Victor Birman

Modeling and Analysis of Functionally Graded Materials and Structures

This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

Review of Mechanics of Shape Memory Alloy Structures

This article presents a review of constitutive theories, mechanics, and structural applications of shape memory alloys. Although these materials possess a number of unique features, this review is concerned with the shape memory effect and superelasticity, since they are most often discussed in the context of possible applications. The article begins with a discussion of these effects and a reference to a number of studies elucidating the properties of shape memory alloys. In the next section, a number of constitutive theories are listed and some recent theories are discussed in detail. The work related to numerous technological problems that arise in the process of manufacturing shape memory alloy structures is considered. Structural problems of shape memory structures, such as buckling, vibration, acoustic control, etc are discussed. The work related to development and design of shape memory sensors and actuators is also reviewed. Finally, some applications of shape memory alloy actuators, particularly those in the aerospace and medical fields, are considered. This review article contains 195 references.

Parametric instability of thick, orthotropic, circular cylindrical shells

SummaryThe dynamic instability of simply supported, finite-length, circular cylindrical shells subjected to parametric excitation by axial loading, is investigated analytically. The shell is taken to be orthotropic, due to closely spaced longitudinal and/or circumferential stiffeners or to many layers of fiber-reinforced composite material either oriented at angles of 0° and 90° (cross-ply) or at +θ and −θ (angle-ply) with respect to the shell axis. The theory used is a general first-order shear deformable shell theory introduced by Hsu, Reddy, and Bert; it can be considered to be the thick-shell version of the popular Sanders-Koiter thin-shell theory. By means of tracers, this theory can be reduced to thick-shell versions of the theories of Love (and Loo) and of Donnell (and Morley). Quantitative results are presented to show the effects of shell geometry, materials, and fiber orientation on the stability boundaries.

Properties and potential for application of steel reinforced polymer and steel reinforced grout composites

The paper introduces steel reinforced polymer (SRP) and steel reinforced grout (SRG) composites that are considered for application in civil engineering for bridge and concrete buildings upgrade. These composites consist of steel cords formed by interwoven steel wires embedded within a polymer resin or cementitious grout matrix. The properties of SRP are evaluated experimentally and compared to micromechanical equations to determine a suitability of these equations for the prediction of material constants. The effectiveness of SRP is evaluated on existing structures (i.e. slab strips of a parking garage) while SRG performance is studied on laboratory-prepared large-scale reinforced concrete beams. It is shown that both composites significantly enhance the strength of the concrete members providing the first evidence of their suitability for practical applications concerned with upgrading the existing infrastructure. Improvements subsequent to the testing to both the cord design and fabric manufacturing process show even greater promise.

Dynamic instability of shear deformable antisymmetric angle-ply plates†

Abstract The effect of shear deformation on dynamic instability of simply supported antisymmetric angle-ply rectangular plates is considered. The boundaries of the principal instability region are conveniently represented in the plane “non-dimensional excitation frequency squared-non-dimensional load amplitude”. The effects of the magnitude of the shear correction coefficients, number of layers, plate aspect ratio, and thickness-to-edge length ratio are illustrated in numerical examples.

On the Choice of Shear Correction Factor in Sandwich Structures

The first-order shear deformation theory (FSDT) is a relatively simple tool that has been found to yield accurate results in the non-local problems of sandwich structures, such as buckling and free vibration. However, a key factor in practical application of the theory is determination of the transverse shear correction factor (K), which appears as a coefficient in the expression for the transverse shear stress resultant. The physical basis for this factor is that it is supposed to compensate for the FSDT assumption that the shear strain is uniform through the depth of the cross section. In the present paper, the philosophies and results of K determination for homogeneous rectangular cross sections are first reviewed, followed by a review and discussion for the case of sandwich structures. The analysis presented in the paper results in the conclusion that K should be taken equal to unity, as a first approximation, for both two-skin as well as for multi-skin sandwich structures.

Buckling and Post-buckling of Composite Plates and Shells Subjected to Elevated Temperature

Effects of temperature on buckling and post-buckling behavior of reinforced and unstiffened composite plates or cylindrical shells are considered. First, equilibrium equations are formulated for a shell subjected to the simultaneous action of a thermal field and an axial loading. These equations are used to predict a general form of the algebraic equations describing the post-buckling response of a shell. Conditions for the snap-through of a shell subjected to thermomechanical loading are formulated. As an example, the theory is applied to prediction of post-buckling response of flat large-aspect-ratio panels reinforced in the direction of their short edges. 19 refs.

An approach to optimization of shape memory alloy hybrid composite plates subjected to low-velocity impact

Abstract The paper presents an approach to the problem of optimum design of composite plates subjected to low velocity impact. The deflections and stresses are reduced by employing prestrained shape memory alloy (SMA) fibers which are in the martensitic phase when embedded within the plate. At an elevated temperature, the SMA fibers transform into the austenitic phase and tend to contract. However, due to a constraint, the contraction is either completely prevented or reduced resulting in significant tensile recovery stresses. This tension reduces deformations and stresses in the plate subjected to low-velocity impact. The solution in the paper addresses an impact of cross-ply plates with SMA fibers embedded within the layers oriented in both directions. An approach to optimization considered in the paper involves variations of the volume fractions of SMA fibers in each direction subject to a constraint on the total volume of the shape memory alloy. It is shown that an application of SMA fibers can significantly reduce deflections and stresses. A further benefit can be achieved by an optimization of a distribution of volume fractions of SMA fibers between the layers.

Mechanisms of Bimaterial Attachment At the Interface of Tendon to Bone

The material mismatch at the attachment of tendon to bone is amongst the most severe for any tensile connection in nature. Attaching dissimilar materials is a major challenge in engineering, and has proven to be a challenge in surgical practice as well. Here, we examine the material attachment schemes employed at this connection through the lens of solid mechanics. We identify four strategies to that the body adopts to achieve effective load transfer between tendon and bone: 1) a shallow attachment angle at the insertion of transitional tissue and bone, 2) shaping of gross tissue morphology of the transitional tissue, 3) interdigitation of bone with the transitional tissue, and 4) functional grading of transitional tissue between tendon and bone. We provide solutions to model problems that highlight the first two mechanisms, discuss the third qualitatively in the context of engineering practice, and provide a review of our earlier work on the fourth. We study these strategies both in terms of ways that biomimetic attachment might benefit engineering practice, and of ways that engineering experience might serve to improve surgical healing outcomes.

Stability of functionally graded shape memory alloy sandwich panels

The stability of sandwich panels subjected to the simultaneous action of a uniform temperature and a uniaxial compression is considered. At elevated temperatures, the buckling load can be increased by using shape memory alloy (SMA) fibers in resin sleeves embedded within the core, at the midplane of the sandwich panel. The best results are achieved when the spacing of SMA fibers across the panel is nonuniform, i.e. the spacing, which is minimum at the centerline, gradually increases with the approach to the edges (sinusoidal distribution). The effectiveness of SMA fibers increases with temperature due to larger tensile recovery stresses. The example of stability of sandwich panels considered in the paper illustrates that functionally graded SMA composites may present significant advantages in engineering design.