Automatic contact detection between rope fibers

Abstract Understanding and modeling contact behavior of rope-like structures imposed by pure torsion represents a very difficult topic among the non-smooth mechanical problems. Apart from the high non-linearities on the boundary conditions, the location of real contact areas between inter fibers becomes a prerequisite difficulty. In this paper, a new three-stages contact searching algorithm based on bounding volume hierarchies and orthogonal projections is developed for fiber contact problems involving large deformation. In particular, an improved axis aligned bounding boxes hierarchy based on the specific geometry component is proposed, which can directly result in vertex-element pairs. The frictional contact forces are solved in a reduced system within the bi-potential framework. The algorithms are implemented into the in-house finite element software FER/Impact and some numerical examples are carried out to illustrate the proposed methods.

[1]  Alexander Konyukhov,et al.  Geometrically exact covariant approach for contact between curves , 2010 .

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

[3]  S. K. Clark,et al.  MECHANICS OF PNEUMATIC TIRES , 1971 .

[4]  Guy E. Blelloch,et al.  Efficient BVH construction via approximate agglomerative clustering , 2013, HPG '13.

[5]  Maher Moakher,et al.  Modeling and numerical treatment of elastic rods with frictionless self-contact , 2009 .

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

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

[8]  Adnan Ibrahimbegovic,et al.  Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods , 2009 .

[9]  Dinesh Manocha,et al.  Fast BVH Construction on GPUs , 2009, Comput. Graph. Forum.

[10]  Peter Wriggers,et al.  Self-contact modeling on beams experiencing loop formation , 2015 .

[11]  Milos Kojic,et al.  A general beam finite element with deformable cross-section , 2001 .

[12]  Markus H. Gross,et al.  Detection of Collisions and Self-collisions Using Image-space Techniques , 2004, WSCG.

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

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

[15]  P. Wriggers,et al.  On contact between three-dimensional beams undergoing large deflections , 1997 .

[16]  Jafargholi Amirbayat,et al.  Mechanics of Flexible Fibre Assemblies , 1980 .

[17]  Tod A. Laursen,et al.  A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations , 2007 .

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

[19]  Alejandro M. García-Alonso,et al.  Solving the collision detection problem , 1994, IEEE Computer Graphics and Applications.

[20]  P. Wriggers,et al.  FINITE ELEMENT FORMULATION OF LARGE DEFORMATION IMPACT-CONTACT PROBLEMS WITH FRICTION , 1990 .

[21]  John Salmon,et al.  Automatic Creation of Object Hierarchies for Ray Tracing , 1987, IEEE Computer Graphics and Applications.

[22]  Peter Wriggers,et al.  Computational Contact Mechanics , 2002 .

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

[24]  Peter Wriggers,et al.  Frictional contact between 3D beams , 2002 .

[25]  Pierre Alart,et al.  Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials , 2005 .

[26]  O. Yeoh Some Forms of the Strain Energy Function for Rubber , 1993 .

[27]  Maher Moakher,et al.  Stability of elastic rods with self-contact , 2014 .

[28]  Philip M. Hubbard,et al.  Approximating polyhedra with spheres for time-critical collision detection , 1996, TOGS.

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

[30]  Edward L. Wilson,et al.  Unified computational model for static and dynamic frictional contact analysis , 1992 .

[31]  Alain Cardou,et al.  A study of helically reinforced cylinders under axially symmetric loads and application to strand mathematical modelling , 1989 .

[32]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[33]  Patrice Cartraud,et al.  Analytical modeling of synthetic fiber ropes. Part II: A linear elastic model for 1 + 6 fibrous structures , 2007 .

[34]  Wolfgang A. Wall,et al.  A Unified Approach for Beam-to-Beam Contact , 2016, ArXiv.

[35]  Masao Fukushima,et al.  Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems , 2000, Comput. Optim. Appl..

[36]  Damien Durville,et al.  Numerical simulation of entangled materials mechanical properties , 2005 .

[37]  Mohammed Raoof Interwire contact forces and the static, hysteretic and fatigue properties of multi-layer structural strands , 1983 .

[38]  D Ciazynski,et al.  Numerical Simulation of the Mechanical Behavior of ITER Cable-In-Conduit Conductors , 2010, IEEE Transactions on Applied Superconductivity.

[39]  Pierre Alart,et al.  A domain decomposition strategy for nonclassical frictional multi-contact problems , 2001 .

[40]  Giorgio Zavarise,et al.  Contact with friction between beams in 3‐D space , 2000 .