ELASTIC-PLASTIC CONTINUA CONTAINING UNSTABLE ELEMENTS OBEYING NORMALITY AND CONVEXITY RELATIONS.
BROWN UNIV PROVIDENCE R I DIV OF ENGINEERING
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A one- , two- , or three-dimensional continuum is supposed to be composed of stable and unstable elements in the conventional structural sense or on the microscale. The initial and each of the subsequent yield surfaces for each element of a structure, or each point in a continuum, are taken as convex in a generalized or actual stress space. The increments or rates of generalized or actual plastic strain are taken as normal to the current yield surface. Initial and subsequent yield surfaces in load space for the entire body are seen to be convex and the vectors representing the corresponding permanent displacement increments or rates are normal to these surfaces, when the elastic response is unaltered by the deformation or remains linear. The character of the elastic and plastic response up to the point of overall instability is described. Conditions for stability and uniqueness of response are given. Author