Research On Ubiquitiformal Constitutive Model Of Elastic Composite Materials

Fractal has been extensively used as a nonlinear mathematical tool to describe various irregular and complex phenomena in many fields of science and technology.In spite of wide applications of fractal,however,there exist still inherent difficulties in fractal applications.On the basis of a concept of ubiquitiform,the inherent difficulty in fractal application can be overcome.In this thesis,based on the ubiquitiformal theory,fracture energy and constitutive model of composite materials is researched.The main research work and achievements of paper are as following:Firstly,the ubiquitiformal fracture energy is proposed,and then the size effect of the traditional fracture energy can be obtained directly.Moreover,the numerical results of the ubiquitiformal fracture energy for concrete are found to be in good agreement with that of the critical strain energy release rate calculated from the fracture toughness relation.Then the discrepancy between the numerical results of the traditional fracture energy and that of the critical strain energy release rate,which has been perplexing researchers for a long time,can be reasonably explained.In addition,it is also found from the numerical results that there is no size effect for the ubiquitiformal fracture energy of concrete.Secondly,a ubiquitiformal model for a bi-material rod is proposed,in which the effect of both aggregate volume ratio and aggregate gradation can be taken into account,and then the explicit analytical expressions for the effective elastic modulus is obtained.For concrete,the calculated numerical results are found to be in good agreement with previous experimental data.Moreover,in the ubiquitiformal model,the interfacial displacements between the two materials are continuous,which avoids the difficulty of the discontinuous interfacial displacements in previous fractal models.Thirdly,a ubiquitiformal stereoscopic constitutive model for a bi-material is proposed,the complexity of the generalized model is obtained directly by the generalized measure,in which the effect of both aggregate volume ratio and aggregate gradation can be taken into account,and then the explicit analytical expressions for the effective elastic modulus is obtained.For concrete,the calculated numerical results are found to be in good agreement with previous experimental data.Finally,a two-dimension ubiquitiformal constitutive model for a bi-material is proposed,in which the effect of both aggregate volume ratio and aggregate gradation can be taken into account,and then the explicit analytical expressions for the effective elastic modulus,effective shear modulus and effective Poisson's ratio and is obtained.For concrete,the calculated numerical results are found to be in good agreement with previous experimental data.