Modeling strategies for multiphase drag interactions using the material point method

Abstract

SUMMARYThis paper presents an investigation of strategies for handling dissipative phase interactions in the context of multi-field material point method formulations in which each phase is assigned its own motion. Different families of phase interaction strategies using both nodal and particle-based approaches are developed, and in particular, a new smoothed volume fraction approach is presented that can handle interaction effects in a general and consistent manner while reducing anomalous effects of phase boundaries and grid crossings. The effectiveness of this approach is demonstrated via convergence studies using a fundamental model problem.

A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

“…in which X and Y are the components of the global coordinate system in the reference configuration, A is the maximum amplitude of displacement (in the numerical simulations, this parameter is assumed to be 0.05 m), t is the time, and C is the constant defined in Equation (29). Using the MMS, the following body forces are found to be required to achieve the assumed displacement field (detailed calculations are presented in Appendix A):…”

“…in which X and Y are the components of the global coordinate system in the reference configuration, A is the maximum amplitude of displacement, t is the time, and C is the constant defined in Equation (29). The deformation gradient is found by taking derivatives with respect to position according to Equation (A4)…”

“…MPM and GIMP have been successfully used in simulation of a range of complicated engineering problems including finite deformation plasticity, thin membranes, cracks and fracture, sea ice dynamics, granular materials, multiscale problems, hypervelocity impact, and dynamic analysis of saturated porous media among others [4][5][6][7][8][9][10][11][12][13][14][15][16]. Also, their basic algorithms and formulations have been studied by a number of authors such as [17][18][19][20][21][22][23][24][25][26][27][28][29]. In MPM, the material domain is represented by a set of material points or particles and uses a mixed Eulerian-Lagrangian method in which Lagrangian particles carry history-dependent state data and an Eulerian background grid is used for calculation of derivatives and solving the momentum equation.…”

Mitigating kinematic locking in the material point method

“…Significant research has focused on applications of this type (e.g., [11,12,17,34,59,61,40]), but much work has also been done in additional areas-pushing the capabilities of the MPM and exploring new applications. These include applications in geotechnical engineering [3,60,66], fracture and material failure [15,19,20,41,44,45,53,55], contact, material interaction, and penetration [6,7,23,24,27,33,38,46,42,64,65], as well as general implementation considerations [5,25,28,29,36,48,50].…”

Avalanche and landslide simulation using the material point method: flow dynamics and force interaction with structures

“…There is a large literature base considering MPM applications-the interested reader is referred to three recent publications [13,14,22] that summarize previous applications, extensions, and numerical implementation details. In the specific context of granular flow, it is important to recognize the works of [15,32,33] in which the MPM is used to simulate granular media in various contexts.…”