#### Vol. 11, No. 5, 2016

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Propagation of waves in masonry-like solids

### Maria Girardi, Cristina Padovani and Daniele Pellegrini

Vol. 11 (2016), No. 5, 505–533
##### Abstract

This paper deals with the propagation of progressive elastic waves in masonry-like solids. The constitutive equation of masonry-like materials models the mechanical behavior of materials (such as masonry, rocks and stones) that do not withstand tensile stresses. The stress function $\mathbb{T}$ delivering the Cauchy stress $\mathbf{T}$ corresponding to an infinitesimal strain tensor $\mathbf{E}$ is nonlinear and differentiable on an open subset W of the set of all strains. We consider the propagation of small amplitude elastic waves in a masonry-like body subjected to a given homogenous strain field $\mathbf{E}$ belonging to W. We obtain the propagation condition, which involves the acoustic tensor $\mathbf{A}$($\mathbf{E}$,$\phantom{\rule{0.3em}{0ex}}\mathbf{n}$), which depends on both $\mathbf{E}$ and the direction of propagation $\mathbf{n}$, and prove that, due to the presence of cracks, the wave propagation velocities in masonry are lower than in a linear elastic material.

##### Keywords
nonlinear elasticity, masonry-like materials, progressive waves, acoustic tensor