Determination of Constitutive Relationships with Multiple Gauges in Nondivergent Waves

Abstract

Constitutive relationships are calculated from multiple Lagrangian gauge records obtained in one‐dimensional wave experiments by integrating the flow equations expressing conservation of mass and momentum along a particle path. Specifically for flow adjacent to a constant state, particle velocity‐stress relationships are calculated from multiple stress‐time profiles by integrating the combined mass and momentum equations, and specific volume‐particle velocity relationships are calculated from multiple particle velocity‐time profiles by integrating the continuity equation; but these relationships are in general approximate because the material derivatives required to perform the integrations are generated from gauges separated by finite distances. Steady‐state, simple isentropic, and simple nonisentropic waves are shown to be the only flows that allow constitutive relationships among stress, particle velocity, and specific volume to be determined exactly with either a pair of stress gauges or a pair of particle velocity gauges. A general procedure for the determination of constitutive relationships with three gauges is formulated and tested with an exact solution for a strong decaying shock wave to indicate errors resulting from the finite separation of gauges when constitutive relationships cannot be calculated exactly.