Abstract
The paper presents a method for modifying the strength criteria and plasticity conditions, based on the fundamental properties of the algebra of matrices. The essence of the method is that applying the basic property of the algebra of matrices, the stress tensor in the solid body is multiplied by the damage function. As a result of this mathematical operation, a stress tensor is obtained in the damaged body. Then, from the component of stress tensor of the damaged body, its invariant characteristics are determined and formed, which are substituted into the known criteria of strength and plasticity. Thus, the new criteria contain damage. The modification of both simple two or three invariant criteria and modern multi-surface criteria capable of changing the shape of the limit surface depending on the value of one of the material parameters is considered.
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