The fiber reinforced rubber composite has attracted interests such as high specific modulus, high specific strength, efficient damping and thermal characteristics. Finite element analyses of the structures made of the fiber reinforced composite require an adequate method to characterize the highly anisotropic behavior due to the one or several embedded layers of fiber cords with different spatial orientation. Most numerical analyses of the fiber reinforced composites are currently based on the theories and techniques originally developed for laminated fiber composites with several arbitrarily oriented cord layers and the matrix material being represented within one single finite element. The material properties are averaged over an element on the basis of an anisotropic material law. An alternative approach is adoption of a rebar element. This model is characterized by defining the overlay rebar element, which separately represents the mechanical properties of fiber and rubber matrix in conjunction with corresponding rubber elements.
In this paper, the continuum based rebar element is newly proposed by considering the orientation of a fiber during the deformation of a composite. As a first step, numerical simulation is carried out in order to evaluate the generally used modeling schemes such as the Haplin-Tsai equation and the rebar element in ABAQUS/Standard. The analysis results with both schemes show the large differences compared to experimental one since the orientation of the fiber that causes change of the mechanical properties of composites during the deformation is not considered in both schemes. In order to improve the analysis accuracy, the mechanical behavior of the embedded fiber is modeled using two node bar elements that enable the description of the relative deformation and spatial orientation of the embedded fiber. A three-dimensional finite element program is constructed based on the total Lagrangian formulation considering both the geometric nonlinearity and the material nonlinearity. The finite element analysis of the tensile test is carried out and simulation results are compared with experimental ones in order to evaluate the validity of the proposed scheme. The proposed method provides more realistic representation of fiber reinforced rubber composites compared with other modeling schemes such as the Haplin-Tsai equation and the rebar element in ABAQUS/Standard. The scheme proposed is then applied to the 3-D finite element analysis of the inflation process of an air-spring. Analytic predictions and experimental results have been in good demonstrating that the scheme proposed is effective in the finite element analysis of the structure made of fiber reinforced composites.
본 논문의 목적은 공기스프링에 사용되는 섬유강화 고무기저 복합재료의 서동을 효과적으로모사할 수 있는 모델링 기법에 대하여 고찰하고 개선하는 데 있다. 본 논문에서는 고무기저 섬유강화 복합재료의 3차원 유한요소해석을 위하여 변형 중 발생하는 보강섬유의 회전을 고려한 리바요소를 제안하였다. 보강섬유의 상대적인 변형과 회전을 고려하기 위하여 보강섬유의 강성을 바요소로 근사하였다. 또한 해석의 정밀도 향상을 위하여 보강섬유의 인장시험 결과인 하중변위 선도를 보강섬유의 강성행렬에 직접적으로 대입하는 방법을 사용하였다. 전라그란지안 수식화를 통하여 재료비선형성과 기하비선형성을 모두 고려한 비선형 유한요소해석 프로그램을 구성하고 본 논문에서 제안한 리바요소를 대입하였다. 본 논문에서 제안한 모델링기법을 평가하기 위하여 섬유강화 고무기저 복합재료의 인장해석을 수행하였다. 각각의 인장시편을 본 논문에서 제안한 기법, Halpin-Tsai 물성치 식을 대입한 이방성 재료 모델과 상용프로그램인 ABAQUS/Standard에서 지원하는 쉘-리바 요소를 이용한 총 세 기법으로 모델링하여 해석하고 시험결과와 비교하였다. 본 논문에서 제안한 모델링기법을 통한 결과가 다른 두 모델과 비교하여 시험결과와 보다 유사한 결과를 나타내었다.