Summary
An attempt is made to develop a theory of inelastic behavior of crystalline materials subjected to arbitrary deformation. The introduced concept of elastic motion leads to a simple decomposition rule: the total velocity gradient is the sum of the elastic velocity gradient and the inelastic velocity gradient. The important role of rotations and relevant constitutive relations is discussed and illustrated by an example of a tensile test of a single crystal. The assumption usual in plasticity that plastic deformation does not change the volume of the body follows in the present theory as a consequence of the second law of thermodynamics and material symmetry.
Zusammenfassung
In dieser Arbeit wird der Versuch gemacht, eine Theorie des inelastischen Verhaltens der kristallinen Werkstoffe zu entwickeln, die in einer beliebigen Weise verformt werden. Das hier eingeführte Konzept der elastischen Bewegung führt zu einer einfachen Zerlegungsregel: Der Gradient der gesamten Geschwindigkeit ist gleich der Summe des Gradienten der elastischen Geschwindigkeit und des Gradienten der inelastischen Geschwindigkeit. Die wichtige Rolle der Drehungen und die entsprechenden Materialgleichungen werden diskutiert und illustriert durch ein Beispiel des Zugversuches an einem Einkristall. Die in der Plastizität übliche voraussetzung, daß die plastische Verformung das Volumen des Körpers nicht verändert, ergibt sich in der dargestellten Theorie als Folgerung aus dem zweiten Hauptsatz der Thermodynamik und der Symmetrie des Materials.
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Kratochvíl, J. On a finite strain theory of elastic-inelastic materials. Acta Mechanica 16, 127–142 (1973). https://doi.org/10.1007/BF01177131
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DOI: https://doi.org/10.1007/BF01177131