced to an integral equation for the components of the applied load associated with crack tips at various locations. This equation, which is equivalent to that previously presented by Planas and Elices (1986), is then generalized to include: (1) time-dependent nonlinear stress-displacement relation for the bridging stresses (rate-effect), and (2) aging viscoelastic behavior of the material in the rest of the structure. The solution leads to an integro-differential equation, whose method of solution by finite differences in space and time is given. The paper presents only the mathematical formulation. Numerical studies applied to concrete, rock and ceramics are planned. © 1990.