||The title of the present text is somewhat unfamiliar and needs to be elucidated first, before describing briefly the aims and scope of this work.
Almost half-a-century ago, the late great J. D. Eshelby advanced the notion of a force on a defect or a singularity in a stressed solid. This notion is radically different from the usual Galilean or Newtonian concept of a force, which engineers of various disciplines encounter daily in their work, concerned perhaps with the determination of flight trajectories of launched satellites, or with stress, deformation and structural stability analysis of high-rise buildings. The Eshelby-type force is always to be understood as a relative change of the total energy of a given system with respect to some quantity which alters the configuration of that system. The latter quantity might be the displacement of a foreign or missing atom in a lattice, the change in location of a dislocation, the change in size or shape of a crack, cavity or inclusion or the change in location of a phase boundary in a material. All such changes of configuration of certain objects occur within the material in which they find themselves, by contrast to changes in the configuation of a bridge under some Newtonian loadings, which occur in what might be called the physical space of our surroundings, in which the bridge finds itself and in which Newton's laws are valid.
Thus the term space, whether physical or material, is used here not in a strictly mathematical sense, as possessing a certain metric and possibly other properties, but in essentially a descriptive meaning.
The realization that it is helpful, in fact most desirable, to distinguish between configurational, Eshelbian forces on one hand, and the common, usual Newtonian forces on the other, may lead naturally to the terminology of material forces on one hand, and physical forces on the other. And, proceeding along this line of thought, it is intriguing to investigate the possibility of constructing the edifice of Mechanics in Material Space in parallel (or in analogy) with the well-established classical mechanics, which now, for reasons of symmetry and aesthetics, shall be referred to as Mechanics in Physical Space.