Multilevel augmented Lagrangian solvers for overconstrained contact formulations

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.

Implicit Contact Model for Discrete Elastic Rods in Knot Tying

Rod–rod contact is critical in simulating knots and tangles. To simulate contact, typically a contact force is applied to enforce nonpenetration condition. This force is often applied explicitly (Euler forward). At every time-step in a dynamic simulation, the equations of motions are solved over and over again until the right amount of contact force successfully imposes the nonpenetration condition. There are two drawbacks: (1) Explicit implementation brings numerical convergence issues. (2) Solving equations of motion iteratively to find this right contact force slows down the simulation. In this article, we propose a simple, efficient, and fully implicit contact model with high convergence properties. This model is shown to be capable of taking large time-steps without forfeiting accuracy during knot tying simulations when compared to previous methods. We introduce a new contact potential, based on a smoothed segment–segment distance function, that is an analytic function of the four endpoints of the two contacting edges. Since this contact potential is differentiable, we can incorporate its force (negative gradient of the energy) and Jacobian (negative Hessian of the energy) into the elastic rod simulation.

First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks

Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.

On the Importance of Displacement History in Soft-Body Contact Models

Two approaches are commonly used for handling frictional contact within the framework of the discrete element method (DEM). One relies on the complementarity method (CM) to enforce a nonpenetration condition and the Coulomb dry-friction model at the interface between two bodies in mutual contact. The second approach, called the penalty method (PM), invokes an elasticity argument to produce a frictional contact force that factors in the local deformation and relative motion of the bodies in contact. We give a brief presentation of a DEM-PM contact model that includes multi-time-step tangential contact displacement history. We show that its implementation in an open-source simulation capability called Chrono is capable of accurately reproducing results from physical tests typical of the field of geomechanics, i.e., direct shear tests on a monodisperse material. Keeping track of the tangential contact displacement history emerges as a key element of the model. We show that identical simulations using contact models that include either no tangential contact displacement history or only single-time-step tangential contact displacement history are unable to accurately model the direct shear test.

ON THE INSTABILITY OF SPINNING CYLINDRICAL SHELLS PARTIALLY FILLED WITH LIQUID

The dynamics and stability of rotating circular cylindrical shells partially filled with ideal liquid is analyzed. The structural dynamics of the shell is modeled by using the first-order shear deformable shell theory and the flow inside the cylinder is simulated by a quasi 2D model based on the Navier–Stokes equations for ideal liquid. The fluid and structural models are combined using the nonpenetration condition of the flow on the wetted surface of the cylinder and the fluid pressure on the flexible shell. The obtained fluid–structure model is employed for the determination of the stable regions of the spinning frequency of the cylinder. A series of case studies are performed on the governing parameters of the instability of the cylinder and some conclusions are outlined.