Continuum skin effect in orthotropic elasticity

Manifested as the accumulation of bulk eigenstates at open boundaries, non-Hermitian skin effects have been studied extensively in various wave systems with either nonreciprocal couplings or on-site gain/loss effects. Here, by unraveling the space-time duality between the elastostatics of two-dimensional continua and the one-dimensional wave mechanics, we show a non-Hermitian topology inherent in the static deformation response of orthotropic, lossless elastic continua with geometry incompatibility between the fiber alignment and sample construction. The eigenstates of the open boundary system are spatially biased towards the boundary, whose degeneracy and chirality are governed by a spectral winding number unique to continuous systems. The directional accumulation of strain energy within a spatial trajectory excited by a quasistatic load emulates a dynamic skin effect, which can be exploited to program the material deformation response. Our study discloses an underlying non-Hermitian topology in static elastic continua with purely passive modulations, and it sheds light on the exploration of the skin effect in other continuous waveguides.