The text presents a 1913 work by R. v. Mises titled "Mechanik der festen Körper im plastisch-deformablen Zustand," which develops a complete set of equations for the mechanics of plastically deformable solids. It builds upon Cauchy's continuum mechanics and incorporates empirical observations. The paper introduces the concept of stress and strain dyades, defining stress components and their transformation, as well as strain and strain-rate dyades. It also defines principal stresses and tangential stresses, and discusses the relationship between stress and strain in elastic and plastic materials. The paper outlines the behavior of plastically deformable solids, noting that once the elastic limit is reached, the material behaves like a viscous, nearly incompressible fluid. It introduces the concept of a proportional factor $ k $, which relates stress to strain rate, and derives equations for the stress tensor in terms of the strain rate tensor. The work also discusses the constancy of work required for plastic deformation, independent of speed, and introduces the concept of the yield surface, which defines the boundary between elastic and plastic behavior. The paper further explores the yield criterion, proposing that the yield surface is a closed curve in the plane $ \tau_1 + \tau_2 + \tau_3 = 0 $, with the maximum and minimum principal stresses determining the limit. It compares the yield surface to a hexagon and a circle, and discusses the implications of these shapes for the behavior of materials under different stress conditions. The paper concludes with the derivation of the complete system of motion equations for plastically deformable bodies, incorporating the yield condition and the continuity equation. It also presents the equations in vector notation, showing their equivalence to the Navier-Stokes equations for viscous fluids. The work provides a foundational framework for the mechanics of plastic deformation, influencing subsequent developments in plasticity theory.The text presents a 1913 work by R. v. Mises titled "Mechanik der festen Körper im plastisch-deformablen Zustand," which develops a complete set of equations for the mechanics of plastically deformable solids. It builds upon Cauchy's continuum mechanics and incorporates empirical observations. The paper introduces the concept of stress and strain dyades, defining stress components and their transformation, as well as strain and strain-rate dyades. It also defines principal stresses and tangential stresses, and discusses the relationship between stress and strain in elastic and plastic materials. The paper outlines the behavior of plastically deformable solids, noting that once the elastic limit is reached, the material behaves like a viscous, nearly incompressible fluid. It introduces the concept of a proportional factor $ k $, which relates stress to strain rate, and derives equations for the stress tensor in terms of the strain rate tensor. The work also discusses the constancy of work required for plastic deformation, independent of speed, and introduces the concept of the yield surface, which defines the boundary between elastic and plastic behavior. The paper further explores the yield criterion, proposing that the yield surface is a closed curve in the plane $ \tau_1 + \tau_2 + \tau_3 = 0 $, with the maximum and minimum principal stresses determining the limit. It compares the yield surface to a hexagon and a circle, and discusses the implications of these shapes for the behavior of materials under different stress conditions. The paper concludes with the derivation of the complete system of motion equations for plastically deformable bodies, incorporating the yield condition and the continuity equation. It also presents the equations in vector notation, showing their equivalence to the Navier-Stokes equations for viscous fluids. The work provides a foundational framework for the mechanics of plastic deformation, influencing subsequent developments in plasticity theory.