Compliant contact force models in multibody dynamics : evolution of the Hertz contact theory

Over the last decades, several compliant contact force models have been proposed. However, no complete and systematic comparison has been done on these models, which provides information on their range of application and accuracy for use in different contact scenarios. Thus, the selection of an appropriate model for a given contact problem is still an important and challenging issue to be addressed. The Hertzian contact theory remains the foundation for almost all of the available force models, but by itself, it is not appropriate for most impacts in practice, due to the amount of energy dissipated during the impact. A good number of contact force models have been offered that augment the Hertzian law with a damping term to accommodate the energy loss during the impact process for small or moderate impact velocities. In this work, the main issues associated with the most common compliant contact force models of this type are analyzed. Results in terms of the dynamic simulations of multibody systems are presented, which allow for the comparison of the similarities and differences among the models considered.Fundação para a Ciência e a Tecnologia (FCT) - DACHOR - Multibody Dynamics and Control of Hybrid Active Orthoses (MIT-Pt/BSHHMS/0042/2008), BIOJOINTS - Development of advanced biological joint models for human locomotion biomechanics (PTDC/EMEPME/ 099764/2008), SFRH/BD/40164/2007, SFRH/BD/64477/200

Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics

This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. The present formulation also includes solid-fluid interactions and material interfaces and, in addition, lays the groundwork for a treatment of shocks

A NonSmooth Contact Dynamics-based multi-domain solver: Code coupling (Xper) and application to fracture

International audienceThis paper presents a micromechanical modeling strategy for complex multibody interactions and the associated numerical framework. The strategy rests on a periodic multibody method in the framework of the NonSmooth Contact Dynamics approach of Moreau (1988) extended to classical domain decomposition problems. Many complex interactions can be taken into account: interactions between discrete elements, between discrete or rigid bodies, (quasistatic) contact or impact, friction or adhesion, decohesion (cracking), etc. The associated numerical platform, Xper, is composed of three independent libraries with Object Oriented Programming. The ability of this computational approach is illustrated by two examples of fracture in heterogeneous materials.Cet article présente d’une part, une stratégie de modélisation dédiée à la simulation micromécanique des interactions entre corps, et, d’autre part, sa mise en oeuvre numérique. Cette stratégie repose sur une formulation de type décomposition de domaines d’une méthode multicorps périodique dans le cadre de l’approche NonSmooth Contact Dynamics de Moreau (1988). Les potentialités de cette méthode sont illustrées par la complexité des interactions possibles : interactions entre éléments d’une discrétisation, entre corps discrétisés ou rigides, en compression (contact) lente ou sous impact, en glissement (frottement) ou en traction (fissuration-rupture), etc. La plateforme numérique associée, Xper, repose sur une architecture orientée objet composée de bibliothèques indépendantes. La pertinence numérique de l’approche est illustrée sur des exemples de fissuration de matériaux hétérogènes

Solving variational inequalities and cone complementarity problems in nonsmooth dynamics using the alternating direction method of multipliers

This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set-valued forces. For the special case of hard frictional contacts, the method solves a second order cone complementarity problem. We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method that draws on few computational primitives. In order to improve computational performance, we reformulated the original ADMM scheme in order to exploit the sparsity of constraint jacobians and we added optimizations such as warm starting and adaptive step scaling. The proposed method can be used in scenarios that pose major difficulties to other methods available in literature for complementarity in contact dynamics, namely when using very stiff finite elements and when simulating articulated mechanisms with odd mass ratios. The method can have applications in the fields of robotics, vehicle dynamics, virtual reality, and multiphysics simulation in general

Exomars Rover Mechanical Modeling with Siconos

This document contains specification and documentation of the tests performed on the exomars planetary rover model using Siconos software. Siconos is an open source scientific software targeted at modeling and simulating nonsmooth dynamical systems. The advantage of using Siconos for mechanical simulations is that it offers efficient friction-contact nonsmooth models. Performing mechanical simulations of the exomars rover appears to be of great importance with respect to verifying its design and estimating energy consumption. Seven different scenarios have been defined in order to simulate the mechanical behaviour of the exomars rover. Dynamics and kinematics models of the exomars rover have been created using HuMAnS software and implemented inside Siconos using its C code generator as plugin functions. The intention of this report is to create a common reference and unification of mechanical tests of the exomars rover across different simulation platforms

Application of the nonsmooth dynamics approach to model and analyze the contact-impact events in cam-follower systems

The dynamic modeling and analysis of planar rigid multibody systems that experience contact-impact events is presented and discussed throughout this work. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. Rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the forces and impulses in the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini’s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The resulting contact-impact problem is formulated and solved as an augmented Lagrangian approach, which is embedded in the Moreau time-stepping method. The effectiveness of the methodologies presented in this work is demonstrated throughout the dynamic simulation of a cam-follower system of an industrial cutting file machine.This work is supported by the Portuguese Foundation for the Science and Technology under the research project BIOJOINTS (PTDC/EME-PME/099764/2008). The first author expresses his gratitude to the Portuguese Foundation for the Science and Technology for the postdoctoral scholarship (SFRH/BPD/40067/2007). This research was conducted during a post-doctoral stay of the first author with Professor Christoph Glocker at the Center of Mechanics, ETH Zurich

6D Frictional Contact for Rigid Bodies

International audienceWe present a new approach to modeling contact between rigid objects that augments an individual Coulomb friction point-contact model with rolling and spinning friction constraints. Starting from the intersection volume, we compute a contact normal from the volume gradient. We compute a contact position from the first moment of the intersection volume, and approximate the extent of the contact patch from the second moment of the intersection volume. By incorporating knowledge of the contact patch into a point contact Coulomb friction formulation, we produce a 6D constraint that provides appropriate limits on torques to accommodate displacement of the center of pressure within the contact patch, while also providing a rotational torque due to dry friction to resist spinning. A collection of examples demonstrate the power and benefits of this simple formulation