A Justification of the Timoshenko Beam Model through $\mathbf{\Gamma }$-Convergence

We validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of $\mathrm{\Gamma }$-convergence theory, in two steps: firstly, we construct a suitable sequence of energy functionals; secondly, we show that this sequence $\mathrm{\Gamma }$-converges to a functional representing the energy of a Timoshenko beam.