In this book, we are interested in the analysis of vibroacoustic systems, which are also called structural acoustic systems or fluid-structure interactions for compressible fluid (gas or liquid). Vibroacoustics concerns noise and vibration of structural systems coupled with external and/or internal acoustic fluids. Computational vibroacoustics is understood as the numerical methods solving the equations of physics corresponding to vibroacoustics of complex structures. Complex structures are encountered in many industries for which vibroacoustic numerical simulations play an important role in design and certification, such as the aerospace industry (aircrafts, helicopters, launchers, satellites), automotive industry (automobiles, trucks), railway industry (high speed trains), and naval industry (ships, submarines), as well as in energy production industries (electric power plants).

Since we are interested in the analysis of general complex structural systems in the sense of computational methods defined here, we do not consider analytical or semianalytical methods devoted to structures with simple geometry, asymptoticmethods mainly adapted to the high-frequency range (statistical energy analysis, diffusion of energy, etc.) and approaches that imply them. Concerning the latter, the coupling of the local dynamic equilibrium equation (finite element method) and power balances (implemented in the spirit of the statistical energy analysis) have been analyzed in Soize (1998); Shorter and Langley (2005); Cotoni et al. (2007).

UNCERTAINTY AND VARIABILITY

The designed vibroacoustic system is used to manufacture the real vibroacoustic system and to construct the nominal computational vibroacoustic model (also called the mean computational vibroacoustic model or sometime the mean model) using a mathematical-mechanical modeling process for which the main objective is the prediction of the responses of the real vibroacoustic system. This system can exhibit a variability in its responses due to fluctuations in the manufacturing process and due to small variations of the configuration around a nominal configuration associated with the designed vibroacoustic system. The mean computational model that results from a mathematical-mechanical modeling process of the designed vibroacoustic system has parameters (such as geometry, mechanical properties, and boundary conditions) that can be uncertain (for example, parameters related to the structure, the internal acoustic fluid, the wall acoustic impedance). In this case, there are uncertainties on the computational vibroacoustic model parameters, also called uncertainties on the system parameters. On the other hand, the modeling process induces some modeling errors defined as the model uncertainties. Figure 9.1 summarizes the two types of uncertainties in a computational model and the variabilities of a real system.

Biological materials

Nature has evolved a palette of biological materials to address different structural requirements such as:

• hardness,

• toughness,

• stretchability,

• light weight.

The intricate and ingenious hierarchical structure is responsible for the outstanding performance. Toughness is conferred by the presence of controlled interfacial features, buckling resistance can be achieved by filling a slender column with a lightweight foam, and armor protection is accomplished by small dermal plates with unique attachment arrangements, resulting in controlled and prescribed flexibility. In Chapters 6–10 we present and interpret selected examples of biological materials. In addition to the structural requirements, there are also functional requirements such as adhesion and optical properties.

The number of elements and compounds that can be synthesized at ambient temperature and in aqueous environments is limited, and therefore the architecture of the structure is of utmost importance.

We introduce the different classes of biological materials in these chapters, following the Wegst–Ashby classification. These were defined in Chapter 2 (Fig. 2.11) as:

• biominerals (Chapters 6 and 7),

• biopolymers (Chapter 8),

• bioelastomers (Chapter 9),

• biocellular materials (foams) (Chapter 10).

Introduction

It is a misunderstanding to think that the ultimate goal of biomimetics is to reproduce living organisms. There are essential differences, as we list in the following.

What we try to do is to emulate the design and assembly principles used in natural materials. In this book we have seen many examples where superior properties are obtained through a hierarchical design and ingenious solutions. Bone, nacre, and dentin have toughnesses significantly superior to those of the mineral constituents, hydroxyapatite and calcium carbonate. Silk reaches strengths higher than 1 GPa using the weak hydrogen bond, through the existence of nano-scale β-sheet crystals with proper dimensions. Bioinspiration requires identification, understanding, and quantification of natural design principles and their replication in synthetic materials, taking into account the intrinsic properties (Studart, 2012). This approach is being pursued not only for structural materials, but also for functional materials and devices. The areas of sensing, optics, architecture, and robotics are exploring biological solutions.

Introduction

Hydroxylapatite or hydroxyapatite (HAP) is a calcium-phosphate-based mineral of the apatite family. Its chemical formula is Ca10(PO4)6(OH)2. It can be found widely in nature and is the major component of bone, enamel, and dentin in teeth, antler, ganoid fish scales (in alligator gar and Senegal bichir), turtle shells, and armadillo and alligator osteoderms. It exists in minute quantities in the brain (brain sand), without significantly affecting its function. Thus, the expression “having sand in the head” is not without reason. The density of HAP is 3.15 g/cm3. Nonstoichiometric minerals can exist with Ca10(PO4)6(OH, F, Cl, Br)2; if the OH group is replaced by F it is called fluoroapatite; if it is replaced by Cl, it is called chloroapatite. It can be occasionally used as a gem, and the cat’s eye is a commonly known use.

In this chapter, we will concentrate on bone and teeth with emphasis on their structure and mechanical properties. They are HAP–collagen composites and their mechanical properties are the result of the complex interplay and hierarchy built by these structures. Selected calcium-phosphate-based bony tissues with unique functionalities, such as antler, turtle shells, alligator osteoderms, and fish scales, will also be described in the second part of this chapter.

Bioinspired materials and biomimetics

The ultimate goal for a materials engineer is to learn from the lessons of nature and to apply this knowledge to new materials and design. This is not a new quest, and humans have sought inspiration from nature since prehistory. The early materials used by humans were primarily natural: stones, bones, wood, skins, bark. The accelerating pace of the civilizing process has been attributed to the introduction of new synthetic materials; thus, the bronze and iron ages followed the stone age. We have now entered the brave new world of the silicon age, which is bound to produce unimaginable change. Homo silicensis, connected 24/7 to computerized contraptions, can already be seen on campuses and elite coffee houses, sipping lattes.

The constant quest for new materials and designs is leading us to a systematic inquiry of nature in order to unravel its secrets. This is the field of biomimetics, and VELCRO® is the standard example of bioinspired design. It is inspired by the burrs of plants that contain small hooks that attach themselves to animal wool or our clothes.

Introduction

The quest to mimic nature is now reaching a new chapter. Whereas in the past, structural and functional characteristics served as inspiration for designs and materials, with attention given to mesoscopic and, perhaps, microscopic aspects, the arsenal of new experimental techniques and computational methods is descending to the nanometer scale. This is the scale at which atoms assemble into molecules, and molecules form molecular arrangements such as DNA, RNA, plasmids, and proteins.

Prominent characterization techniques available to modern researchers are (e.g. Gronau et al., 2012):

• transmission and scanning electron microscopy at higher and higher resolutions;

• micro and nano computerized tomography;

• atomic force microscopy;

• fluorescence spectroscopy;

• Fourier transform infrared spectroscopy (FTIR);

• dynamic light scattering;

• X-ray diffraction.

• small-angle X-ray scattering (SAXS);

• nanomechanical testing (nanoindentation);

The principal computational methods are:

• density functional theory (DFT);

• quantum-mechanical and ab initio methods;

• coupled cluster method (CCSD);

• reactive and nonreactive molecular dynamics;

• coarse graining;

• finite element method;

• computational fluid mechanics.