A semi-explicit algorithm for solving multibody contact dynamics with large deformation

This work is devoted to the numerical modeling of contact problems in the context of multibody dynamics. Non-linearities including large deformation and frictional contact are modeled based on the finite element method. An improved approach by means of a semi-explicit calculation is applied to integrate the equation of motion. The frictional contact forces and the relative velocity establish an implicit relationship within the bi-potential framework. A hybrid methodology consisting of the Octree structure and the bounding volume hierarchy is proposed to reduce exhaustive contact inspections. Two numerical examples implemented in our in-house finite element software FER/Impact are given to illustrate the efficiency and accuracy of the resulting methods.

[1]  R. Brach.  Formulation of rigid body impact problems using generalized coefficients , 1998 .

[2]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[3]  Christer Ericson,et al.  Real-Time Collision Detection , 2004 .

[4]  Qi-Chang He,et al.  Finite deformations of Ogden's materials under impact loading , 2006 .

[5]  Baba C. Vemuri,et al.  Fast Collision Detection Algorithms with Applications to Particle Flow , 1998, Comput. Graph. Forum.

[6]  S. Chan,et al.  A finite element method for contact problems of solid bodies—Part I. Theory and validation , 1971 .

[7]  Zhi-Qiang Feng,et al.  The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms , 1998 .

[8]  Jane Wilhelms,et al.  Octrees for faster isosurface generation , 1992, TOGS.

[9]  William L. Ko,et al.  Application of Finite Elastic Theory to the Deformation of Rubbery Materials , 1962 .

[10]  B. Fredriksson.  Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems , 1976 .

[11]  Genki Yagawa,et al.  A dynamic contact buckling analysis by the penalty finite element method , 1990 .

[12]  David J. Benson,et al.  Sliding interfaces with contact-impact in large-scale Lagrangian computations , 1985 .

[13]  Anil Chaudhary,et al.  A SOLUTION METHOD FOR PLANAR AND AXISYMMETRIC CONTACT PROBLEMS , 1985 .

[14]  J. C. Simo,et al.  A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems , 1993 .

[15]  F. Jourdan,et al.  A Gauss-Seidel like algorithm to solve frictional contact problems , 1998 .

[16]  Dinesh Manocha,et al.  I-COLLIDE: an interactive and exact collision detection system for large-scale environments , 1995, I3D '95.

[17]  J. Moreau,et al.  Unilateral Contact and Dry Friction in Finite Freedom Dynamics , 1988 .

[18]  J. C. Simo,et al.  An augmented lagrangian treatment of contact problems involving friction , 1992 .

[19]  Ming C. Lin,et al.  A fast algorithm for incremental distance calculation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[20]  Yu Wang,et al.  Modeling impact dynamics for robotic operations , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[21]  David J. Benson,et al.  A single surface contact algorithm for the post-buckling analysis of shell structures , 1990 .

[22]  Kazuya Yoshida,et al.  Modeling of collision dynamics for space free-floating links with extended generalized inertia tensor , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[23]  Robert L. Taylor,et al.  On a finite element method for dynamic contact/impact problems , 1993 .

[24]  Stephen Cameron,et al.  Enhancing GJK: computing minimum and penetration distances between convex polyhedra , 1997, Proceedings of International Conference on Robotics and Automation.

[25]  Marcus G Pandy,et al.  Simultaneous prediction of muscle and contact forces in the knee during gait. , 2010, Journal of biomechanics.

[26]  Mengyan Zang,et al.  LC-Grid: a linear global contact search algorithm for finite element analysis , 2014 .

[27]  Gino van den Bergen.  Efficient Collision Detection of Complex Deformable Models using AABB Trees , 1997, J. Graphics, GPU, & Game Tools.

[28]  Carme Torras,et al.  3D collision detection: a survey , 2001, Comput. Graph..

[29]  Finite Element (FE) Shear Modeling of Woven Fabric Textile Composite , 2014 .

[30]  Mark O. Neal,et al.  Contact‐impact by the pinball algorithm with penalty and Lagrangian methods , 1991 .

[31]  Jean-Michel Cros,et al.  The bi-potential method applied to the modeling of dynamic problems with friction , 2005 .

[32]  Benjamin J Fregly,et al.  Multibody dynamic simulation of knee contact mechanics. , 2004, Medical engineering & physics.

[33]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three-dimensional space , 1988, IEEE J. Robotics Autom..