# Dynamics of Pseudo-Rigid Bodies

>Research in the dynamics of coarsely deformable continua, such as
pseudo-rigid bodies and Cosserat points, is driven by the need to develop
inexpensive, yet sufficiently accurate models of the long-term dynamics of
particulates and other discrete systems, especially in the presence of
boundary interactions, such as contact. This type of analysis is particularly
relevant for systems in which rigid-body modeling is insufficient to
capture the overall dynamic behavior, while full continuum modeling is
computationally intractable. Representative applications
include the flow of rocks, sands, and aggregates, the dynamics of traffic
accidents involving platoons of vehicles, etc..

The following animation depicts the impact between two
non-linearly elastic pseudo-rigid bodies which, in their reference
configuration, have the shape of identical superellipsoids:

### Related Publications:

E. Kanso and P. Papadopoulos.
``Dynamics of Pseudo-rigid Ball Impact on Rigid Foundation'',
Int. J. Nonl. Mech., 39,
pp. 299-309, (2004).

P. Papadopoulos.
``On a Class of Higher-order Pseudo-rigid Bodies'',
Math. Mech. Sol., 6, pp. 631-640, (2001).

J.M. Solberg and P. Papadopoulos.
``Impact of an Elastic Pseudo-rigid Body on a Rigid Foundation'',
Int. J. Engrg. Sci., 38, pp. 589-603, (2000).

P.C. Varadi, G.-J. Lo, O.M. O'Reilly and P. Papadopoulos.
``A Novel Approach to Vehicle Dynamics using the Theory of a Cosserat Point
and its Application to Collision Analyses of Platooning Vehicles'',
Veh. Sys. Dyn., 32, pp. 85-108, (1999).

J.M. Solberg and P. Papadopoulos.
``A Simple Finite Element-based Framework for the Analysis of Elastic
Pseudo-rigid Bodies'',
Int. J. Num. Meth. Engrg., 45, pp. 1297-1314, (1999).