Similarities between force- and eigenstrain-induced dynamic displacements in linear elastic and viscoelastic bodies – part I: generalized body force analogies

Following a research strategy that dates back to Ernst Mach, we study similarities and analogies that may exist for linear elastic and viscoelastic bodies when dynamically loaded by forces and eigenstrains. Particularly, we treat equivalence of displacements in two problems with different sets of loadings and possibly different constitutive behavior. Special interest is given to the presence of singular waves. In the present first part of our treatise, we deal with generalized body force analogies, while displacement control, i.e. shape control and displacement tracking will be treated in the forthcoming second part of our study. Besides a review on previous work, with an emphasis on unification of works of our group, some novel results in the form of generalizations are presented, and perspectives for prospective future work are given.