Controllable Motions of Compressible Simple Materials of Various Types

Controllable Motions of Compressible Simple Materials of Various Types. I t is shown tha t a motion is possible in every compressible homogeneous isotropie simple solid having a certain range of memory, in the presence of a constant body force field, if and only if it is homogeneous and uniformly accelerated after a certain time. I n the class of solids having perfect memory, the only motion of this kind which can be smoothly ini t iated in a body at rest is a rigid one. For the class of solids having finite memory of durat ion T and init ially at rest, the motions of the type considered need be homogeneous and uniformly accelerated only after t ime T. For those solids having fading memory, the motion must reduce to a fixed homogeneous deformation. Similar results are developed for simple fluids and anisotropie simple solids.