Research On A Novel Smoothed Rebar Element Technique For Simulation Of Composites

Composite materials are widely used in industry and also have attracted the interest in academia due to their superior properties.The numerical methods are usually employed for evaluating the microscopic mechanical properties of composite materials.The Smoothed Finite Element Method(S-FEM)and the Rebar Element are both numerical methods based on the traditional finite element method(FEM).These two methods not only have all the advantages of the finite element method,but also make up the defects of the finite element method in some respects.Such as,for the S-FEM,the complex domain integral is transformed into a simpler boundary integral by using the smoothing integral technique and Green’s divergence theorem,and the element is allowed to be arbitrary shape without the need for element mapping and Jacobian matrix calculation.Therefore,for irregular elements,reliable solutions can also be obtained.The rebar elements also can be characterized as "overlay" elements that represent two or more different materials within one single element.The number of DOFs is significantly reduced due to without introduce additional elements for the calculation of fibers.In this paper,an efficient numerical approach named Smoothed Rebar Element Technique(SRET)was developed by combining the strain smoothing technique and rebar-concept base on the framework of traditional FEM.This method combines the advantages of these two methods and is used to predict the equivalent elastic modulus of composites.Firstly,the discrete governing equations for plane problems and the theoretical knowledge of S-FEM are introduced.At the same time,the reason why the smoothed finite element method can get the ideal solution to the irregular element is discussed theoretically and tested by a patch test.Secondly,the theory of the Smoothed Rebar Element Technique is proposed and tested by calculating two-dimensional plate with inclusion.This method is used to calculate the equivalent elastic modulus of polymer nanocomposites and good numerical simulation results are obtained.Then the theory of this method is derived when the element type is hexagonal element,and the feasibility of this method is verified by an example.Then,the theory of calculating the phase model with interface is deduced and verified,and the convenience of the method in calculating multiphase composites is found by numerical simulation.Based on the calculated results,the influence of interface on the elastic properties of composites is discussed.Finally,the method is extended to the two-dimensional axisymmetric problem,and the smoothed rebar element method for the two-dimensional axisymmetric problem is derived.The effectiveness of the method is verified by numerical examples,and the method is applied to the performance evaluation of carbon nanotubes reinforced composites.The results obtained are in good agreement with those of the references.