Find the relation between k and tx- find the reaction force

Question

Consider a plane-strain square element with unit depth as shown in the figure. Use the St. Venant-Kirchhoff isotropic material model with two Lame's constants λ and μ. A uniformly distributed force T_x (force per area) is horizontally applied at the top surface. Assuming it is a simple shear problem, the deformation of the element can be written as

(a) Find the relation between k and T_x,

(b) find the reaction force in the X₂ direction at the top surface, and

(c) compare the results with that of the linear elastic model.