Micro-Macro Analysis of Viscoelastic Unidirectional Laminated Composite Plates Using DR Method

Abstract

The Dynamic Relaxation (DR) technique together with finite difference discritization is used to study the bending behavior of Mindlin composite plate including geometric nonlinearity. The overall behavior of the unidirectional composite is obtained from a three-dimensional (3D) micromechanical model, in any combination of normal and shear loading conditions, based on the assumptions of Simplified Unit Cell Method (SUCM). The composite system consists of nonlinear viscoelastic matrix reinforced by transversely isotropic elastic fibers. A recursive formulation for the hereditary integral of the Schapery viscoelastic constitutive equation in multiaxial stress state is used to model the nonlinear viscoelastic matrix material in the material level. The creep tests data is used for verification of the predicted response of the current approach. Under uniform lateral pressure, the laminated plate deformation with clamped and hinged edged constraints is predicted for various time steps.

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

“…The matrix subcells obey the nonlinear viscoelastic law of Eq. 1 in which the stress-strain relations in normal directions of composite material [8,24]. The equilibrium equations of the RVE in normal directions consist of three equations for external normal loadings.…”

“…where the hereditary integrals in 3-D form, q t n;ij , are as defined in [8,24]. D 0 is the instantaneous compliance value.…”

“…The mentioned relations, together with the boundary conditions, in their finite difference form, establish the set of equations suitable for the DR method. A Detailed description of stability, convergence and damping factors of the DR algorithm can be found elsewhere [17,24].…”

“…In the present work, as an extension of the previous study of the authors [24], the closedform formulation of three-dimensional micromechanical model is joined with the macromechanical relations of the composite plate to analyze the bending response of annular laminated composite sector plate. In the analytical formulation of SUCM the nonlinear viscoelastic representation of Schapery with recursive formulation for the polymeric matrix is employed to characterize the properties of unidirectional fiber reinforced single layer composite in any combination of normal and shear loading conditions.…”

“…Recently, Haj-Ali and Muliana [22] and Muliana and Haj-Ali [23] studied the nonlinear viscoelastic pultruted composite structures with Aboudi's MOC in finite element code ABAQUS. Nonlinear bending analysis of unidirectional fiber reinforced laminated composite plate is examined by the authors [24] considering material nonlinearity for viscoelastic matrix material through a Micro-macro analysis. The analytical Micro model of SUCM with recursive formulation joined with governing equations of the rectangular plate based on FSDT that were solved by DR technique.…”