Computational Contact Mechanics: Advances and Frontiers in Modeling Contact (14w5147)
Vincent Acary (INRIA Rhône-Alpes)
Robert Bridson (University of British Columbia)
Danny Kaufman (Columbia University)
Jong-Shi Pang (University of Southern California)
Jeff Trinkle (Rensselaer Polytechnic Institute)
Modeling the complexities of contacting behavior is an outstanding computational challenge critical to a wide variety of application areas including medical simulation, robotics, structural engineering, biomechanics, computer animation, haptics, and industrial manufacturing. Accurately capturing the effects of contact processes is essential for the physical modeling of many poorly understood phenomena at all scales. These include prosaic domestic phenomena such as the chattering of chalk on a board and the excitation of violin strings, large-scale geophysical phenomena such as earthquakes and the the calving of icebergs (crucial to understanding the rapid changes in the Antarctic Ice Sheet), as well as the small-scale dissipation in high-frequency MEMS and NEMS devices, to name just a few.
Indeed, contact is ubiquitous and often unavoidable and yet accurately modeling contacting systems continues to stretch the limits of available methods. In part this is due to the unique hurdles posed by contact problems. Contact and related contact-driven dissipative phenomena introduce nonsmoothness, nonconvexity, and strong nonlinearity into many already complex mechanical systems.
We propose a workshop to address these challenges in order to enable the design and analysis of predictive and efficient computational methods for contact simulation. Our objective is to bring active researchers in contact mechanics together, along with practitioners in aligned areas, to assess the state of the art, discuss technical grand challenges, consider compelling applications, and to chart a course to attack identified open problems.
Advancing computational contact mechanics is a fundamentally multidisciplinary effort. Nevertheless, we observe that disparate research groups in contact modeling have evolved independently with largely complementary scientific skill sets. Thus we expect this workshop to both forge new interdisciplinary links between mathematicians, computational scientists, and mechanicians, and enrich ongoing collaborative efforts.
In particular, specific goals of this workshop will include consideration of a trio of identified high-need areas:
1. Well-posedness, validation, and verification of contact models.
Standard notions of well-posedness are challenged by contact problems where non-uniqueness is often the norm and existence remains an open question for many models regularly employed. Nevertheless, physical systems must be modeled and, in turn, these models will necessarily be discretized and simulated. It is thus important to consider questions of how these models can be best validated and verified. We are inviting mathematicians who have conducted significant research on contact model existence questions as well as mechanicians and industrial colleagues who regularly employ contact simulation in intensive computing environments for computational experiments and industrial applications. We expect to open a dialogue in which the entire research pipeline can be considered from the theoretical considerations of model formulation and analysis through to end user applications.
2. Numerical integration of nonsmooth systems.
Collisions and impacts introduce sharp, often discontinuous, jumps in state. Under discretization these contact forces are often generated by corresponding nonsmooth interaction potentials with unbounded second derivatives. Such models thus challenge many of the standard smooth assumptions that guarantee good behavior in favored numerical integration methods. Bringing together foremost experts in the area, we will review recent developments in nonsmooth numerical integration and consider the next steps towards ensuring stability, structure preservation, and accuracy when simulating contact.
3. Scalable optimization methods for inequality constrained dynamics.
Discretized contacting systems generally require the solution of constrained optimization problems whose form and scale exercise the limits of existing technologies. Indeed, robust and accurate numerical solutions to many of the large scale optimization problems we generally encounter in high-dimensional contact simulations are often lacking. Nevertheless, many unique structural properties exist and can be leveraged in such problems. Lead by invited area experts in constrained optimization will review related developments in optimization theory, discuss the limitations and suitability of current methods, and consider the specialized properties and requirements of contact derived optimization problems for the future development of suitable numerical methods.
Towards these objectives we plan to invite experts who have conducted significant research in the various areas of contact mechanics, and the aligned topics of constrained optimization and numerical integration. We will be including active researchers evenly distributed from the many diverse communities currently contributing to the area. Twenty-two individuals have already been contacted and agreed to participate. Their names are shown at the top of the list below. Additional names of people who will be invited are shown following those twenty-two names. We expect to have a total of forty-two participants from all over the world.
By bridging communities and bringing these researchers together in the focused environment of BIRS we hope to foster the rapid advance of our field well beyond the expected progress of independent research threads cross-fertilized by publication and sporadic conference exchanges. We anticipate that these advances will lead to the accurate and reliable computational tools currently demanded by today’s contact intensive scientific and industrial applications.