Macroscopic Mechanical Property Prediction Of Periodic Composites By Homogenization Finite Element Method

In order to analyze the field response of composite materials in a more comprehensive and scientific way,relationship of macroscale and microscale was built.The macroscopic equivalent properties were determined by studying properties of composite materials on microscale.Based on micromechanical theory,raw material structure was replaced by inhomogeneous periodic microstructure and homogeneous macrostructure.The equivalent properties of macroscopic homogeneous composite material can be calculated by homogenization method from microscopic inhomogeneous material structure,and built the bridge for two dimensions analysis of composite material properties.On the basis of the previous research results and based on microscopic mechanics and elastic mechanics knowledge,composite material microstructure was simplified,assuming that homogeneous and periodic,which was composed of the representative volume element with periodic arrangement,the homogenization finite element method was applied to calculate the properties of composite materials,solving the related problems,which provided a more accurate estimate in average sense.Around this issue,the research conducted and the conclusions drawn were as follows:(1)Micromechanical model of composite materials was established,and the ratio of the macroscale and microscale was regarded as small parameter,and established relationship of macroscale and microscale.By applying uniform displacement boundary conditions on the representative volume element,the stress and strain were calculated in the representative volume element.According to the relationship between average stress and strain,homogenization coefficients were obtained,namely the effective stiffness coefficient.Then,macroscopic elastic constants of composite material were calculated based on the relationship between engineering elastic constants and stiffness coefficients.(2)The representative volume element model of the material was determined by microstructure model.The elastic properties of representative volume element model were calculated,which reflected the macroscopic elastic properties of composite material.ANSYS finite element program was made for there-dimensional modeling based on symmetry of the load and geometry,and predicted macroscopic mechanical properties of unidirectional fiber reinforced composite material,spherical particle reinforced composites.Results show that the homogenization finite element method is feasible for the property prediction of composite materials.Several factors influenced on the material properties were studied at the same time,involving the representative volume unit,volume content,arrangement,and finite element mesh.(3)Considering the two dimensional plane stress state,the uniform coefficients were obtained by three different loading,the macroscopic mechanical properties of composite materials were predicted.The elastic constants of unidirectional fiber reinforced composites were obtained in two-dimension,which were very close to the results of the three-dimensional model.The method was applied to the predict properties of the masonry wall material and concrete material.