Development of a robust cyclic plasticity model and its application to soil-structure interaction problems

Abstract

Constitutive modeling for engineering materials is a great concern for the numerical modeling of engineering structures. In the last four decades, the constitutive modeling has evolved considerably. Starting from pioneering work by Druker and Prager [1952], various improvements, extensions and alternative constitutive models have been proposed. As materials often are subjected to repetitive loading during their service load such as wind load, earthquake load, moving traffic load etc. it is very essential for a complete model to simulate the cyclic behavior of the material accurately like the monotonic one. In this regard, several cyclic constitutive model have been proposed within the framework of the classical plasticity theory such as Prager [1956], Armstrong and Frederick [1966], Mroz [I967J, Dafaslias and Popov [1975, 1976], Chaboche and his coworkers [1979, 1986J, Ohno and Wang [1993], Hossain, Siddiquee and Tatsuoka [2005J etc. All of these models have the ability to simulate the cyclic stress-strain behavior of various materials with some limitations of their own. In this research work an attempt is made to develop a robust cyclic constitutive model within the framework of the theory of plasticity. To construct a generalized constitutive model for both the pressure independent and dependent materials, a general framework for the cyclic modeling has been proposed. In this framework a nonlinear kinematic hardening rule is derived from the concept of the instantaneous slope of the stress-strain relationship. For this purpose a proportional rule and a drag rule is formulated. By using the proportional rule, the modified Masing's rule is fulfilled which has been observed for many materials. Using the drag rule, the overshooting or the undershooting of the stressstrain relationship can be modeled. A nonlinear stress-strain relationship is indispensable to develop a constitutive model. Often a simple hyperbolic equation (Konder, R.L. [1963]) IS used. In the present research a nonlinear stress-strain relationship is proposed which is simple but fulfills all the necessary requirements. Using this equation the instantaneous slope is calculated. By using this instantaneous slope for kinematic hardening rule, models for both the pressure independent and dependent materials have been developed. The Von-Mises and Druker-Prager yield functions are used for pressure independent and pressure dependent materials respectively. Then an associative flow rule is adopted for the pressure independent material and a stressdilatancy rule proposed by Tatsuoka et. al. [2003] is used with some modification for pressure dependent material. For the integration of the of the incremental stress-strain relationships, several integration algorithms are available. In the present work, Return Mapping algorithm is used (Ortiz and Popov [1985], Simo and Taylor [1986] and Ortiz and Simo (1986]). Finally, for the nonlinear solution of the finite element analysis Dynamic Relaxation technique is used. To verify the model, a single four node quadrilateral element is chosen with single gauss point integration for plane strain simulation. Masuda et. al. [1999] performed a series of plane strain cyclic loading tests on Toyoura sand. In this research, an attempt is made to simulate the cyclic plane strain behavior of Toyoura sand and the results have been found quite reasonable. The proposed model can be applicable for any type of structural as well as soil-structure interaction problems.