The Hot Optimal Transportation Meshfree (HOTM) method for materials under extreme dynamic thermomechanical conditions

We present a monolithic incremental Lagrangian framework based on meshfree methods, the Hot Optimal Transportation Meshfree (HOTM) method, for a robust and efficient solution of the dynamic response of materials under extreme thermomechanical conditions, possibly involving extremely large deformation, phase transition and multiphase mixing. The HOTM method combines the Optimal Transportation Meshfree (OTM) method and the variational thermomechanical constitutive updates. The variational structure of a dynamic system with general internal dissipative mechanisms is discretized in time by applying the Optimal Transportation theory, while material points and nodes are introduced for the spatial discretization. A phase-aware constitutive model is developed to describe the history-dependent material behavior in various phases due to melting, vaporization and solidification. The fully discretized conservation equations of linear momentum and energy are solved simultaneously using an operator splitting algorithm to predict the deformation, temperature and internal variables of the computational domain. The convergence property of the meshfree solution of the energy conservation equation is studied in a three-dimensional transient heat conduction problem by comparing to the analytical solutions. Accuracy of the HOTM method is also assessed in the example of upsetting a metallic billet up to a compression ratio of 95% under various external heating and cooling strategies. The scope and robustness of the HOTM method are demonstrated in the application of the laser cladding technology.