Inelastic finite strain analysis of structures subjected to nonproportional loading

The inelastic behaviour of elasto‐plastic materials is nonlinear, path‐dependent, and is a function of the total plastic strain. For finite strain problems, the total inelastic strain in Lagrangian co‐ordinates cannot be decomposed additively. A generalized logarithmic strain which is formulated in ‘updated’ Lagrangian coordinates and obtained by numerical integration of the Lagrangian strain rate is therefore introduced in this paper. By the use of this strain measure, which is additively decomposable, the plasticity model proposed by the authors can be extended to the finite strain range. It is shown that by correlating the generalized plastic modulus in the constitutive relations with the experimental uniaxial true stress‐logarithmic strain diagrams, the inelastic behaviour of steel structures subjected to nonproportional loading can be analyzed numerically by using the finite element method.