Transition conditions: the yield condition

Seth, B. R. (1970) Transition conditions: the yield condition International Journal of Non-Linear Mechanics, 5 (2). pp. 279-285. ISSN 0020-7462

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The transformation of a continuum from a state A through a state T into a state B may be represented as a mapping. T is asymptotic in character, and hence is characterised by a contraint on the invariants of the strain or stress tensor of the field, giving rise to a functional relation between the otherwise independent invariants, I1,I2,I3. At present ad-hoc forms are used for this relation. It should be obtained from the condition that the modulus of transformation from A to B tends to become zero or infinite. As a consequence the corresponding reciprocal deformation ellipsoid degenerates into a cylinder, a plane or a point. For an isotropic medium the normalised yield condition is found to be; 3I'2 + 2(27I3 + 3/2I1I'2 - I3)=2, I'2=2I21-6I2. This includes the classical yield conditions and also the Bauchinger effect. A similar condition is obtained for orthotropic bodies.

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