Eventos Anais de eventos
DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
NONLINEAR DYNAMIC RESPONSES OF LAMINATED COMPOSITE STRUCTURE INVOLVING LARGE DEFLECTION AND MATERIAL UNILATERAL DAMAGE
Submission Author:
Saber Mahmoudi , France , France
Co-Authors:
Saber Mahmoudi, frederique trivaudey, NOUREDDINE BOUHADDI, Lamine Boubakar
Presenter: Saber Mahmoudi
doi://10.26678/ABCM.DINAME2017.DIN17-0219
Abstract
To reduce the weight of the structures, composite materials are on significant expansion in all industry domains since they are light as well as strong. These structures are often thin, and therefore, they can have large vibration amplitudes inducing significant geometric nonlinearities. In addition, for their heterogeneity characteristic and the security requirements, the knowledge of the damage mechanisms that may occur in composite materials is need. Composite structures are subjected to one or more forms of damage such as matrix cracking, fiber fracture and delamination. They evolve gradually resulting in the mechanical degradation of the structure properties and the modification of its mechanical behavior. Over the last decades, the behavior of damaged composites has been the subject of several investigations where many models have been proposed. For laminated composite structures, fiber rupture generally occurs in the final phase of layer rupture whereas matrix cracking is considered as the first damage mechanism and presents a common defect in laminated composites. Using a phenomenological modelling of cracked structures, the dynamic behavior of damaged composite structures under an impact load is investigated in works of Mahmoudi et al where a bilateral damage model is used. The bilateral damage model does not exactly describe the material behavior when the structure is subjected to a harmonic load since the closing of cracks is not taken into account. The aim of this paper is to present the nonlinear dynamic responses of laminated composite structure involving large deflection and a novel unilateral damage model. Using a meso-macro approach, the material behavior is only needed at the level of one ply. It represents the degradation of the elastic properties due to the initiation and the growth of cracks in the matrix along the fibers directions. Although the damage is anisotropic, it can be described by a single scalar variable representing the degradation of the transverse Young’s modulus. Only the matrix cracking is retained as damage form and the investigated structures are made of unidirectional layers of polymer matrix reinforced with long fibers. In order to analyze the cracks opening/closure effect, the normal stress component to the fiber direction is chosen as a parameter to control the state of the cracks. If it is positive, the cracks are supposed to be opened and the damage effect is applied. If the sign of the normal stress component is negative, the cracks are closed and the virgin material behavior should be recovered. Based on the first-order shear deformation theory and the Von Karman’s large deflection plate theory, a Serendip finite element with five degree of freedom incorporating a nonlinear strain displacement relation due to large deflection is developed using the updated total Lagrangian approach. Since the damage induces nonlinearity, the resulting nonlinear system of equations, combining the geometric and material nonlinearities, is solved in time domain using Newmark method and Newton-Raphson incrementaliterative method. Numerical examples of composite structures are considered and the influence of geometrical nonlinearity on the dynamic responses and the resulting damage is demonstrated. The stiffness degradation due to impact damage is also investigated. In addition, the proposed model permits the detection and the localization of the damage in laminated structures in large deflection. Thereby, this method can be used in life time estimations and monitoring strategies of complex composite structures.
Keywords
Unilateral damage, laminated composite, geometric nonlinearity, dynamic analysis
