Asynchronous collision integrators: Explicit treatment of unilateral contact with friction and nodal restraints

• Published in: International Journal for Numerical Methods in Engineering Vol. 95; no. 7; pp. 562 - 586
• Main Authors: Wolff, Sebastian, Bucher, Christian
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 17.08.2013; Wiley; Wiley Subscription Services, Inc
• Subjects: Constraints; Contact; Exact sciences and technology; explicit; Friction; Fundamental areas of phenomenology (including applications); Hamiltonian; Integrators; Mathematical analysis; Mathematical models; Mathematics; Mechanical contact (friction...); nonlinear dynamics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Physics; Projection; Sciences and techniques of general use; Solid mechanics; Structural and continuum mechanics; time integration; time integration, explicit; variational methods; Constraint; Automatic mesh generation; Modeling; Adaptive method; Finite element method; System with n degrees of freedom; variational methods; Discretization; contact; Variational calculus; nonlinear dynamics; Numerical convergence; Collision; Step method; Mechanical contact; Contact surface; explicit; Time domain method; Linear system; Asynchronism; Friction; Equivalent circuit; Unilateral; Hamiltonian mechanics; Hamiltonian; Time integration; time integration, explicit
• ISSN: 0029-5981; 1097-0207; 1069-8299
• DOI: 10.1002/nme.4516

SUMMARYThis article presents asynchronous collision integrators and a simple asynchronous method treating nodal restraints. Asynchronous discretizations allow individual time step sizes for each spatial region, improving the efficiency of explicit time stepping for finite element meshes with heterogeneous element sizes. The article first introduces asynchronous variational integration being expressed by drift and kick operators. Linear nodal restraint conditions are solved by a simple projection of the forces that is shown to be equivalent to RATTLE. Unilateral contact is solved by an asynchronous variant of decomposition contact response. Therein, velocities are modified avoiding penetrations. Although decomposition contact response is solving a large system of linear equations (being critical for the numerical efficiency of explicit time stepping schemes) and is needing special treatment regarding overconstraint and linear dependency of the contact constraints (for example from double‐sided node‐to‐surface contact or self‐contact), the asynchronous strategy handles these situations efficiently and robust. Only a single constraint involving a very small number of degrees of freedom is considered at once leading to a very efficient solution. The treatment of friction is exemplified for the Coulomb model. Special care needs the contact of nodes that are subject to restraints. Together with the aforementioned projection for restraints, a novel efficient solution scheme can be presented. The collision integrator does not influence the critical time step. Hence, the time step can be chosen independently from the underlying time‐stepping scheme. The time step may be fixed or time‐adaptive. New demands on global collision detection are discussed exemplified by position codes and node‐to‐segment integration. Numerical examples illustrate convergence and efficiency of the new contact algorithm. Copyright © 2013 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd.