A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems

• Published in: Journal of computational physics Vol. 230; no. 17; pp. 6546 - 6562
• Main Author: Hansen, Glen
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.07.2011; Elsevier
• Subjects: CLADDING; Computational techniques; Computer simulation; COMPUTERIZED SIMULATION; Contact; EQUATIONS; Exact sciences and technology; FINITE ELEMENT METHOD; FUEL PELLETS; FUEL RODS; Fuels; HEAT; HEAT FLUX; HEAT TRANSFER; HELIUM; INTERFACES; IRRADIATION; MATHEMATICAL METHODS AND COMPUTING; Mathematical methods in physics; Mathematical models; Mortar finite element method; NONLINEAR PROBLEMS; Pellet cladding interaction; Pellets; Physics; Reactor fuel performance; Reactor multiphysics simulation; REACTORS; THERMAL EXPANSION; Thermomechanical contact; TRANSIENTS; Tubes; URANIUM DIOXIDE; Thermomechanical contact; Pellet cladding interaction; Mortar finite element method; Reactor multiphysics simulation; Reactor fuel performance; Heat equation; Thermal behavior; Calculation methods; Finite element method; Lifetime; Lagrange multiplier; Newton Krylov method; Algebraic equation; Models; Modelling; Calculation; Performance; Nonlinear systems; Heat transfer
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.04.038

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO 2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.