Dissertation submitted to the Graduate School of Northwestern University
in partial fulfillment of the requirements for the degree Doctor of Philosophy

Evanston, March 1993

## MODELING OF FRACTURE AND DAMAGE IN QUASIBRITTLE MATERIALS

Milan Jirásek
Northwestern University
Evanston, Illinois 60208, U.S.A.

### Abstract

The dissertation has been prepared under the supervision of Zdenek P. Bazant, Walter P. Murphy Professor of Civil Engineering at Northwestern University. It presents several mathematical models useful for the simulation of fracture and damage propagation in quasibrittle materials, which are characterized by the development of a large nonlinear process zone prior to failure. The simplest one is the R-curve model based on the replacement of the nonlinear fracture process zone by an equivalent linear elastic crack with a variable resistance against crack propagation. This approach is generalized by taking into account the effect of the loading rate. The emphasis is on the static loading rates rather than the dynamic ones, and creep in the bulk of the specimen is incorporated into the mathematical description.

Another important class of models is based on the representation of a mechanical system by an assembly of interacting particles. A dynamic particle model is developed for the simulation of fracture of large sea ice floes during their impact on obstacles such as platforms or artificial islands. It is demonstrated that this model is capable of producing realistic results in terms of both the contact force history and the fracture pattern. Macroscopic fracture energy of random particle systems is studied as a function of the microscopic parameters using the size effect method. An effective numerical procedure for tracing a piecewise linear load-displacement curve is developed.

The previously proposed continuum-based microplane model is carefully analyzed and shown to perform poorly in certain situations. The conditions under which the model gives unsatisfactory results are described and the reasons for the poor performance are explained. Modifications on the microscopic level do not remedy the problem and a macro-level modification is unavoidable. A promising concept of the revised version is advocated by presenting improvements of the behavior in several elementary situations.

The dissertation is concluded by a localization analysis for a new type of nonlocal averaging, strictly based on a micromechanically justified derivation. The analysis of the bifurcation at peak stress is followed by an incremental analysis of the post-peak behavior. It is shown that the new formulation preserves the essential properties of the original nonlocal approach and has some interesting added features.