An element mapping material point method for tracking interfaces in transient nonlinear heat conduction with sources

The Generalized Interpolation Material Point method (GIMP), based on both material-point discretization and Eulerian space meshing, which is appropriate for nonlinear problems. However, it is difficult to identify physical boundaries and material interfaces, leading to numerical oscillations in the thermal analysis. Therefore, an Element Mapping Material Point method (EMMP) is proposed to handle with the deficiency. EMMP redesigns a particle-element mapping algorithm for transmitting the information through physical and numerical fields, deduces an efficient solution scheme for the control equation system, proposes an approach for identifying boundary and interface, as well as a method for marking elements with the information of loads and constraints. There are four numerical examples of heat conduction under various scenarios, validating the thermal analysis performance of EMMP. The results indicate that EMMP is capable of solving transient nonlinear heat conduction problems with high boundary resolution and numerical stability, effectively avoiding temperature oscillations throughout the field. It is observed that EMMP is approximately 36% and 68% more efficient than the Finite Element method (FEM) and GIMP, respectively. Additionally, EMMP maintains relative errors within the order of 10−5 compared to analytical solutions. It is also verified that EMMP is proficient in simulating the phase transition and ignition processes of the energetic material, HMX, subjected to the thermal contact load.