A procedure for obtaining a lower bound estimate of the critical load for arbitrary incompressible hyperelastic solids is presented. By considering a lower bound estimate for the Hadamard functional based on the Korn inequality, we establish sufficient conditions for the infinitesimal stability of a distorted configuration. We then determine an optimal lower bound estimate of the critical load in a monotonic loading process and specialize our procedure to the case of homogeneous deformations of incompressible, hyperelastic bodies. We apply our procedure to some representative dead-load boundary value problems for Mooney–Rivlin elastic solids and discuss its effectiveness and handiness for applications by comparing our results to other estimates.

We illustrate a procedure based on the Magnus expansion for studying mechanical problems which lead to non-autonomous systems of linear ODE’s. The effectiveness of the Magnus method is enlighten by the analysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. In particular, for an isotropic compressible elastic tube subject to an azimuthal shear primary deformation we study the possibility of axially periodic twist-like bifurcations. The approximate matricant of the resulting differential problem and the first singular value of the bifurcating load corresponding to a non-trivial bifurcation are determined by employing a simplified version of the Magnus method, characterized by a truncation of the Magnus series after the second term.

We study the implementation of Stable Unbonded Fiber-Reinforced Elastomeric Isolators (SU-FREI) for the seismic protection of a typical historical masonry construction from Puglia. The effectiveness of this innovative isolation technique is analyzed by means of a non-linear dynamic analysis, which shows substantial improvements of the seismic response with respect to the corresponding fixed base construction.

We characterize the elastic response of Apricena marble by using advanced ultrasonic nondestructive techniques. An innovative experimental device for ultrasonic immersion tests is employed for the determination of ultrasonic velocities of waves travelling into the sample for any angle of propagation. The interpretation of the experimental results within the theoretical framework of wave propagation in elastic materials allows for both the classification of the anisotropy and the determination of the elastic moduli.

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

We study the possibility of toroidal twist-like bifurcations for an isotropic Levinson–Burgess compressible elastic tube subject to a pure circular shear. We intend to model forms of instability for solids that are analogous to the classical Taylor–Couette patterns observed in the flow of viscous fluids. We first establish that the axisymmetric circular shear deformation is a fundamental solution of the equilibrium problem, and then investigate the possibility that this primary deformation may bifurcate into an axially periodic toroidal twist-like mode by analyzing the related incremental boundary-value problem. The analysis of the bifurcation problem and the evaluation of the critical load are carried out by following a novel effective procedure, based on the Magnus expansion.