An Adaptive Meshless Method for Modeling Large Mechanical Deformation and Contacts

Growing new robotic applications in agriculture, food-processing, assisted surgery and haptics, which requires handling of highly deformable objects, present a number of design challenges; among these are methods to analyze deformable contacts. Recently, meshless methods (MLM), which inherit many advantages of finite element method (FEM) and yet need no explicit mesh structure to discretize geometry, have been proposed as an attractive alternative to FEM for solving engineering problems where automatic re-meshing is needed. This paper offers an adaptive MLM (automatically inserting nodes into large error regions) for solving contact problems. We employ the sliding line algorithm with the penalty method to handle contact constraints; it does not rely on small displacement assumptions and thus, it can solve non-linear contact problems with large deformation. Along with three practical applications, we validate the method against results computed using commercial FEM software and analytical solutions.