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Highlights • Local stability analysis for incompressible elastic solids under dead-load surface tractions. • Explicit necessary and sufficient algebraic local stability conditions are found. • The special case of a Gent-Thomas incompressible, isotropic elastic parallelepiped is considered. • The response of the parallelepiped as the material parameters vary is described. Abstract We study the equilibrium and the local stability for an incompressible elastic solid under arbitrary dead-load surface tractions on the boundary. We particularize the analysis to homogeneous deformations of a homogeneous, isotropic parallelepiped, finding necessary and sufficient algebraic local stability conditions consistent with the further requirement of the zero moment condition. We specialize the study for a uniform distribution of dead-load surface tractions s > 0 on two pairs of faces and –s on the remaining two faces, and we find that two classes of equilibrium solutions may occur: symmetric and asymmetric solutions, respectively. For the symmetric solutions we also determine local stability inequalities. For the special case of a Gent-Thomas material we show that both equilibrium symmetric and asymmetric solutions may occur if the material parameters satisfy certain inequalities. Then, we completely describe the response of the parallelepiped in a loading process starting from the unloaded state for five ranges of the values of the material parameters. In particular, for one of these ranges we show that symmetric solutions are the unique locally stable homogenous equilibrium deformations until a critical value s cr of the load; at s cr , symmetric solutions lose their uniqueness, and a bifurcation into asymmetric solutions may occur. [ABSTRACT FROM AUTHOR]

The acoustoelastic effect – that is the correlation between the acoustic properties and the stress state for a solid body – can be profitably employed for experimental measurements of applied and/or residual stress, for example starting from the results of ultrasonic tests. Usually, the interpretation of the results of acoustoelastic experiments is performed in the theoretical framework of the so-called third-order elasticity. In the recent past, more general theoretical models aimed at overcoming some limitations of the third-order elasticity for acoustoelastic stress measurements have been developed. In particular, here we refer to a model developed within the linearized finite elasticity theory and describing the propagation of small amplitude waves in prestressed elastic materials. In this model, no assumption on the origin of initial stress neither on the initial anisotropy of the material is made, but the only hypothesis is that ultrasonic waves superimposed on the stressed reference configuration behaves elastically; then, this theoretical approach is also applicable for the experimental stress analysis of plastically deformed bodies and of anisotropic materials. Moreover, this model leads to “universal relations” relating ultrasonic velocities to the stress in a prestressed configuration of a body. Ultrasonic acoustoelastic tests on specimens under known stress states allows us for showing that the application of the above mentioned theoretical model, together with the use of a suitable experimental setup developed at our laboratory, may lead to stress measurements with an high level of accuracy. [ABSTRACT FROM AUTHOR]

We study the possibility for an isotropic elastic body to support forms of instability induced by shear stress states which are reminiscent of the planar Couette and the Taylor–Couette patterns observed in the flow of viscous fluids. Here, we investigate the emergence of bifurcating periodic deformations for an infinitely long compressible elastic block confined between and attached to parallel plates which are subject to a relative shear displacement. We specialize our analysis by considering a generalized form of the Blatz–Ko strain energy function and show through numerical representative examples that planar Couette modes are always preferred with respect to the twisting Taylor–Couette modes. Finally, we introduce a suitably restricted form of the strong ellipticity condition for the incremental elasticity tensor and discuss its significance in this bifurcation problem. [ABSTRACT FROM AUTHOR]

In the recent papers [1,2] we studied a new procedure based on the Korn inequality for determining sufficient conditions for the Hadamard stability, aimed at determining optimal lower bound estimates for the critical load in bifurcation problems. Here, we discuss the effectiveness of our approach for the classical representative problem of uniaxial compression of a Mooney-Rivlin circular cylinder. We find that our lower bound estimate is effective and advantageous for applications, since it is easily implementable in numerical codes. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We study an innovative experimental approach for the characterization of the elastic response of anisotropic composite materials by ultrasonic immersion tests. In particular, the class of anisotropy and the elastic moduli can be determined starting from measurements of the velocities of ultrasonic waves propagating in suitable directions. To this aim, we have designed and developed a goniometric ultrasonic test bench and a software for the management of the test and the processing of the acquired data. By employing this experimental device, we determine in a non-destructive way the five elastic moduli of a transversely isotropic unidirectional CFRP composite. The experimental analyses are supported by numerical simulations, which are useful for a deeper insight of the propagation phenomena and for enhancing the experimental strategies to be adopted. [ABSTRACT FROM AUTHOR]