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.

REFERENCES

[1] Y.P. Lian, X.Zhang, Y. Liu. Coupling of finite element method with material point method by  local multi-mesh contact method Computer Methods in Applied Mechanics and Engineering, 200, 3482–3494, 2011.

[2] G. Pietrzak, A. Curnier, "Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment", Computer Methods in Applied Mechanics and Engineering, 177, 351-381, 1999

[3] Glowinski, R., T.-W. Pan, and J. Periaux (1994). A fictitious domain method for dirichlet problem and applications. Computer methods in applied mechanics and engineering 111, 283-303.