The Material Point Method (MPM) has been developed as a special finite element-based method for large deformation analysis, material flow and contact problems. When it comes to applications in soil, MPM can provide solutions where conventional FEM faces its limitations. Examples of geotechnical applications include landslides, silo filling and emptying, soil pushing and shoveling, as well as structure-soil penetration and installation problems (piles, anchors). In offshore geotechnics one can find several applications of the latter type where an MPM analysis can provide significant added value, such as for monopile penetration, (suction) anchor installation, spud can punch-through and trenching for pipelines and cables. In order to use MPM on a daily basis in practical applications, several numerical difficulties had to be overcome, such as inaccuracies, (numerical) instability, irregularities in strain and stress, contact formulation, boundary determination (applying boundary conditions), and last but not least, dealing with the required computing power. The latter is relevant, since MPM calculations are far more demanding than FEM calculations with a similar calculation grid. In this paper we highlight important numerical solutions that we have implemented for a practical use of MPM in geotechnical applications. Examples are the use of high-order elements and the Dual Domain Material Point method (DDMP) to smoothen strains and stresses, the use of an implicit integration scheme to stabilize calculations, the use of an augmented Lagrangian formulation to enhance the contact algorithm, and the use of dynamics and inertia to deal with local soil failure. Furthermore, the paper demonstrates a number of practical cases where MPM can provide added value in offshore geotechnical applications. @en

Material point method (MPM) is very suitable for modelling extreme deformation of materials, where the traditional finite element method (FEM) often encounters mesh distortion. However, FEM is more accurate and efficient than MPM for problems with small deformation. A large number of engineering applications involve modelling of contact interaction between two bodies where only one of them experiences large deformation. Examples are pile driving or spudcan penetration in soil mechanics, cutting, wear etc. Most of the work on contact modelling within MPM framework reports algorithms that simulate all contact bodies using MPM. One publication [1] presents explicit algorithm where one contact body is modelled with FEM, while the other with MPM.

In this work we present an algorithm for implicit modelling of such FEM/MPM contact interaction. The algorithm is based on minimization of the energy functional with constraint terms, formulated as in classical contact mechanics, using Augmented Lagrangian method [2]. However, instead of the distance function, we use level set function which zero contour tracks the boundary of the contact body modelled with MPM. Since the boundary of the FEM-based body is immersed into the MPM-based domain, the contact contribution is applied similar to fictitious domain methods [3]. The presented numerical examples validate the algorithm against the results, known from literature, as well as demonstrate its applicability for geomechanical calculations.@en

A finite element analysis of implant positioning inside a bone requires the creation of many meshes that model various implant orientations. This process can be very labour intensive and is difficult to automate. In order to facilitate this type of modelling, we present a large sliding contact algorithm that does not require the creation of a conforming discretization for the bone. The cavity inside the bone, necessary to accommodate the implant, is modelled with a Heaviside function calculated on the level set field, which is defined in terms of material coordinates of the bone. The algorithm is based on the minimization of the energy functional with a constraint term, formulated as in classical contact mechanics; however, instead of the distance function, we use the above-mentioned level set function. The presented numerical 2D and 3D examples validate the algorithm against the solutions obtained with commercial finite element software. Keywords: contact; level set; finite element method; Lagrange multipliers: implant positioning@en