Generalization of Integration Methods for Complex Inelastic Constitutive Equations with State Variables

- Journal title : Transactions of the Korean Society of Mechanical Engineers A
- Volume 24, Issue 5, 2000, pp.1075-1083
- Publisher : The Korean Society of Mechanical Engineers
- DOI : 10.22634/KSME-A.2000.24.5.1075

Title & Authors

Generalization of Integration Methods for Complex Inelastic Constitutive Equations with State Variables

Yun, Sam-Son; Lee, Sun-Bok; Kim, Jong-Beom; Lee, Hyeong-Yeon; Yu, Bong;

Yun, Sam-Son; Lee, Sun-Bok; Kim, Jong-Beom; Lee, Hyeong-Yeon; Yu, Bong;

Abstract

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

Keywords

Unified Viscoplastic Constitutive Equation;Implicit Integration;FEM;Inelastic Analysis;Time Increment Control;

Language

Korean

Cited by

References

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 1, Equations, Development and Analytical Procedures,' J. Engng. Mat. Tech., Vol.98, p.97

3.

Chaboche, J. L., and Nouaihas, D., 1989, 'A Unfied 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.l

5.

Orits, M., and Simo, J. C, 1986, 'An Analysis of a New Class of Integration Algorithms for Elastoplastic Constitutive Equations,' Int. J. Num. Meth. Engng,, Vol.23, p.353

6.

Honberger, K., and Stamm, H., 1989, 'An Implicit Integration Algorithms with a Projection Method for Viscoplastic Constitutive Equation,' Int. J. Num. Meth. Engng., Vol.28, p.2397

7.

Chaboche, J. L. and Cailletaud, G., 1996, 'Integration Methods for Complex Plastic Constitutive Equations,' Comp. Meth. Appl. Mech. Engng., p. 125

8.

ABAQUS, User's manual, Version 5.4, 1995, HKS, USA

9.

Numerical recipes in Fortran, 1992, Cambridge Press

10.

Nemat-Nasser, S and Li, Y.F.,1992, 'A New Explicit Algorithm for Finite-Deformation Elastoplasticity and Elastoviscoplasticity: Performance Evaluation,' Computer and Structures, Vol,44, No.5, p.937

11.

Schwertel, J., and Schinke, B., 1996, 'Automated Evaluation of Material Parameters of Viscoplastic Constitutive Equations,' J. Eng. Mat. Tech., Vol.118. p. 273