Constitutive Modeling Of Particle-Reinforced Composites In Finite Deformation

The research on mechanics of composites in finite deformation still hasn't achieve significant breakthrough due to the difficulty from the coupling of the geometry nonlinearity and material nonlinearity.This paper proposes the constitutive models of particle-reinforced composites as well as porous materials in finite deformation via a unique combination of numerical and analytical work.In accordance to the constitutive models developed,this paper solves a fundamental problem in mechanics of particle-reinforced composites in finite deformation: how to predict or estimate the “overall” mechanical properties of the particle-reinforced composites with given mechanical properties of the constitutions and the microstructures.In this paper,representative volume element(RVE)models,which can accurately represent the real materials,are firstly developed to simulate the mechanical responses of the particle-reinforced composites subjected to various boundary conditions and deformations in finite deformation.Based on the numerical results and utilizing the macro-mechanics approach together with the micro-mechanics approach,it is obtained that the composites with randomly distributed particles still behave with the character of incompressible neo-Hookean model if both its matrix and particle are considered as incompressible neo-Hookean materials.Moreover,its effective shear modulus can be estimated precisely by the three phase model(TPM)[1].Consequently,the constitutive responses of the composites with randomly distributed particles in finite deformation can be characterized according to the features obtained above.The experimental method is also developed to explore the overall responses of the particle reforced composite under finite deformations.By comparing the results obtained from the constitutive model and the experiments,we proved that the embedded particles strengthen the polymer matrix not only in the continuum level but also in the molecular level via changing the mechanical properties of molecular chains.The mechanical properties of chain-structured particle reinforced composites in finite deformation are also investigated in this paper.The chain-structured particle reinforced model is transformed to “virtual fiber” reinforced model via considering the particle chains and some surrounding matrix as “virtual fibers”.Therefore,the constitutive model of fiber-reinforced composite in finite deformation is employed to capture the constitutive behaviors of chain-structured particle reinforced compostites.The constitutive model is validated by the numerical method.Furthermore,the constitutive model is employed to analyze the effect of particle denseness as well as the influence of “virtual fiber” choice.The constutitve model of porous materials in finite deformation is also constructed with the method of multiplicative decompositeion.Utilizing this method,a general deformation is decoupled into the volumetric part and isochoric part.Thus,the strain energy function of porous materials can be determined by deriving the corresponding two parts and summarizing them.Numerically validated by finite element method(FEM),the constitutive model is proved to well predict the “overall” responses such as strain energy,stress,lateral deformation and volume change under various finite deformations.