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Remark on a distortion tensor for elastic displacements. (English) Zbl 0063.07365

From the text: One of the most successful of the various conditions for yield resulting from a state of stress produced by mechanical means is that due to R. von Mises [Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1913, 582–592 (1913; JFM 44.0918.06)]. This condition states that yield will occur when the energy per unit volume produced by a change of shape alone reaches a certain value characteristic of the material under consideration. It would thus appear that distortion, i.e., change of shape as distinct from change of volume, is one of the primary factors in the occurrence of yield. This suggests that in addition to the ordinary tensors of stress and strain (related by Hooke’s law) we consider a distortion tensor and seek to express the condition of yield directly in terms of this tensor.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)

Citations:

JFM 44.0918.06
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