Janse van Rensburg, N.F. (Nicolaas)Du Toit, SonjaLabuschagne, Madelein2022-02-032021-10Janse van Rensburg, N.F., Du Toit, S. & Labuschagne, M. Local linear Timoshenko rod. Acta Mechanica 232, 4057–4079 (2021). https://doi.org/10.1007/s00707-021-03048-8.0001-5970 (print)1619-6937 (online)10.1007/s00707-021-03048-8http://hdl.handle.net/2263/83602In this article, we consider a variant of the Simo–Reissner theory for a rod but restrict the study to two-dimensional motion where the rod undergoes flexure, shear and extension but not torsion. Linear elastic behaviour is assumed to formulate constitutive equations; the constitutive equations of the Timoshenko theory adapted for extension and large rotation. We call the model the local linear Timoshenko rod model. We show that this model serves as a framework for a class of simpler mathematical models for slender solids in various applications. The advantage is that the more general model can be used to evaluate and compare the simpler models.en© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature. The original publication is available at : http://link.springer.com/journal/707.Simo–Reissner theory for a rodTwo-dimensional motionLinear elastic behaviourLocal linear Timoshenko rodTimoshenko theoryMathematical modelSlender solidsPostprint Article