This book is about the pattern formation and the evolution of crack
propagation in engineering materials and structures, bridging
mathematical analyses of cracks based on singular integral equations, to
computational simulation of engineering design. The first two parts of
this book focus on elasticity and fracture and provide the basis for
discussions on fracture morphology and its numerical simulation, which
may lead to a simulation-based fracture control in engineering
structures. Several design concepts are discussed for the prevention of
fatigue and fracture in engineering structures, including safe-life
design, fail-safe design, damage tolerant design.
After starting with basic elasticity and fracture theories in parts one
and two, this book focuses on the fracture morphology that develops due
to the propagation of brittle cracks or fatigue cracks.
In part three, the mathematical analysis of a curved crack is precisely
described, based on the perturbation method. The stability theory of
interactive cracks propagating in brittle solids may help readers to
understand the formation of a fractal-like cracking patterns in brittle
solids, while the stability theory of crack paths helps to identify the
straight versus sharply curved or sometimes wavy crack paths observed in
brittle solids.
In part four, the numerical simulation method of a system of multiple
cracks is introduced by means of the finite element method, which may be
used for the better implementation of fracture control in engineering
structures.
This book is part of a series on "Mathematics for Industry" and will
appeal to structural engineers seeking to understand the basic
backgrounds of analyses, but also to mathematicians with an interest in
how such mathematical solutions are evaluated in industrial
applications.
