Smeared-tip Superposition Method for Nonlinear and Time-dependent Fracture

A crack with bridging stresses is treated as a superposition o f many cracks whose tips are continuously distributed (smeared) along the crack line. The solution is reduced to an inteEral 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: (I) time-dependent nonlinear stress-displacement relation for the bridEing stresses (rate-effect), and (2) aEin E 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 Eiven. The paper presents only the mathematical formulation. Numerical studies applied to concrete, rock and ceramics are planned. INTRODUCTION Although the f in i t e e lement and boundary element methods are powerfu l and genera l approaches to f r a c t u r e problems with nonlinear and t ime-dependent ma te r i a l p roper t ies , the usefulness of analyt ica l or semianaly t ica l approaches cannot be denied. These methods o f f e r much deeper insight into the mechanics of f r a c t u r e and are more e f f ic ien t , more accura te , foo lproof and unlikely to fail . For this reason, Green ' s funct ion methods or solutions based on dis locat ions are widely used. These methods, however, become too d i f f i cu l t f o r complex geomet r ies as well as complex ma te r i a l laws. This paper will present a new semianalyt ical method based on superposi t ion of exac t solutions of l inear e las t ic f r a c t u r e mechanics. This method, which will t r e a t the crack as a superposi t ion of many l inear ly e las t ic cracks whose t ips are continuously d is t r ibu ted (smeared) along the crack line, will 343 I I I l -351, . ri 13/90 . yri t r i -TIP POSITION OD I R DENT E