Benchmark solution
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Calculation method used for the reference solution
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The analytical reference solution can be deduced from a very simple calculation. Since the Poisson's ratio is zero, the uniaxial deformation is written as :math:`\varepsilon \mathrm{=}{U}_{0}\mathrm{/}\mathit{HD}\mathrm{=}–0.1\mathrm{/}2.` The pressure is then equal to :math:`E\varepsilon \mathrm{=}–{10}^{5}\mathit{Pa}`.


Benchmark results
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The contact pressure is constant and equal to :math:`–{10}^{5}\mathit{Pa}` over the entire contact surface. Likewise, the vertical displacement (according to :math:`y`) is constant on the contact surface and equal to :math:`{U}_{0}/2=–0.05\text{m}`.


Bibliographical reference
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1. N. EL- ABBASI and K.J. BATHE: "*Stability and Patch Test Performance of Contact Discretizations and a New Solution Algorithm* ", Computers & Structures, 79, 1473-1486, 2001