Fracture Mechanics: Inverse Problems and Solutions (Solid Mechanics and Its Applications (139))

This book presents, in a unified manner, a variety of topics in Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate students. Emphasizing physical or experimental back-grounds, then analysis and theoretical results, this monograph is intended for use by students and researchers in solid mechanics, mechanical engineering and applied mathematics.

Today, Fracture Mechanics is a well known topic within the scientific community. Applications of Fracture Mechanics can be found in various fields ranging from solid mechanics and structures to materials sciences and computational mechanics. However, most of these results apply only to linear fracture mechanics of two-dimensional and homogeneous isotropic solids. Therefore there are still incompletely solved problems; such as non-linearity, frictional contact cracks, residual stresses in fracture mechanics, three-dimensional crack geometry, coupled cracked solid/fluid, etc. Recently, new topics related to crack detection based on different physical phenomena have appeared.

This book is an attempt to present, in a unified manner, different topics of Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate students. These new topics take into consideration the thermodynamics of continuous media, including thermal and dynamical aspects. In addition, the book introduces the notion of duality or symmetry in Solids Mechanics. The loss of symmetry is exploited to provide a unique and powerful tool, called the reciprocity gap functional introduced by the author’s groups, to solve explicitly some important inverse problems arising in crack determination as well as in the earthquake inverse problem.

With its emphasis, initially on physical or experimental back-grounds, and then on analysis and theoretical results, rather than on numerical computations, this monograph is intended to be used by students and researchers in solids mechanics, mechanical engineering and applied mathematics.

This book is an outgrowth of my involvement in two groups of research in solid mechanics, created in 1960 for the French nuclear energy program. At this time, it was decided that France, as a no-oil reservoir country, must be powered by nuclear energy, which represents today 80% of the total - tional energy supply. Long before the construction of the first nuclear plant at Fessenheim in 1973, Electricité de France (EdF) created its first solid mechanics laboratory, appointed researchers and sent them to the universities or abroad in order to learn about theories and new methods of assessment of the safety of structures. Working at EdF, I was training in Professor Jean Mandel's laboratory at Ecole Polytechnique (LMS), Paris. My friend René Labbens, working at Framatome (the builder of nuclear plants) was training at the Lehigh University, under the guidance of professors G. R. Irwin and G. C. Sih. We had to work hard, both academically at the u- versities laboratories and performing engineering tasks for our employer. This dual position was a great chance for many of us, since we discovered that real industrial problems are the source of new subjects and research problems to be solved by theoreticians in the universities and conversely we immediately knew if our theoretical work was good or not for appli- tions as revealed in our daily works conducted for our industrial employer. front-matter.pdf......Page 1 1-28.pdf......Page 22 29-59.pdf......Page 50 61-95.pdf......Page 81 97-112.pdf......Page 116 113-133.pdf......Page 132 135-171.pdf......Page 153 173-198.pdf......Page 190 199-231.pdf......Page 216 233-251.pdf......Page 249 253-266.pdf......Page 268 267-291.pdf......Page 282 293-322.pdf......Page 307 back-matter.pdf......Page 337 Presents various topics of Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. This book also introduces the notion of duality or symmetry in Solids Mechanics