Micromechanical Simulation Of Effective Properties Of Piezoelectric Composites For Structural Health Monitoring

Health monitoring system can provide data for the structural damage detection and evaluation,lay the foundation for the prediction of structural performance change and post maintenance.It is a safe and reliable work guarantee in the whole life cycle of the structure,a great significance to the safety of people’s lives and property,and a positive response to the concept of green sustainable development.Intelligence is the main development direction of structural monitoring system at present,piezoelectric material is a kind of intelligent material which has many advantages,such as fast response,high precision,good stability and approximate linear relationship,the strain can be directly associated with the electrical signal.However,there are many defects in the piezoelectric sensor element material,such as the brittleness of piezoelectric ceramics,poor durability and high maintenance cost of quartz crystal.The piezoelectric composites can be formed by composite technology,which can effectively solve the problems,for instance,compatibility,interface matching,sensitivity,durability and so on.Heterogeneity,anisotropy and randomness of mechanical properties of piezoelectric composites,high cost and limitations of the experiment,dispersion and complexity of results,these factors make it difficult to solve the effective properties of composite materials.However,the effective property is the basis of numerical analysis and application research,the premise of material optimization design,the basis of the study on the deformation and failure of composite materials and structures,the core of the development of high fidelity sensing devices,so it is necessary to develop a general theory and convenient method to predict the effective properties of piezoelectric composites.The traditional micromechanics analysis method are based on the assumption of the shape,distribution and periodic boundary conditions,require a large number of average postprocessing,and the accuracy of results is affected by many factors.The general applicability of the method is low and there is no follow-up study in the local field.This paper was supported by the National Natural Science Foundation of China: the variational asymptotic fine model and its application in multi field coupling analysis of functionally graded piezoelectric laminated plates(Grant No.11272363).The mechanical properties of typical piezoelectric composites in smart sensor elements were studied basing on the variational asymptotic homogenization theory.The relationship between macro and micro variables of composite materials was established by means of asymptotic series expansion of displacement and potential function when using ratio of fine macro scale as small parameter.The wave function which was used to represent the local vibration characteristics was introduced as the basic unknown quantity by separating variables,thus a physical reality micromechanical model had established;Basing on the principle of minimum potential energy,a series of governing differential equations for micromechanical analysis were obtained by calculating the extreme-value problem.This paper mainly analyzed and solved the following problems:(1)A micromechanical model of piezoelectric composite materials basing on second kinds of piezoelectric equations was constructed,the numerical expressions of effective properties of piezoelectric composites whose precision was the same as the wave function were obtained by the discretization of generalized wave function.The periodic boundary conditions for the micromechanical analysis of piezoelectric composites were derived on account of the variational principle,at this point,the periodic boundary was no longer a computational assumption,but an inherent feature of the macro-meso scale analysis of piezoelectric composites.(2)Analysed the local field expansion of the basic unit of piezoelectric composites in view of the asymptotic macro-meso variables relationship between the unknown force and electric field function.Further research showed that the local wave function was the key to the reconstruction,the expressions of the local displacement,strain and stress in the cell were achieved through reconstruction calculation.The numerical examples indicated that the variational asymptotic homogenization method could effectively capture the disorder of the local field under the action of the force field;(3)Traditional finite element method required 9 sets of different boundary and load conditions to extract all the mechanical and electrical parameters of the composite,only 2 sets of periodic boundaries were selected in the two-dimensional model by using the variational asymptotic homogenization procedure,this method was also applicable to predict fully anisotropic materials.The calculation process was small,convenient and reliable.(4)Polymer materials often exhibited obvious viscoelastic behavior,the numerical example indicated that the mechanical and electrical parameters of the polymer based piezoelectric composites were not fixed,and both of them had displayed asymptotic stability with time.It was found that the variational asymptotic homogenization method had high accuracy in predicting and analyzing in viscoelastic behavior The micromechanical model was suitable for multi field coupling analysis.This method enriched the theory of predicting the performance of composite materials in a certain extent.