Concrete Nonlinear Finite Element Analysis Mesh Size Effect

In this paper, material properties of concrete were studied. By studying the behavior especially nonlinear behavior of concrete subjected to variety of loadings, non-linear damage constitutive relations were presented. The program of non-linear concrete structure finite element analysis is worked out, by which the computed results strongly depend on the analyst's choice of finite element size were studied. An idea of eliminate the effect of finite element size was present. The following are primary contents and results of the paper:1. This paper studies the material nonlinearity existing theories, following the pre-researches, sets up a concrete constitutive model which can general reflect material nonlinear properties. Then based on theories of damage mechanics, using strain normalization, damage constitutive relations were established. This makes the finite element program analysis more convenient.2. Applying damage constitutive relations, the nonlinear finite element analysis program of concrete structure's all processes from damage to fracture is worked out. Simplifies the works of adjustment of stiffness matrix, computation of non-equilibrium nodal force and surplus stresses, etc in finite element analysis. Its another advantage is makes unloading and reloading more convenient.3. A program with various functions was made out. Its pre-analysis Part could present the mesh of concrete structure. Its post-analysis part could be used to simulate all processes from damage to failure by graph.4. A beam is analyzed using different finite element size. The influence of the element size on the response of the beam is investigated. The computed results present the drawback from the strength-based criterion. Then discussed the potential reasons of the effect of finite element size.5. With an appropriate adjustment of the value of the ultimate tensile strain as a function of only the element size, to sure the energy dissipation in the structure under-going the fracture process is a constant, irrespective of the finite element size used. A simple formula for calculating the ultimate tensile strain of concrete was developed. The proposed model has eliminated the mesh size effect effectively.6. Finally, some examples include concrete uniaxial compressive, uniaxial tensile and specimens with notch were simulated with different element size. The results showed that the different element size could lead to a closed result. It means that the proposed method isefficacious and reliable.