Logarithmic Convexity, Continuous Dependence and Uniqueness in Elastodynamics with Higher Gradients

Abstract We investigate Hölder continuous dependence in theories of linear elastodynamics, assuming the elastic coefficients are not sign-definite. This is important with modern products such as auxetic materials where Poisson’s ratio may be negative. This study focusses on a class of linear elastic bodies where there are gradients of the strain and second gradients of the strain, and we also analyse a theory of elastodynamics with strain gradients where voids are also present in the body.