I am trying to solve the problem of the mud cracks in the attached pdf, but I am not really sure I have the right understanding of the problem. As far as I can understand we look at what will happen when mud dries and contract. The contraction of the mud modifies the strain by a term β on the RHS of the equation for uxx, which is the strain in the x-direction. However there is also a stress term, which I interpret like this. When the mud contracts the contact force with the ground will create a shear stress in the mud opposing the contraction. But I am not sure if this is the correct understanding. Either way I am not sure how to approach the question: Formulate the force balance equation for the system. There is a force opposing the contraction, but are there other forces?