One-dimensional nonlocal elastodynamics: constitutive modeling, hyperbolicity, Riemann invariants, characteristic directions

Motivated from one-dimensional viscoelasticity theory we give general constitutive expressions for linear as well as nonlinear one-dimensional nonlocal elasticity theory. Substituting these constitutive laws to the elastodynamic equations, we arrive at a first-order system of integrodifferential equations for which we give conditions for hyperbolicity. We evaluate Riemann invariants and characteristic directions and write the system of equations using Riemann invariants.