Arbitrary particle domain interpolation method and application to problems of geomaterial deformation

Abstract The two types of numerical techniques related to the Material Point Method (MPM) are reported; one is the alternative interpolation function called Arbitrary Particle Domain Interpolation (APDI), and the other is the particle-element coupled method. APDI interpolation function is one of the domain integration methods, which can consider the arbitrary shape of particle domain in MPM. The numerical domain integration employed in APDI method has realized the simpler algorithm in both 2- or 3-dimensional implementation. Especially in 3-dimensional formulation, the simple formulation and implementation is inevitable for the integrity of the numerical method. On the other hand, the particle-element coupled method is the numerical framework to reduce the computational cost such as memory, storage and computational time. The basic idea of the particle-element method is to divide the target domain physically into subdomains, and they are combined together numerically by using the numerical grid. This technique enables us to apply the different interpolation function to the different parts of the target domain, realizing the complex calculation using both particle and element in the same procedure. In this paper, the formulations and the demonstrations of both APDI method and the particle-element coupled method are reported, and the applicability and effectiveness of the methods to geomaterial are clarified.