An Analysis of Materials of Differential Type

Abstract

<p> An investigation of general Materials of Differential Type [MDT], and Motions With Constant Stretch History [MCSH] is presented. Rivlin-Ericksen tensors An are shown to result from a Taylor series expansion of the relative strain tensor Ct(T). Internal constraint in MDT is discussed. General Solutions of Motions of Differential Type are worked out. Dynamically possible stresses are found for certain irrotational motions. Theorems regarding necessary and sufficient conditions for MCSH are proved. A class of MCSH is introduced, and an approximate MCSH is suggested. Necessary equations regarding gradients of a scalar-valued tensor function are derived. </p>