Applied Mechanics Reviews

Laminated composite materials are used extensively in aerospace and other applications. With their high specific modulus, high specific strength, and the capability of being tailored for a specific application, these materials offer definite advantages compared to more traditional materials. However, their behavior under impact is a concern, since impacts do occur during manufacture, normal operations, or maintenance. The situation is critical for impacts which induce significant internal damage, undetectable by visual inspection, that cause large drops in the strength and stability of the structure. Impact dynamics, including the motion of both the impactor and the target and the force developed at the interface, can be predicted accurately using a number of models. The state of stress in the vicinity of the impact is very complex and requires detailed analyses. Accurate criteria for predicting initial failure are generally not available, and analyses after initial failure are questionable. For these reasons, it can be said that a general method for estimating the type and size of impact damage is not available at this time. However, a large amount of experimental data has been published, and several important features of impact damage have been identified. In particular, interply delaminations are known to occur at the interface between plies with different fiber orientation. Their shape is generally elongated in the direction of the fibers in the lower ply at that interface. The delaminated area is known to increase linearly with the kinetic energy of the impactor after a certain threshold value has been reached. The effect of impact damage on the properties of the laminate has obvious implications for design and inspection of actual structures. Experimental results concerning the residual strength of impact damaged specimens subjected to tension, compression, shear, bending, and both static and fatigue loading are available. Analyses concentrate primarily on predicting residual tensile and compressive strength. In order to fully understand the effect of foreign object impact damage, one should understand impact dynamics and be able to predict the location, type, and size of the damage induced and the residual properties of the laminate. This article is organized along these lines and presents a comprehensive review of the literature on impact of laminated composites, considering both experimental and analytical approaches.

Hysteresis is a widely occurring phenomenon. It can be found in a wide variety of natural and constructed systems. Generally, a system is said to exhibit hysteresis when a characteristic looping behavior of the input-output graph is displayed. These loops can be due to a variety of causes. Furthermore, the input-output graphs of periodic inputs at different frequencies are generally identical. Existing definitions of hysteresis are useful in different contexts but fail to fully characterize it. In this paper, a number of different situations exhibiting hysteresis are described and analyzed. The applications described are: an electronic comparator, gene regulatory network, backlash, beam in a magnetic field, a class of smart materials and inelastic springs. The common features of these widely varying situations are identified and summarized in a final section that includes a new definition for hysteresis.

The 36 forms of the acoustic wave equation derived in an earlier review (Campos, L. M. B. C., 2007, “On 36 Forms of the Acoustic Wave Equation in Potential Flows and Inhomogeneous Media,” Appl. Mech. Rev., 60, pp. 149–171) were grouped in four classes, of which the last (Class IV) concerned sheared mean flows; another type of vortical flow is swirling flow, and thus the present review completes the preceding by starting with Class V of linear, nondissipative acoustic wave equations in axisymmetric swirling, and also sheared, mean flow. These include general swirl and, in particular, rigid body and potential vortex swirl, combined or not with shear, for axisymmetric or general nonaxisymmetric acoustic modes, in two types of media: (i) inhomogeneous isentropic and (ii) homogeneous homentropic. Besides the 14 acoustic wave equations in sheared and swirling mean flows, the remaining ten acoustic wave equations derived in the present review all concern waves in homogeneous and steady media at rest, with dissipation or nonlinear effects to second-order or a combination of these two opposing effects, viz., (i) Class VI of linear, nondissipative wave equations with weak or strong thermoviscous dissipation in a homogeneous medium at rest; (ii) Class VIIA nonlinear one-dimensional wave equations in steady, homogeneous medium at rest without dissipation, or with viscous or thermoviscous dissipation, also in the case of a duct of varying cross section; (iii) Class VIIB of weakly nonlinear, three-dimensional waves or beams with thermoviscous dissipation in a homogeneous steady medium at rest. The 24 forms of the acoustic wave equation derived in the present review add to the 36 forms in the preceding review to form the set of 60 acoustic wave equations, whose interconnections are indicated in a family tree at the end. Numerous examples of the applications of the wave equations to the physical world are given at the end of each written section.

Propagating fatigue cracks can have detrimental effects on the reliability of rotating machinery. An early crack warning can considerably extend the durability of these very expensive machines, increasing their reliability at the same time. Vibration monitoring as a means of detecting crack initiation has been receiving much interest. A detailed study of the vibrational behavior of cracked rotating shafts, therefore, is an important problem for engineers working in the area of the dynamics of machines. This article presents a review of the field of the dynamics of cracked rotors, including the modeling of the cracked part of the structure and finding different detection procedures to diagnose fracture damage. The material should be helpful to scientists and researchers working in this area or planning to work in it in the future. Since the study of nonrotating, cracked structural elements obviously is relevant to the cracked rotor problem, the review can also be a basis for discussing the dynamics of cracked beams and columns.

A review is made of the different approaches used for modeling multilayered composite plates. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; and first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite plates on the accuracy of the static and vibrational responses predicted by six different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. Some of the future directions for research on the modeling of multilayered composite plates are outlined.

A review of equivalent–single–layer and layerwise laminated plate theories and their finite element models is presented. The layerwise theory advanced by the senior author is presented and a variable displacement finite element model and mesh superposition techniques are described. A simultaneous multiple model approach that is based on the variable kinematic theory and the mesh superposition method are also described. The objective of the simultaneous multiple model approach is to match the most appropriate mathematical model with each subregion based on the physical characteristics, applied loading, expected behavior, and level of solution accuracy desired in that subregion. Thus solution economy is maximized without sacrificing the solution accuracy.

The focus of this review is on the hierarchy of computational models for sandwich plates and shells, predictor-corrector procedures, and the sensitivity of the sandwich response to variations in the different geometric and material parameters. The literature reviewed is devoted to the following application areas: heat transfer problems; thermal and mechanical stresses (including boundary layer and edge stresses); free vibrations and damping; transient dynamic response; bifurcation buckling, local buckling, face-sheet wrinkling and core crimping; large deflection and postbuckling problems; effects of discontinuities (eg, cutouts and stiffeners), and geometric changes (eg, tapered thickness); damage and failure of sandwich structures; experimental studies; optimization and design studies. Over 800 relevant references are cited in this review, and another 559 references are included in a supplemental bibliography for completeness. Extensive numerical results are presented for thermally stressed sandwich panels with composite face sheets showing the effects of variation in their geometric and material parameters on the accuracy of the free vibration response, and the sensitivity coefficients predicted by eight different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the analytic three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of sandwich plates and shells are outlined.

We review a number of instances in which classical acoustic wave scattering from submerged elastic shells can be analyzed in the resonance region of their spectra. We recently reviewed (Refs 42, 43, 12) the cases dealing with acoustic resonance scattering from solid elastic bodies, or with elastic resonance scattering from fluid or solid inclusions in elastic media. It only remains for us to address the works dealing with submerged shells, which we analyze here. We study scattering by bare or viscoelastically coated spherical and cylindrical shells in water, by means of (exact) normal-mode solutions, and by spheroidal shells by numerical approaches, particularly via the T-matrix method. We consider the shell responses mostly in unbounded media and when the interrogating waves are plane and c.w., although some recent findings valid for pulsed incidences and in the vicinity of environmental boundaries are also included. We use the methodology of the resonance scattering theory (RST) as much as possible, emphasizing its post-1981 results. High-frequency findings, obtained by asymptotic methods, are extrapolated to lower frequencies, to confirm RST predictions for the intermediate spectral regions in which the most important structural resonances are known to reside. A large number of bibliographical entries are collected and discussed in connection with our approach.

Models for thermo-hydro-mechanical behavior of saturated/unsaturated porous media are reviewed. The necessary balance equations are derived using averaging theories. Constitutive equations are obtained using the Coleman-Noll procedure and thermodynamic equations for the model closure are introduced. A particular form of the governing equations is then solved numerically and the numerical properties are discussed. Application examples conclude the paper. There are 165 references in this review article.

The problem of effective moduli of cracked solids is critically reviewed. Various approaches to the problem are discussed; they are further assessed by comparing their predictions to results for sample deterministic arrays. These computer experiments indicate that the approximation of non-interacting cracks has a wider than expected range of applicability. Some of the deficiencies of various approximate schemes seem to be related to inadequacy of the conventionally used crack density parameter (insensitive to mutual positions of cracks). An alternative parameter that has this sensitivity, is suggested. Finally, the problem of effective moduli is discussed in the context of “damage mechanics”. It is argued that, contrary to the spirit of many damage models, there is no direct quantitative correlation between progression of a microcracking solid towards fracture and deterioration of its stiffness; thus, the effective moduli may not always serve as a reliable indicator of damage.