Preface

Wave propagation in solids has been widely studied in the past and recent years and principal advances in this field have been achieved not only for the improvements of calculus methods, but also for the high progresses attained in the description of new types of materials with peculiar thermo-mechanical properties.

This book presents innovative and original research studies describing some enhancement in both directions. In particular, the first section is devoted to the propagation of linear and nonlinear waves in complex materials, porous media and cylindrical shells mainly, and related dispersion relations are deeply investigated; theoretical results are usually compared with numerical results and experimental data. Instead the second section is dedicated to principal advances and new applications for the study of wave processes in classical solids; applied numerical analyses and methods are linked to simulation applications and the attention is focused on explanation of the long tested approaches and comprehensive but succinct description in procedures such as finite element method. The emphasis is posed on various simulation availabilities as well as associated programs for simulation in the fields of seismology, damaging, geo- and nano-materials and multi-wave propagation.

The audience of this book includes students, professors, seismologists, engineers, and other advanced scientists with knowledge, and interest, of wave propagation in solids.

> **Pasquale Giovine** Department of Mechanics and Materials (MECMAT) "Mediterranean" University of Reggio Calabria, Italy

**Section 1** 

**Wave Propagation in Complex Materials** 

**Wave Propagation in Complex Materials** 

**Chapter 1** 

© 2012 Ba et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Nonlinear Acoustic Waves in Fluid-Saturated** 

**Porous Rocks – Poro-Acoustoelasticity Theory** 

The two elastic constants of bulk and shear moduli are insufficient to describe the nonlinear acoustic nature of solid materials under higher confining pressure. The theory of third-order elastic constants (nonlinear acoustics) has long been developed to analyze the velocity *vs* stress relationships in theoretical and experimental research for hyperelastic solid materials

The 3rd order constants theory in solid material was completed with the papers by Toupin and Bernstein, Jones and Kobett and Truesdell [8-10]. Truesdell used four 3rd-order elastic constants in his general theory for isotropic solid. Brugger [11] gave the thermodynamic definition of higher order elastic constants. In 1973, Green reviewed 3rd-order constants measurements of various crystals, and gave the relations between the 3rd-order constant

From late 1980s to the present, 3rd-order nonlinear elasticity theory has been applied to rock experiments [13, 14]. For the special case of porous solid materials, Winkler et al. [15] measured third order elastic constants based on pure solid's acoustoelasticity theory in a variety of dry rocks and found that pure solid's third-order elasticity could successfully describe dry rock's velocity-stress relationships. A similar approach performed on watersaturated rocks showed that traditional 3rd-order elasticity theory for the isotropic solid could not fully describe the stress dependence of velocities in water-saturated rocks [16]. For fluid-saturated porous material, as the confining pressure increases, the unrelaxed fluid's effect must be taken into account when probing into the quantitative relationships between

For the fluid/solid composite, Biot derived the two-phase wave equations on the basis of the linear elasticity, in which the coupling motion of solid and fluid was first analyzed. Based

and reproduction in any medium, provided the original work is properly cited.

Jing Ba, Hong Cao and Qizhen Du

http://dx.doi.org/10.5772/48550

**1. Introduction** 

[1-7].

Additional information is available at the end of the chapter

notations in isotropic solids by different authors [12].

two-phase rock's velocities and confining pressures.
