Variational Asymptotic Micromechanics Model For Viscoelastic (Viscoplastic) Behavior Of Heterogenous Composite Materials

With the increasing importance of heterogeneous composite materials in the related field of production and life, accurately grasping of material properties is the basis of structural optimizing design and the premise of guaranteeing personal safety. However, due to the complexity of the heterogeneous composite materials and the limitations of theory research, the prediction of effective properties mostly based on approximate methods have certain errors compared to the accurate result. Therefore, in the research of composite materials, the appropriateness of method will help to improve the accuracy and also is the inevitable trend of academic development.The viscoelastic and elasto-viscoplastic characteristics of composite materials are research focuses in recent years. Deeply studying of these characteristics can play the role of foster strengths and circumvent weaknesses, fully grasp the material properties, effectively analyze the failure criterion and provide a good guidance for the optimizing design. The main studying contents of this graduation thesis are micromechanics modeling the viscoelasticity of polymer matrix composite materials and elasto-viscoplasticity of heterogeneous composites based on the variational asymptotic method. The effective relaxation and creep are obvious viscoelasticity phenomena in the polymer matrix composites. The commonly analysis method is elasto-viscoelastic correspondence principle by Laplace transformation based on the elastic analysis or the asymptotic expansion in the time domain. The elasto-viscoplastic mechanics of heterogeneous composite materials(especially metal matrix composite materials) cannot be ignored and the influence of elastic, viscous, plastic and hardening, yield criterion of material in the process of analysis make it difficult to predict material properties and analyze the macroscopic response. Based on the unit cell energy functional, the micromechanics model was established by using the variational asymptotic method. Firstly, the representative unit cell was selected in the heterogeneous composite materials. Then, energy functional under service loading was established based on the energy method. The energy functional was asymptotic extended by taking advantage of the small parameters(the ratio of macro to micro scale), which can simplify the complexity of the energy functional analysis(the problem was converted into solving the minimum problem of functional). The variational asymptotic method combined with traditional finite element method can improve the accuracy of result and provide a powerful technical support for the effective prediction of the material properties.The main conclusion of this graduation thesis is that variational asymptotic method is an effective method to predict material properties. Without introducing unnecessary hypothesis, the method can successfully establish the micromechanics model to predict the effective stress relaxation and creep of polymer matrix composites and elasto-viscoplastic composites. It can also predict the effective stress relaxation and creep changing with the time and the stress-strain relationship of elasto-viscoplastic mechanics. The effectiveness and accuracy of the model are verified by comparing with other finite element results.The innovations in this graduation thesis are listed as follows:(1) Based on the variational asymptotic method, the definite solution problem of viscoelastic and viscoplastic mechanics of composite material are converted into the functional extremum problem, which can avoid the Laplace conversion and reverse conversion in the calculation of traditional linear viscoelastic and viscoplastic composites. This method can accurately predict the effective material properties, simplify the solving difficulty and improve the computational efficiency. Therefore, this method has certain innovation in some extent.(2) The combination variational asymptotic theory with finite element method makes full use of the advantages of both methods, making up for the faults that traditional approximate method cannot predict very well the effective properties of complex microstructure. Meanwhile, it can effectively simulate mechanical behavior of viscoplastic material under complex loading conditions and loading paths.(3) The variational asymptotic method is essentially different from the traditional approximate methods. Without introducing a priori assumption, the fluctuation function is used as basic unknown quantity and the energy functional is asymptotically solved by taking advantage of the small parameters. The theoretical result is a breakthrough in the micromechanics development, which can provide a broader perspective for mechanical development.