Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials.

We consider the time evolution of a one dimensional n-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, referred to as microscopic because they are living on a smaller space scale. We validate our construction by proving a convergence theorem of the microscopic system to the given continuum, as the scale parameter goes to zero. [ABSTRACT FROM AUTHOR]