Nonlinear Laminate Theory Research Articles

Mechanics and Finite Element for the Nonlinear Response of Active Laminated Piezoelectric Composite Plates

A theoretical framework for analyzing piezoelectric composite laminates that includes nonlinear effects as a result of large displacements and rotations is presented. Nonlinear mechanics equations are incorporated into a coupled mixed-field piezoelectric laminate theory. Using the nonlinear laminate theory, a nonlinear finite element methodology and an incremental-iterative solution are formulated for the analysis of nonlinear adaptive laminated plate structures with piezoelectric actuators and sensors. An eight-node nonlinear plate finite element is also developed. The mechanics models are applied on the nonlinear active response of composite plates with piezoelectric actuators. Various application cases quantify the nonlinear active flexural response of beams and plates with piezoelectric actuators.

Nonlinear Dynamics Analysis of a Laminated Printed Wiring Board

Nonlinear laminate theory is applied for the printed wiring board (PWB) dynamic response analysis. Equations of motion for the nonlinear elastic deformation of the isotropic laminates are derived for the dynamic response of a simply supported PWB. Numerical results are generated for the nonlinear response characterization of the PWB deformation. Comparisons are made between the response of linear and nonlinear systems. Results show that PWB is in large deflection under high acceleration or certain pressure load. Nonlinear theory gives more accurate results for the large deflection than the linear theory does. Besides, lamina stresses are analyzed and illustrated from finite difference computation. The analytical derivation in modal approach and the stress analysis provide the basis for PWB reliability studies, especially the defect and failure induced by the dynamic stress field.

Ply-Cracking Damage and Nonlinear Deformation of CFRP Cross-Ply Laminate

This paper deals with progressive ply-cracking damage and nonlinear deformation of CFRP cross-ply laminate. Tensile tests in 0°-axis direction and in off-axis direction are carried out on five kinds of CFRP cross-ply laminates which are different in stacking lay-up. Under 0°-axis tension, initiation and evolution of the ply-cracking damage in 90° plies are observed, and corresponding stress-strain relation is slightly nonlinear after the damage. On the other hand, under off-axis tension, the stress-strain response exhibits nonlinear deformation, while the ply-cracking damage is not remarkable except for the specimen with large fracture strain. Therefore, it is concluded that the nonlinear deformation of the laminates under off-axis tension is mainly attributed to the nonelastic deformation of the matrix resin. Numerical analyses for the progressive ply-cracking damage and the nonlinear deformation of the CFRP cross-ply laminates are conducted based on a ply-cracking damage theory and a nonlinear lamination theory, respectively, and applicability of these theories are discussed based on the experimental and numerical results.

The safety-factor calibration of laminates for long-term applications: behavior model and reliability method

This paper presents a method for determining safety factors which must be taken into account when designing laminates for long-term applications. The method requires two steps: the first is a behavioral model able to predict time-dependent phenomena, and the second is a reliability method. The meso/macro approach is used in the behavioral model. This paper presents a damaged elasto-viscoplastic model able to predict the behavior of a layer made of a polymer reinforced with unidirectional fibers. This model requires a non-linear laminate theory which provides the response of laminate structures. The method for calibrating safety factors is based on the first-order reliability method. A description of the behavioral model in this method is presented. Finally, as a working example, the design of filament-wound pipe for fluid transportation is presented. A functional criterion is introduced to prevent leakage. The effect of material parameters is analyzed.

Off-Axis Tensile Properties of CFRP Laminates and Non-Linear Lamination Theory Based on Micromechanics Approach.

This paper deals with the deformation and damage of CFRP cross-ply laminates under off-axis tension and develops a non-linear lamination theory. Off-axis tensile tests were carried out on five kinds of CFRP cross-ply laminates which were different in stacking lay-up. On the laminates under off-axis tension, the stress-strain response shows the non-linear deformation, while the ply-cracking damage is not remarkable except for the specimen with large fracture strain. Therefore, It is concluded that the non-linear deformation of the laminates under off-axis tension is mainly attributed to the non-linear deformation of the matrix resin. In order to describe the deformation of the laminates, a non-linear lamination theory is developed. An incremental constitutive relation of the unidirectional composite containing elastic long fibers in the elastic-plastic matrix is derived based on Eshelby's equivalent inclusion method and Mori-Tanaka mean field concept. Then, this constitutive relation is introduced Into the classical lamination theory. Numerical results by the present theory for off-axis tension of the CFRP unidirectional and cross-ply laminates well described the experimental stress-strain relations.

Probabilistic strength analysis of rectangular FRP plates using Monte Carlo simulation

Probabilistic strength analysis of simply supported rectangular anti-symmetric cross-ply and angle-ply fibre reinforced plastic laminated plates is performed by applying the Monte Carlo simulation method. Various limit state equations are derived from non-linear laminate theory with different anisotropic plate failure criteria. Transverse lateral pressure load, elastic moduli, geometric and ultimate strength values of the laminates are considered as basic design variables and assumed to follow both normal and two-parameter Weibull probability distributions. Reliability of the laminates is estimated and the sensitivities of basic design variables to the estimated reliability is viewed by varying their mean values systematically.

307 マイクロメカニクスの手法を用いた非線形積層理論(O.S.7. 計算力学とシミュレーション)

307 マイクロメカニクスの手法を用いた非線形積層理論(O.S.7. 計算力学とシミュレーション)

An Experimental Investigation of the Mini-Sandwich Laminate as Used to Obtain Unidirectional Composite Compression Strengths

A mini-sandwich laminate configuration was used to test unidirectional AS4/3501-6 carbon/epoxy and S-2/5216 glass/epoxy composite material systems in established shear- and end-loaded compression test fixtures. Four different analysis techniques were used to predict the unidirectional lamina strength and stiffness from the measured tabbed and untabbed mini-sandwich specimen strength. The unidirectional composite compressive strengths obtained from both co-cured and adhesively bonded mini-sandwich specimens tested in the IITRI fixture using a nonlinear laminate theory analysis technique produced the highest strength values. Although the unidirectional composite compressive strengths measured using these specimens were higher than strengths typically obtained using conventional unidirectional specimen configurations, the adhesive bond between the face sheets and the 3501-6 epoxy resin core of the co-cured mini-sandwich specimens and the Poisson's effect in the core material were identified as possible limitations to this test method.

Interfacial debonding in laminated titanium matrix composites

Abstract The results of an experimental program in which multiaxial loads were applied to [0 4 ] and [±45] s silicon carbide/titanium (SiC/Ti) tubes are reviewed showing that stress coupling, matrix viscoplasticity (including room temperature creep) and fiber/matrix interfacial damage all contribute to nonlinear response and permanent strains in titanium matrix composites (TMC). A micromechanical model that explicitly considers the aforementioned phenomena is presented herein. The model assumes a periodic microstructure and uses finite elements to analyze a representative volume element. The composite is assumed to be in a state of generalized plane strain making it possible to discretize only a generic transverse plane while still being able to apply three-dimensional loading through appropriate boundary conditions. The response of laminated composites is predicted by incorporating the micromechanical results into nonlinear lamination theory. Predictions are presented to show the influence of the model parameters on the effective composite response of unidirectional [0 4 ] and angle-ply [±45] s TMC laminates.

Numerical modelling of damage development and viscoplasticity in metal matrix composites

Metal matrix composites can exhibit inelastic response due to matrix viscoplasticity as well as fiber/matrix interfacial damage. This paper presents a numerical procedure that can be used to implement a micromechanical model based on a periodic array of continuous fibers embedded in a metallic matrix. The model incorporates elastic-viscoplastic constitutive equations for the matrix and non-linear interfacial traction-displacement relations for the fiber/matrix interface. Generalized plane strain finite elements are formulated in such a way to allow the application of multiaxial loadings while only having to discretize a generic transverse plane. Non-linear lamination theory provides the link between the micro- and macro-level responses of laminated composites subjected to thermomechanical loading. Numerical results indicate that a relatively small number of elements are required to achieve mesh convergence. Also, the axial tensile response is independent of the condition of the fiber/matrix interface, while debonding significantly influences the transverse tensile and axial shear responses.