539.3 Modeling the effective characteristics of transversely isotropic incompressible composites with finite strains

Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Karimov S. B. (Bauman Moscow State Technical University), Kolzhanova D. Y. (Bauman Moscow State Technical University)

LAYERED COMPOSITES, INCOMPRESSIBLE MEDIA, TRANSVERSELY ISOTROPIC MEDIUM, FINITE STRAINS, ASYMPTOTIC HOMOGENIZATION METHOD, UNIVERSAL MODELS OF ELASTIC MEDIA, ENERGY TENSOR PAIRS


doi: 10.18698/2309-3684-2018-4-7292


The paper considers a model of effective constitutive relations for a transversal-isotropic incompressible composite with finite strains. The model belongs to the so-called class of universal models that connect several pairs of energy stress and strain tensors simultaneously. A method is proposed for separating coupled problems of micro- and macroscopic deforming composites with finite strains that arise when the method of asymptotic homogenization (AH) of periodic structures is used. The method is based on the application of the effective constitutive relation model as an approximation dependence of the results of numerical simulation of the composite deformation curves obtained using the exact AH method. To find the elastic constants of the transversely isotropic composite model the method of minimizing the deviation of the approximation of deformation diagrams from the AH diagrams is used for a series of problems of standard deforming at finite strains. To solve minimization problems, the Nelder—Mead method is used. The results of numerical simulation by the proposed method for nonlinear elastic layered composites are presented, which showed good approximation accuracy, achieved due to application of the proposed method for the separation of coupled problems of micro- and macroscopic deforming.


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