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hw8 - occurs when one applies approximately 4.5 kg of...

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ME 577 – Human Motion Kinetics Homework #8 Due Friday, April 22 1. Derive an expression for the apparent modulus in terms of the microscale modulus for the open cell hexagonal cellular solid shown below. Fig. 1 Schematic of a hexagonal open cell cellular solid model (a) for porous materials. The structure has a depth, w , and the oblique and vertical struts have length, L and h , respectively. The angle between oblique struts and the horizontal is θ . You may assume that each strut is made out of a homogeneous material with diameter d 0 (not two materials as shown in (b)).
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2. Hertz Contact Theory. In 1973, an experiment was performed to estimate the mechanical properties of the cartilage on the tibial plateau. They determined that failure of the cartilage
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Unformatted text preview: occurs when one applies approximately 4.5 kg of “pressure” to a steel ball with a 1.5 mm diameter. A similar result was obtained when they pressed a 3 mm diameter steel ball with a “pressure” of 9.5 kg. You may assume that the cartilage has a modulus of 1.12 MPa. If the tibial plateau is flat, determine the contact radius, indentation depth, peak contact pressure, and peak tensile stress at the failure point. p = 3 F 2 π a 2 σ tensile = 1 2 1 − 2 ν ( ) p 3. Re-derive the governing differential equations for a blow to the helmet. Explain the assumptions as you go. Extra credit: plug the equations into Matlab and solve them. Extra, extra credit: how do the equations change if you add a dashpot into the padding of the helmet?...
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