The transient heat conduction MPM and GIMP applied to isotropic materials

In the material point method (MPM)/generalized interpolation material point (GIMP), the material domain is discretized into a set of Lagrangian particles. The interaction between these particles will be confirmed using the Eulerian background grid. In each time step, the momentum equations and the spatial derivatives are integrated using the background grid. Thus, the MPM/GIMP take the advantages of both the Eulerian and Lagrangian methods and avoid their respective defects. Especially, the MPM/GIMP have the advantage in the numerical simulation of extreme large deformation, fracture and impact problems in which the heat flow appears. Compared with other meshless methods, the MPM/GIMP applied to the transient heat transfer problems obtain much less attention. In order to extend the applied fields of the MPM and GIMP, this paper will present two- and three-dimensional MPM/GIMP to carry out and discuss the transient heat conduction analysis in the isotropic materials. The availability and accuracy of the present method are tested through three numerical examples, i.e. the transient heat conductions in a square plate and a complex shaped plate, and a high conductive cuboidal copper block with complex shape. The results from the MPM/GIMP are compared with those from the analytical solution or finite element method.