Uniqueness in Kelvin–Voigt elasticity with higher gradients

We investigate uniqueness in theories of linear elasticity with a Kelvin–Voigt effect, assuming the elastic coefficients are not sign-definite. This is important with modern materials such as auxetic materials where Poisson’s ratio may be negative. In addition to studying classical linear elasticity with Green–Naghdi thermodynamics of type II, we also analyse a theory which incorporates higher gradients of both elastic displacement and temperature. To allow for non-sign definite elastic coefficients we employ a logarithmic convexity technique. Due to the special nature of the governing partial differential equations it is necessary to construct a novel functional with which one may use logarithmic convexity.