Tensors associated with time-dependent stress

Abstract

It is assumed that six functional relations exist between the components of stress and their first m m material time derivatives and the gradients of displacement, velocity, acceleration, second acceleration, . . . , ( n − 1 ) \left ( {n - 1} \right ) th acceleration. It is shown that these relations may then be expressed as relations between the components of m + n + 2 m + n + 2 symmetric tensors if n m n \> m , and 2 m + 2 2m + 2 symmetric tensors if m n m \> n . Expressions for these tensors are obtained.