Surface waves in deformed Bell materials

Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain. The surface wave propagates in a principal direction of strain and is attenuated in another principal direction, orthogonal to the free surface. For these waves, the secular equation giving the speed of propagation is established by the method of first integrals. This equation is not the same as the secular equation for incompressible half-spaces, even though the Bell constraint and the incompressibility constraint coincide in the isotropic infinitesimal limit

The dynamics of a shear band

A shear band of finite length, formed inside a ductile material at a certain stage of a con- tinued homogeneous strain, provides a dynamic perturbation to an incident wave field, which strongly influences the dynamics of the material and affects its path to failure. The investigation of this perturbation is presented for a ductile metal, with reference to the incremental mechanics of a material obeying the J 2-deformation theory of plasticity (a special form of prestressed, elastic, anisotropic, and incompressible solid). The treatment originates from the derivation of integral representations relating the incremental mechan- ical fields at every point of the medium to the incremental displacement jump across the shear band faces, generated by an impinging wave. The boundary integral equations (under the plane strain assumption) are numerically approached through a collocation technique, which keeps into account the singularity at the shear band tips and permits the analysis of an incident wave impinging a shear band. It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, par- allel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band

Surface waves in orthotropic incompressible materials

The secular equation for surface acoustic waves propagating on an orthotropic incompressible half-space is derived in a direct manner, using the method of first integrals

Band gaps in the relaxed linear micromorphic continuum

In this note we show that the relaxed linear micromorphic model recently proposed by the authors can be suitably used to describe the presence of band-gaps in metamaterials with microstructures in which strong contrasts of the mechanical properties are present (e.g. phononic crystals and lattice structures). This relaxed micromorphic model only has 6 constitutive parameters instead of 18 parameters needed in Mindlin- and Eringen-type classical micromorphic models. We show that the onset of band-gaps is related to a unique constitutive parameter, the Cosserat couple modulus $\mu_{c}$ which starts to account for band-gaps when reaching a suitable threshold value. The limited number of parameters of our model, as well as the specific effect of some of them on wave propagation can be seen as an important step towards indirect measurement campaigns

Generation of seismic waves by explosions in prestressed media

The mechanisms of generation of seismic waves by an explosion in prestressed media are studied using both field seismograms and controlled laboratory experiments. LRSM seismograms from the underground nuclear explosion BILBY are analyzed to determine the source parameters from the radiated Love and Rayleigh waves. From the normalized amplitudes of Rayleigh waves as well as the Love-Rayleigh amplitude ratios, a composite source consisting of an isotropic explosion and a double couple is synthesized for the explosion and the associated tectonic strain release. From BILBY and other explosions studied by similar techniques, it is found that the tectonic strain energy release strongly depends on the medium properties in the immediate vicinity of the explosion. For “harder” media (such as granite) the tectonic strain energy release and the relative amplitude of Love waves are significantly higher than for softer media such as alluvium. Source-time functions of Love waves associated with the explosions are closer to time functions of earthquakes than to those of explosions. The mechanisms of the pre-existing strain energy release by explosive sources are studied in two separate laboratory experiments. In a one-dimensional experiment where an explosive source is detonated in a rod stressed in torsion, the S-wave amplitudes are found to be linearly proportional to prestrain. In the second experiment, radiation of seismic waves and the near-source phenomena of explosive sources in prestressed plates are studied by photoelastic as well as strain gauge observations. The generation of S-waves is greatly enhanced by the prestress condition. It is found that extended cracking (faulting) occurs along directions determined by the prestress field. The transverse (SH) waves are generated primarily by the relaxation of the stress field along these cracks. The explosion-generated cavity alone could not account for the radiated transverse seismic energy

Anomalous surface waves from Lop Nor nuclear explosions: Observations and numerical modeling

Surface waves from the Chinese test site of Lop Nor are analyzed using long-period and broadband stations located at regional and teleseismic distances and at different azimuths. For most azimuths, strong Love waves between 0.02 and 0.045 Hz are observed with an amplitude of up to 10 times that of the Rayleigh waves. In addition, an anomalous early Rayleigh wave train is observed at some stations in western Europe. Due to a particularly favorable station and source configuration, it is possible to isolate the areas where the anomalies are created. The high-amplitude Love waves must be attributed to either source effects or path effects immediately north of Lop Nor. The early wave train is shown to be due to a partial energy conversion between Love and Rayleigh waves, probably at the Tornquist Zone. To estimate the possible contribution from surface wave conversions to the observed anomalies, numerical simulations are carried out with the indirect boundary element method. The simulations show that a relatively small variation of crustal thickness can induce Rayleigh to Love wave conversions between 0.02 and 0.1 Hz frequency. The calculated amplitudes of the Love waves are significant (up to 35% of the amplitude of the incoming Rayleigh waves), but they are too small to fit the observed amplitude anomaly. The observed converted waves and the numerical results nevertheless indicate that surface wave conversions can be significant across strong lateral crustal heterogeneities. In particular, the conversions due to changes in crustal thickness are located in the period interval which is routinely used for estimation of Ms