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We derive a general crack propagation law for slow brittle cracking, in twoand three dimensions, using symmetry, gauge invariance, and gradientexpansions. Our derivation provides explicit justification for the ``principleof local symmetry,'' which has been used extensively to describe twodimensional crack growth, but goes beyond that principle to describe threedimensional crack phenomena as well. We also find that there are new materialsproperties needed to describe the growth of general cracks in three dimensions,besides the fracture toughness and elastic constants previously used todescribe cracking.Comment: 31 pages, including several figure

Derivation of a general three-dimensional crack-propagation law: A generalization of the principle of local symmetry