Parametric Random Unit Cell Model For Composites And Its Application

Composite materials are widely used in various industries. The Relationshipbetween structure and properties of composite materials has been the hot and difficulttopic of common interest for mechanics researchers and material scientists.Micromechanics study the medium which are deemed as homogeneous in macroscopiclevel but inhomogeneous at microscopic level. The purpose of micromechanics is toestablish the quantitative relationship between the microstructure and the macroscopiceffective properties of heterogeneous materials, and to clarify the failure mechanism andprovide guidance to the optimization optimal design of composites. Research oncomposite materials by using a micromechanical method become one of the hotspots insolid mechanics in recent ten years. Establishing appropriate micromechanics unit cellmode to simulate and analyze the microstructure of composites and to understand therelationship between the microstructure and the macroscopic properties has the veryvital significance.Based on micromechanics and homogenization theory, some preliminaryinvestigations such as microscopic unit cell modeling, calculation of effective elasticproperties of composite and analysis of tensile and/or compressive mechanical behavioranalysis of the composite, etc. were conducted in the present thesis by implementation offinite element method in ANSYS software. The major achievements and conclusions aresummarized as follows.1. An approach for generating parametric random unit cell model for composites isdeveloped in the present thesis. The developed approach is valid not only for simpleperiodic composites and but also for composites with complex and randommicrostructures, it can be used to generate microscopic unit cell for both the simpleshape inclusions and complex shape inclusions. The adjustable parameters in unit cellmodels include unit cell size, inclusion content, inclusion shape, inclusion size and itsstatistical distribution, inclusion spacing distance and interface layer thickness. Throughre-development of ANSYS, the program package for unit cell modeling and meshgeneration are developed with ANSYS Parametric Design Language (APDL), and thecorresponding module menu are customized and embedded in ANSYS software by usingthe User Interface Design Language(UIDL), through which the geometrical modeling of unit cell and its finite element meshing can be quickly accomplished with thehuman-computer interaction interface.2. Based on perturbation theory, the asymptotic homogenization formulae forheterogeneous composites were derived in detail by introducing small parameter. Thethree dimensional finite element formulae for calculation of the effective elastic moduluswere derived based on the homogenization method. A post-processing program packagewas compiled with APDL for calculating the effective elastic modulus of theheterogeneous composite. As an example, the effective elastic modulus of compositewith ellipsoidal inclusions was determined, and the influences of particle volumefraction and the particle stiffness on the effective elastic modulus of the composites wereexamined. It is demonstrated that the effective elastic modulus varies with inclusioncontent in a similar way with that predicted by Mori-Tanaka method, and self-consistentmethod, and the calculated values by asymptotic homogenization method is between theclassic upper and lower bound values.3. The parametric random unit cell modeling approach was applied to carbon filledrubber and concrete. The microscopic stress fields were obtained by finite elementanalysis, and they may clarify the possible microscopic failure mechanisms in thecomposite considered. For carbon black filled rubber composites, the carbon blackparticles were assumed to be linear elastic, while the rubber matrix is considered to behyperviscoelastic media, the simple tension and cyclic tension were simulated using theproposed random unit cell model. It is demonstrated that the rigidity of rubber compositeis enhanced due to the addition of filled particles and the hysteresis loop is enlarged aswell because of the magnified viscosity. However, the random dispersion of the filledparticles has few influences on the global stress-strain response of the composite. Forconcrete, it is regarded as a three phase composite heterogeneous material, consisting ofcoarse aggregates, mortar matrix and the interface layer between the aggregates and themortar matrix. The static compression behavior of two typical concrete specimens, i.e.specimen with crushed stone aggregates and specimen with gravel aggregates, werenumerically simulated, and the influence of the spatial distribution and volume fractionof aggregates to the effective elastic modulus of the concrete were discussed, and thefirst and third principal stress distribution were also obtained which can be used forevaluating the strength of the two specimens. It can be concluded that the aggregate typevaries the strength of the concrete, and while the spatial distribution of the aggregate hasfew influence on the effective elastic modulus of the concrete. This work was supported by NSFC (11172256), NCET (NCET-08-0685), KeyProject of Chinese Ministry of Education (209085) and Scientific Research Fund ofHunan Provincial Education Department (08A069).