For an isotropic elastic medium subjected to a hydrostatic state of stress, σxx = σyy = σzz = −p and σxy = σxz = σyz = 0, where p denotes pressure [FL−2]. Show that for this state of stress p = −Ke, where K = E/[3(1 − 2ν)] is the bulk modulus and e = ϵxx + ϵyy + ϵzz is the classical small-displacement cubical strain (also called the volumetric strain).
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