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 [3].

  • [1] H. Berjamin, N. Favrie, B. Lombard, G. Chiavassa, "Nonlinear waves in solids with slow dynamics: an internal-variable model", Proceedings Royal Society London A 473 (2017), 20170024.
  • [2] H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie, "Modeling longitudinal wave propagation in nonlinear viscoelastic solids with softening", International Journal of Solids and Structures 141-142 (2018), 35-44.
  • [3] H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie, "A finite-volume approach to 1D nonlinear elastic waves: application to slow dynamics", Acta Acustica united with Acustica, 104 (2018), 561-570.
  • [4] H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie, "Plane-strain waves in nonlinear elastic solids with softening", Wave Motion 89 (2019), 65-78.