Nonlinear waves in solids with softening
Bruno Lombard (LMA, Marseille)
Wave propagation in damaged media, such as rocks and concrete, exhibits a strong nonlinear behavior.
Besides the classical nonlinearity, it is observed that the speed of sound diminishes slowly under a dynamic loading.
To reproduce this non-classical behavior of time-dependent material, an internal-variable model of continuum is developed,
including a constitutive law for the stress in finite deformation (for instance of Murnaghan's type), and an evolution equation for the internal variable [1,2,4].
Doing so leads to a first-order hyperbolic system with relaxation. A finite-volume method is developed to solve these equations.
Simulation results are compared with experimental results of nonlinear acoustics .