MODELLING OF THE LARGE STRAINS. THE MESSAGE 1. MULTIPLICATE DECOMPOSITION IN THE PRESENCE OF FOUR TYPES OF STRAINS
DOI:
https://doi.org/10.20535/2305-9001.2012.64.40243Keywords:
large strains, multiplicate decomposition, thermoelastic, plastic, creepAbstract
The authors generalizes an idea of Lee's multiplicative decomposition for the case of simultaneous presence of four types of strains: thermal, elastic, plastic and creep. This decomposition uses group properties of operators of reflection from an abstract algebra.Using multiplicative decomposition of matrix of Cauchy-Green strain gradient for three times, the matrix is found to be equal to the product of four matrices of gradients separately from each type of strain. This allowed writing Green's-Lagrange's tensors for the different types of strains, as well as exactly additive decomposition of the matrix of the spatial gradient of the strain rate for each type of strain. The matrix of the spatial gradient of strain rate is multiplied on the transpose matrix of the gradient of the elastic strain on the left side and on the normal matrix of the gradient of the elastic strain on the right side for use of the energetically integrated second stress tensor of Piola-Kirhgof. The resulting expressions will be used for an establishment of the equations of thermoelasto-plasticity and creep in the case of large strains by means of the second law of the thermodynamics that is written down in the form of Clausius-Duhem's inequality
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