A Variational Asymptotic Micromechanics Model For The Hygro-thermo-elastic(plastic) Properties Of Composite Materials Used In Bridges

Composite materials have been widely used in aerospace,automobile manufacturing and other fields for their high specific strength,high specific modulus,and outstanding designability characteristic.With the development of modern transportation,the requirements of construction speed,construction cost and usability of bridge become increasingly higher.Composite materials with excellent properties have also been extended to bridge engineering.Broad scope of application and the complex service conditions(such as wet and heat coupling field,etc.)require engineers to have full understanding of the properties of composite,in order to give full play to the excellent characteristics of composite materials.It is also a difficult problem to calculate the mechanical properties of composite materials because of its complex properties such as heterogeneity and anisotropy.This research is supported by the national natural science fund projects "Variational asymptotic fine model and its application in multi field coupling analysis of functionally graded piezoelectric laminated plates"(grant number: 11272363).On the bases of existing microscopic mechanics research,we introduce variational asymptotic method to microscopic mechanics analysis.The variational asymptotic homogenization theory has been established without introducing special assumptions and specific boundary conditions,in order to predict the mechanical properties of composite materials accurately.The specific achievement of this paper is as follows:(1)A micromechanics model has been developed for predicting effective hygrothermoelastic properties of composite materials and recovering the local fields within the unit cell based on the framework of the variational asymptotic homogenization theory.Starting from the functional of free energy of composite materials,the leading variable item in the functional was asymptotically analyzed by taking advantage of the small ratio of microscale to macroscale.The recovery relationships between micromechanics model and local fields for the hygrothermoelastic problem were obtained and implemented by using finite element method.The numerical example shows that compared with ABAQUS results the present model can effectively and accurately predict the effective properties and reconstruct the distributions of local wet and thermal stress-strain field.(2)Based on the Armstrong-Frederick nonlinear hardening model and the Hill yield criterion,the elastoplastic constitutive model given the back stress evolution is established.In the foundation of Armstrong-Frederick nonlinear hardening model and Hill yield criterion,the stress integration algorithm is proposed by complete implicit stress integration algorithm that is based on a rigorous second-order radial return algorithm.The numerical formulations for the model are outlined.The generalized consistent tangent modulus of integral points,which is based on the discrete constitutive model and necessary for whole nodal equilibrium iteration of finite element calculation,is derived.(3)Based on the variational asymptotic homogenization theory,a variational asymptotic homogenization micromechanics model for elastoplastic composites is established.The functional of free energy for homogenization is formulated using the variational asymptotic method,discretized in a finite-dimensional space,and solved macro-mechanical response using a multilevel Newton–Raphson method.The versatility and accuracy of the present approach are demonstrated through homogenizing long fiber-reinforced metal matrix composites(MMCs).The simulation results show that the method can accurately simulate the elastoplastic behavior of metal matrix composites under different loading conditions and loading paths,which provide a new idea for the characterization of elasto-plastic materials.