MODELING OF LARGE STRAINS. MESSAGE 7. FOUR TYPES OF STRAINS, TOTAL LAGRANGIAN FORMULATION

It was considered in previous articles (Reports 1,2,3 and 4) how the idea of Lee's multiplicative decomposition of the elastic-plastic Cauchy-Green deformation gradient can be implemented to a generalized decomposition on the thermal, elastic, plastic and creep deformations gradient; and the admissible forms of the constitutive state equations were established. The objective of the 5-th Reports is to determine which type of the reference configuration 'unloaded' or 'initial' is more suitable in case of thermo-elasticity with respect to general hyper-elastic postulates. In the 6-th Reports variant of effective variant of algorithm for a solution of boundary problems of thermo-elastoplasticity with large strains is justified at Total Lagrangian formulation. The purpose of this Message – to offer version of effective algorithm for the solution of thermoelasto-plasticity and creep boundary problems with the large strains at Total Lagrangian formulation. Applied proved on the basis of the second law of thermodynamics creep theory, multiplicative decomposition of a gradient deformations Koshi-Green, Total Lagrangian formulation and the approach when elastic, plastic and creep strains are determined concerning the "unloaded" condition. A material – isotropic metal. Have justified effective is finite-element algorithm of an evaluation of stresses and large strains in a solid body from an isotropic material at creep, in Total Lagrangian formulation. With its use and algorithm 6-th Reports have offered effective algorithm of a solution of boundary problems in case of simultaneous presence of four types of strains. This algorithm is programmed in author's finite-element program ОКА-3D. The developed effective algorithm is generalisation of the algorithms offered by the author in 1989 for small strains.