# Viscoplastic Solution of Thick Walled Cylinder Considering Axial Constraint

• 발행 : 2003.09.01

#### 초록

Finite element analysis using modern constitutive equation is one of the most general tools to simulate the deformation behavior and to predict the life of the structure. Constitutive equation becomes complicated so as to predict the material behavior more accurately than the classical models. Because of the complexity of constitutive model, numerical treatment becomes so difficult that the calculation should be verified carefully. One-element tests, simple tension or simple shear, are usually used to verify the accuracy of finite element analysis using complicated constitutive model. Since this test is mainly focused on the time integration scheme, it is also necessary to verify the equilibrium iteration using material stiffness matrix and to compare FE results with solution of structures. In this investigation, viscoplastic solution of thick walled cylinder was derived considering axial constraints and was compared with the finite element analysis. All the numerical solutions showed a good coincidence with FE results. This numerical solution can be used as a verification tool for newly developed FE code with complicated constitutive model.

#### 참고문헌

1. Bodner, S. R. and Partom, Y., 1975, 'Constitutive Equations for Elasto - Viscoplasticity Strain Hardening Materials, ' J. Appl. Mech., Vol. 42, p. 235
2. Miller, A. K., 1976, 'An Inelastic Constitutive Model for Monotonic, Cyclic and Creep Deformation: Part I, Equations, Development and Analytical Procedures,' J. Engng. Mat. Tech., Vol. 98, p. 97 https://doi.org/10.1115/1.3443367
3. Chaboche, J. L., and Nouaihas, D., 1989, 'A Untied Constitutive Model for Cyclic Viscoplasticity and Its Application to Various Stainless Steels,' J. Pres. Vessel. Tech., Vol. 111, p. 424
4. Inoue, T., Yoshida, F., Ohno, N., Kawai, M., Niitsu, Y, and Imatani, S., 1991, 'Evaluation of Inelastic Constitutive Models under Plastic-Creep Interaction in Multiaxial Stress State,' Nuclear Engng. Design, Vol. 126, p. 1 https://doi.org/10.1016/0029-5493(91)90200-2
5. Boresi, A. P., and Sidebottom, O. M., 1985, Advanced Mechanics of Materials, 4th ed., John Wiley & Son
6. V. K. Arya, 1989, 'Analytical and Finite Element Solution of Some Problems Using a Viscoplastic Model, Computer and Structures,' Vol. 33, pp. 957-967 https://doi.org/10.1016/0045-7949(89)90430-6
7. Lemaitre. J., and Chaboche, J.-L, 1990, Mechanics of Solid Materials, Cambridge University Press, Cambridge
8. Youn, S., Lee, S.-B., Kim, J.-B., Lee, H.-Y., and Yoo, B., 2000, 'Generalization of Integration Methods for Complex Inelastic Constitutive Equations with State Variables,' Transaction of the KSME, A, Vol. 24, No.5, pp. 1075-1083