MODELING OF LARGE STRAINS. MESSAGE 7. FOUR TYPES OF STRAINS, TOTAL LAGRANGIAN FORMULATION
DOI:
https://doi.org/10.20535/2305-9001.2016.76.66198Keywords:
large strains, thermo-elasticity, plasticity, creep, Total Lagrangian formulation, multiplicative decomposition, algorithm, FEMAbstract
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.References
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