This ebook offers with a few contemporary advances in conservation legislation and effort liberate premiums. in contrast to their traditional functions in Fracture Mechanics for unmarried crack difficulties, the contents of this ebook are regularly concemed with the conservation lawsand strength unlock premiums insomerelatively complicated difficulties, i. e., strongly interacting cracks, microcrack harm, and microcrack protecting difficulties in f ive types of materiaIs, respectively. The 5 different types of fabrics contain 4 conventional structural materiaIs: brittIe solids, metallceramic bi materiaIs, anisotropic elastic solids, and numerous anisotropic solids; and one practical fabric: piezoelectric ceramics. even though this e-book begins from the unique thoughts of the Jk vector, the Mintegral, and the L quintessential in sin gle crack difficulties proposed by way of Eshelby (1956, 1970, 1975), Rice (1968a, b), Knowies and Stemberg (1972), Budiansky and Rice (1973), Berges (1974), Freund (1978), Cherepanov (1974, 1979), and Herrman and Herrman (1981), etc., the extension from investigations of unmarried crack difficulties to these of a number of crack interacting difficulties or microcrack harm difficulties relies at the author's (andlor co-workers) works released in recent times. From precise manipulations and numerical examinations the writer want to express readers a few new insights of the conservation legislation and effort liberate premiums. Readers will see that even supposing those 'old' recommendations have been confirmed greater than 30 or forty years in the past, they play a really very important position in a number of crack interacting difficulties or microcrack harm difficulties of either structural and practical materials.