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Моделирование слоистых композитов с конечными деформациями…
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Modeling of laminated composites with finite deformations
by asymptotic homogenization method
© Yu.I. Dimitrienko, E.A. Gubareva,
D.Yu. Kolzhanova
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article covers a problem of elastic characteristic modeling for laminated composites
with finite deformations. The problem is impotent for design of rubber-like and elastomer
structures. A variant of asymptotic homogenization method is suggested for laminated
elastic composites with finite deformations and periodical structures. Proposed by Yu.
Dimitrienko, a universal representation of nonlinear constitutive relation for materials
under finite deformations, is applied for composite model developed. Computational
method for solution of nonlinear elasticity problem over periodicity cell of composite
with finite deformation is suggested. The method is implemented in C++ program codes.
The method allows to calculate an effective stress-strain diagrams in terms of averaged
Piola—Kirchhoff deformation gradient for laminated composites with finite defor-
mations. Examples of calculations demonstrate feasibility and efficiency of the method
developed for prediction of elastic characteristic of laminated composites with finite de-
formations.
Keywords:
laminated composites, finite deformation, asymptotic homogenization method,
Piola—Kirchhoff stress tensor, deformation gradient, universal representation of nonlin-
ear constitutive relation.
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