ISSN Print: 2152-2057
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Composites: Mechanics, Computations, Applications: An International Journal
PROCEDURES TO BUILD PLATE MICROMECHANICAL MODELS FOR COMPOSITES LIKE PERIODIC BRICKWORKS: A CRITICAL REVIEW
Department of Architecture Construction Conservation (DACC), University IUAV of Venice, Dorsoduro 2206, Venice, 30123, Italy
Procedures for constructing plate models to describe the out-of-plane mechanical behavior of regular brickwork are proposed. Both asymptotic homogenization procedures and direct identification procedures methods based on balance by internal work in the discrete model and in the continuous model for a class of regular motions have been proposed to obtain relations between the 3D discrete model and the 2D plate continuum model. A crucial problem, with the choice of identification procedures, is how kinematic, dynamic, and constitutive prescriptions of a discrete system are transferred to the continuous one. Hence, constitutive functions of the plate may be different. A Love−Kirchhoff plate model based on standard homogenization, for linear elastic periodic brickwork, has been already proposed by Cecchi and Sab (2002b). This model has been also developed in the case both of infinitely rigid blocks and of elastic blocks connected by elastic interfaces taking into account shear effects leading to the identification of a new Mindlin−Reissner homogenized plate model (Cecchi and Sab, 2004, 2006). In this case, the identification between the 3D block discrete model and the 2D plate continuum model is based on a relation at the order 1 in the displacement and at the order 0 in the rotation. The Mindlin−Reissner model when blocks are rigid blocks based on a compatible identification at the order 1 both in the displacement and in the rotation has been performed by Cecchi and Rizzi (2003, 2005). Here these models have been implemented also in the case of elastic blocks. The idea is to critically analyze the accuracy of these identification models by comparison with a 3D F.E. model for some meaningful case.
KEY WORDS: periodic brickwork, Love–Kirchhoff plate, Mindlin–Reissner plate, asymptotic homogenization, equivalent compatible method
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