Numerical implementation of modified Chaboche kinematic hardening model for multiaxial ratcheting - Han, Jungmoo; Marimuthu, Karuppasamy Pandian; Koo, Sungyong; Lee, Hyungyil (Computers & structures, 2020)
•Implicit numerical implementation of the modified Chaboche model is discussed.•By using Voigt notations, all equations in numerical algorithm are solved by matrix operations.•Transition of the fourth hardening rule is reflected in the iterative calculation process.•A simple way for verification of consistent tangent operator is presented.•Cyclic indentation test is simulated as a numerical example of multiaxial ratcheting. For simulating multiaxial ratcheting behavior, the modified Chaboche kinematic hardening model was numerically implemented by using the framework of a small-strain elastic-plastic theory. Unlike early models, this improved multiaxial model is difficult to implement using finite element methods owing to its complicated constitutive relations, such as radial evanescence terms and the fourth hardening rule with a threshold. We present an effective procedure for numerical implementation using Voigt notations and the implicit radial return method with Newton-Raphson iterations. All the equations of constitute numerical integration and consistent tangent operator (CTO) are simply solved using matrix operations. The integration algorithm is validated by using both numerical examples and analytical solutions. The CTO is verified by additional stress calculations. The model detects variations in the cyclic indentation response with changes in a multiaxial-dependent parameter. The numerical implementation allows simulations of both biaxial and general multiaxial ratcheting behaviors.