An elastic block of side length 1 is snugly fit between three fixed, frictionless walls and...

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An elastic block of side length 1 is snugly fit between three fixed, frictionless walls and a rigid plate on top, as shown in the figure on the left. A compressive force F is applied to the plate in the -z-direction and the block can deform freely in the x-direction. The material of the block is homogeneous, isotropic, and linear-elastic with Young's modulus E and Poisson's ratio v. The volumetric strain in the block is defined as: AV V = Exx + Eyy + Ezz where V is the original volume and AV is the volume change. Rigid plate F F Rigid plate Z Fixed wall Block y Fixed wall Fixed wall Block Fixed wall a) Find an expression for yy in terms of F, l, E, and v. b) Find an expression for zz in terms of F, 1, E, and v. c) Find an expression for xx in terms of F, l, E, and v. Fixed wall [5 points] [5 points] [5 points] d) The left wall is replaced with a uniform pressure p, as shown in the figure on the right. Find an expression for AV in terms of p, F, l, E, and v. [10 points] An elastic block of side length 1 is snugly fit between three fixed, frictionless walls and a rigid plate on top, as shown in the figure on the left. A compressive force F is applied to the plate in the -z-direction and the block can deform freely in the x-direction. The material of the block is homogeneous, isotropic, and linear-elastic with Young's modulus E and Poisson's ratio v. The volumetric strain in the block is defined as: AV V = Exx + Eyy + Ezz where V is the original volume and AV is the volume change. Rigid plate F F Rigid plate Z Fixed wall Block y Fixed wall Fixed wall Block Fixed wall a) Find an expression for yy in terms of F, l, E, and v. b) Find an expression for zz in terms of F, 1, E, and v. c) Find an expression for xx in terms of F, l, E, and v. Fixed wall [5 points] [5 points] [5 points] d) The left wall is replaced with a uniform pressure p, as shown in the figure on the right. Find an expression for AV in terms of p, F, l, E, and v. [10 points]