The ideal pseudo-rigid continuum

Abstract

In the literature on pseudo-rigid bodies and their applications, it is generally assumed that these bodies can undergo only a restricted class of motions, without questioning how this restriction is to be strictly enforced. In 2004, I proposed in these Proceedings that such a restriction may be regarded as a ‘global constraint’ on a deformable continuum, and influenced by ideas of Antman & Marlow from the early 1990s, I assumed that the constraint is enforced by a field of reactive stresses, and I constructed a mathematical model that idealizes pseudo-rigid bodies as globally constrained continua of finite size. In a recent article in Proceedings of the Royal Society A , the validity of this model was challenged. Essentially, the controversy revolves around the issue of working definitions versus idealized mathematical models of pseudo-rigid bodies.