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Calculation of effective mechanical properties of textiles by asymptotic approach
Author(s) -
Nam Alexander,
Orlik Julia
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700093
Subject(s) - stiffness , computation , boundary value problem , elasticity (physics) , moduli , limit (mathematics) , mathematical analysis , mathematics , materials science , composite material , physics , algorithm , quantum mechanics
We consider plates with 2‐D periodic rod or fabric structure, used as geotextiles or textiles. The period of structure as well as the hight of a plate are much smaller compared to its depth and width. This makes a direct numerical computation of boundary value or contact elasticity problem too expensive. Three small parameters are introduced for the asymptotic analysis: the first one connected with the period of structure, the second one with the thickness of fibers or beams inside the periodicity cell and the last one – with the hight of a plate. The overcoming to the limit with respect to period of structure provides equivalent homogenized plate of the finite hight. Calculation of its outer‐plane stiffness is a new aspect of this work. The next overcoming to the limit with respect to the hight reduces the 3‐D problem to the homogenized equations, fourth order PDEs. The effective elasticity moduli and outer‐plane stiffness can be obtained numerically solving cell experiments. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)