Figure 1
From: Nonreciprocal elasticity and the realization of static and dynamic nonreciprocity
Maxwell–Betti reciprocal theorem. (a) Linear elastic materials versus (b) nonlinear elastic materials according to the Maxwell–Betti reciprocal theorem. (a) A linear elastic material that is subjected to two different forces, \({F}_{A}\ne {F}_{B}\). At instant \({t}_{1}\), the material exhibited a displacement at point B of \({u}_{B}\) when subjected to a force \({F}_{A}\) at point A. According to the Maxwell–Betti reciprocal theorem, we expect that the material deforms at instant \({t}_{2}\) such that its displacement at point A due to an applied force \({F}_{B}\) at point B is \({u}_{A}={F}_{A}{u}_{B}/{F}_{B}\) (thus, \({F}_{B}{u}_{A}={F}_{A}{u}_{B}\)). (b) A nonlinear elastic material that is subjected to two different forces, \({F}_{A}\ne {F}_{B}\). This material disobeys the Maxwell–Betti reciprocal theorem such that \({F}_{B}{u}_{A}\ne {F}_{A}{u}_{B}\).
