Rigid Body Interaction with Highly Deformable Solids, a Material Point Approach in 3D
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In geotechnical engineering a range of problems involve the interaction between stiff mechanical objects and highly deformable solids. From a numerical perspective these problems involve non-linear material behaviour, large deformations, contact and friction, and occur over a relatively large amount of time and/or distance. The combination of these non-linearities is challenging, particularly the significant deformations which pose challenges for \textit{de facto} Finite Element (FE) methods due to element distortion. A natural alternative is the Material Point Method (MPM), a continuum method where the material and kinematic information is stored at Material Points (MPs). During a load step the solution is solved using a background FE grid and the MPs are used as integration points. Once convergence is achieved the mesh is reset to its initial position, but the MPs remain in their deformed positions and state, enabling significant deformation to occur whilst avoiding mesh distortion. However, as the MPs no longer align with the mesh the definition of the domain's boundary becomes non-trivial as there is no formal definition of the surface. For the interaction of two bodies, through contact and friction, a description of a surface is critical. A 2D solution to this problem was presented by Bird \emph{et al.} [1] and this contribution extends that approach to 3D. The method requires Generalised Interpolation MPs, where each MP's domain can used to both detect and apply contact conditions with no boundary reconstruction. The mechanical object, modelled as a rigid body, is constructed from triangular facets which interact with the vertices of the MP boundary. The 3D implementation is validated using a range of analytical and experimental results, culminating in the simulation of the trajectory of an anchor being pulled through a sand bed over a range of relatively densities.
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