The article "Mechanik der festen Körper im plastisch- deformablen Zustand" by R. v. Mises, published in 1913, addresses the mechanics of bodies in a plastic or residual form-deforming state. The author builds upon Cauchy's general concept of stress and discusses the limitations of Saint-Venant's theory for plastic deformation. The paper introduces a comprehensive set of motion equations for plastic-deformable bodies within the framework of Cauchy's mechanics, supported by specific empirical observations. Mises defines the stress state at a point in a body using normal and shear stresses, represented by a stress dyad \(\bar{\sigma}\). He also introduces the deformation dyad \(\bar{\varepsilon}\) and the velocity dyad \(\bar{\lambda}\), and provides formulas for their components. The paper derives the principal stresses and principal shear stresses, and discusses the relationship between stress and deformation, noting that for elastic bodies, there is a unique mapping between stress and deformation. The author then outlines empirical principles that underpin the motion equations. These include the assumption that all solid bodies behave elastically under sufficiently small stresses, the behavior of bodies at the yield point, and the constancy of work done during plastic deformation regardless of the speed of deformation. These principles lead to the conclusion that the stress state of a plastic-deformable body remains on the elastic limit. Finally, Mises presents the complete system of motion equations for plastic-deformable bodies, which includes the continuity equation and the constitutive relation between stress and velocity. The equations are expressed in both component form and vector notation, and the dissipation function is derived, confirming the consistency with the empirical principles discussed earlier.The article "Mechanik der festen Körper im plastisch- deformablen Zustand" by R. v. Mises, published in 1913, addresses the mechanics of bodies in a plastic or residual form-deforming state. The author builds upon Cauchy's general concept of stress and discusses the limitations of Saint-Venant's theory for plastic deformation. The paper introduces a comprehensive set of motion equations for plastic-deformable bodies within the framework of Cauchy's mechanics, supported by specific empirical observations. Mises defines the stress state at a point in a body using normal and shear stresses, represented by a stress dyad \(\bar{\sigma}\). He also introduces the deformation dyad \(\bar{\varepsilon}\) and the velocity dyad \(\bar{\lambda}\), and provides formulas for their components. The paper derives the principal stresses and principal shear stresses, and discusses the relationship between stress and deformation, noting that for elastic bodies, there is a unique mapping between stress and deformation. The author then outlines empirical principles that underpin the motion equations. These include the assumption that all solid bodies behave elastically under sufficiently small stresses, the behavior of bodies at the yield point, and the constancy of work done during plastic deformation regardless of the speed of deformation. These principles lead to the conclusion that the stress state of a plastic-deformable body remains on the elastic limit. Finally, Mises presents the complete system of motion equations for plastic-deformable bodies, which includes the continuity equation and the constitutive relation between stress and velocity. The equations are expressed in both component form and vector notation, and the dissipation function is derived, confirming the consistency with the empirical principles discussed earlier.