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Consider a body B of infinite domain, which at time t = 0 contains a spherical cavity of radius A centered at a point O, as in the figure below.
Consider a body B of infinite domain, which at time t = 0 contains a sphericalcavity of radius A centered at a point O, as in the figure below. Without loss ofgenerality, let the two orthonormal bases EA and ei coincide and originate at O.At time t = 0 an explosion occurs inside the cavity and produces a sphericallysymmetric motion of the formx =f(R, t)RX , (1)where R = pXAXA is the magnitude of the position vector X for an arbitrarypoint P in the reference configuration. Since it can be easily verified from (1)that the cavity remains spherical at all times, let its radius be denoted by a(t).ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€ô€€€OXP(a) Determine the deformation gradient tensor F.(b) Find the velocity and acceleration fields using the referential and spatialdescription.(c) If the motion is assumed isochoric, show that
