THEORETICAL INVESTIGATIONS OF THE BEHAVIOR OF BRITTLE MATERIALS AT VARIOUS RANGES OF TEMPERATURE.
Final rept., 1 Jan-31 Dec 62,
UNIVERSITAET DES SAARLANDES SAARBRUECKEN (WEST GERMANY)
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A new theory of elasticity was developed which will provide a mathematical treatment of the behavior of brittle materials. By postulating two axioms concerning the invariance of the deformation energy under any coordinate transformation and the continuous transition of the volume dilatation from the elasticic to the plastic range it was possible to establish a general invariant non-linear stress-strain relation for the three-axial state of stress. For the extension of the theory to anisotropic media some group theoretical considerations are performed in order to establish the general form of the deformation energy for these media. Author