This paper presents a general theory of an elastic-plastic continuum, utilizing thermodynamic equations. The theory is developed based on previous work, but the constitutive equations are discussed in the context of modern nonlinear continuum mechanics. The paper focuses on a "rate-type" theory, without assuming small strains or isotropic materials. The results are valid for non-isothermal deformation with thermodynamic restrictions.
The origins of plasticity theory can be traced back to works by TRESCA, SAINT-VENANT, and LEVY in the late 19th century. Later, VON MISES (1913) and others contributed to the field, which became more active in Germany during 1924–1933. The field saw significant development in the following years, with emphasis on rigid-plastic solids. However, there is still no complete agreement among different schools of plasticity theory.
The paper discusses the need for a more unified approach to plasticity, citing contributions by DRUCKER (1951), KOITER (1960), and NAGHDI (1960). These authors proposed general theorems and developed constitutive equations based on DRUCKER's postulate. Alternative approaches to constitutive equations were also proposed by MELAN (1938), PRAGER (1949), and extended by PRAGER (1958).
The paper outlines the basic theory in sections 2 and 3, including kinematical results and dynamical and thermodynamic equations. Section 4 discusses large deformation elasticity, including thermodynamic equations in terms of free energy and Gibbs function. Sections 5 and 6 focus on the construction of constitutive equations, using a geometrical formalism and referring the state of stress and temperature to a point in 7-stress and temperature space. The paper aims to provide a comprehensive and unified theory of elastic-plastic continua, addressing both mechanical and thermodynamic considerations.This paper presents a general theory of an elastic-plastic continuum, utilizing thermodynamic equations. The theory is developed based on previous work, but the constitutive equations are discussed in the context of modern nonlinear continuum mechanics. The paper focuses on a "rate-type" theory, without assuming small strains or isotropic materials. The results are valid for non-isothermal deformation with thermodynamic restrictions.
The origins of plasticity theory can be traced back to works by TRESCA, SAINT-VENANT, and LEVY in the late 19th century. Later, VON MISES (1913) and others contributed to the field, which became more active in Germany during 1924–1933. The field saw significant development in the following years, with emphasis on rigid-plastic solids. However, there is still no complete agreement among different schools of plasticity theory.
The paper discusses the need for a more unified approach to plasticity, citing contributions by DRUCKER (1951), KOITER (1960), and NAGHDI (1960). These authors proposed general theorems and developed constitutive equations based on DRUCKER's postulate. Alternative approaches to constitutive equations were also proposed by MELAN (1938), PRAGER (1949), and extended by PRAGER (1958).
The paper outlines the basic theory in sections 2 and 3, including kinematical results and dynamical and thermodynamic equations. Section 4 discusses large deformation elasticity, including thermodynamic equations in terms of free energy and Gibbs function. Sections 5 and 6 focus on the construction of constitutive equations, using a geometrical formalism and referring the state of stress and temperature to a point in 7-stress and temperature space. The paper aims to provide a comprehensive and unified theory of elastic-plastic continua, addressing both mechanical and thermodynamic considerations.