A Finite Element Study of Bimodulus Materials with 2D Constitutive Relations in Non-Principal Stress Directions

This paper extends the application of bimodulus elasticity theory by formulating a constitutive relation applicable to non-principal stress directions, building upon the established framework based on principal stresses. The paper develops four full-scale finite element models-the 3-node triangular, the 4-node quadrilateral, the 6-node triangular, and the 8-node quadrilateral elements-with the latter two showcasing higher precision in complex stress simulations. This formulation enables a more detailed analysis of material behavior under varying stress states. An effective iterative solution approach is introduced to address the nonlinearity of bimodulus materials, ensuring model convergence and reliability. The accuracy of the model has been verified through rigorous ANSYS 2022 R1 simulations, and the solution results have been compared with those in the existing literature, emphasizing the importance of the tension-to-compression modulus ratio in determining structural displacement and stress distribution. The developed models and methods provide useful numerical tools for the analysis and design of structures incorporating bimodulus materials.