# Smeared-tip superposition method for cohesive fracture with rate effect and creep

Zdeněk P. Bažant*, Stephen Beissel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

## Abstract

A recent formulation of the smeared-tip superposition method presented by Bažant [1], which itself was a generalization and modification of an integral equation formulation with an asymptotic series solution derived by Planas and Elices [2], is further improved, generalized and adapted to an efficient finite difference solution scheme. A crack with bridging stresses is modeled as a superposition of infinitely many LEFM cracks with continuously distributed (smeared) tips having infinitely small intensity factors. Knowledge of the stress intensity factor as a function of the location of the crack tip along the crack path is all that is needed to obtain the load-displacement relation. The solution is reduced to a singular integral equation for a function describing the components of applied load associated with crack tips at various locations. The integral equation is complemented by an arbitrary relation between the bridging stress and the crack opening displacement, which can be rate-independent or rate-dependent. Furthermore, using the creep operator method, the equation is extended to aging linearly viscoelastic behavior in the bulk of the specimen. The previously presented finite difference solution is improved and generalized in a form that leads to a system of nonlinear algebraic equations, which can be solved by an optimization method. Application of the smeared-tip method to the analysis of recent measurements of the size effect in three-point-bend fracture specimens of different sizes is presented and a crack opening law that yields the main qualitative characteristics of the test results, particularly an increase of brittleness with a decreasing loading rate, is presented.

Original language English (US) 277-290 14 International Journal of Fracture 65 3 https://doi.org/10.1007/BF00035708 Published - Feb 1994

## ASJC Scopus subject areas

• Computational Mechanics
• Modeling and Simulation
• Mechanics of Materials

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