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Resolving force indeterminacy in contact dynamics using compatibility conditions

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Abstract

Contact dynamics (CD) is a powerful method to solve the dynamics of large systems of colliding rigid bodies. CD can be computationally more efficient than classical penalty-based discrete element methods (DEM) for simulating contact between stiff materials such as rock, glass, or engineering metals. However, by idealizing bodies as perfectly rigid, contact forces computed by CD can be non-unique due to indeterminacy in the contact network, which is a common occurence in dense granular flows. We propose a frictionless CD method that is designed to identify only the unique set of contact forces that would be predicted by a soft particle method, such as DEM, in the limit of large stiffness. The method involves applying an elastic compatibility condition to the contact forces, which maintains no-penetration constraints but filters out force distributions that could not have arisen from stiff elastic contacts. The method can be used as a post-processing step that could be integrated into existing CD codes with minimal effort. We demonstrate its efficacy in a variety of indeterminate problems, including some involving multiple materials, non-spherical shapes, and nonlinear contact constitutive laws.

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Notes

  1. An interesting observation, however, is that the impulse delivered by the elastic part of the constitutive law is impacted by changing the damping behavior. The effect of viscous damping appears to be, as expected, dissipating energy during a collision by affecting the path c(t).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA

    Tyler Olsen & Ken Kamrin

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  1. Tyler Olsen
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  2. Ken Kamrin
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Correspondence to Ken Kamrin.

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Olsen, T., Kamrin, K. Resolving force indeterminacy in contact dynamics using compatibility conditions. Granular Matter 20, 69 (2018). https://doi.org/10.1007/s10035-018-0839-5

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