Editing Rolling (section)

== Deformable bodies ==

When an axisymmetric deformable body [[Contact mechanics|contacts]] a surface, an [[Contact patch|interface]] is formed through which normal and shear forces may be transmitted. For example, a [[tire]] contacting the road carries the weight (normal load) of the car as well as any shear forces arising due to acceleration, braking or steering.  The deformations and motions in a steady rolling body can be efficiently characterized using an [[Lagrangian and Eulerian specification of the flow field|Eulerian]] description of rigid body rotation and a [[Lagrangian and Eulerian specification of the flow field|Lagrangian]] description of deformation.<ref>{{cite journal |last1=Padovan |first1=J. |last2=Zeid |first2=I. |title=Finite element modeling of rolling contact |journal=Computers & Structures |date=1980 |volume=12 |issue=1 |pages=77–83 |doi=10.1016/0045-7949(80)90095-4 |url=https://www.sciencedirect.com/science/article/abs/pii/0045794980900954 |access-date=28 December 2022|url-access=subscription }}</ref><ref>{{cite journal |last1=Qi |first1=J. |last2=Herron |first2=J. R. |last3=Sansalone |first3=K. H. |last4=Mars |first4=W. V. |last5=Du |first5=Z. Z. |last6=Snyman |first6=M. |last7=Surendranath |first7=H. |title=Validation of a Steady-State Transport Analysis for Rolling Treaded Tires |journal=Tire Science and Technology |date=2007 |volume=35 |issue=3 |pages=183–208 |doi=10.2346/1.2768974 |url=https://meridian.allenpress.com/tst/article/35/3/183/187072/Validation-of-a-Steady-State-Transport-Analysis |access-date=28 December 2022|url-access=subscription }}</ref> This approach greatly simplifies analysis by eliminating time-dependence, resulting in displacement, velocity, stress and strain fields that vary only spatially. Analysis procedures for [[finite element analysis]] of steady state rolling were first developed by [[Joseph Padovan|Padovan]], and are now featured in several commercial codes.