Annals of Solid and Structural Mechanics

Kirchhoff type shells are continuum models used to study the mechanics of thin elastic bodies; these are largely based on the theory of surfaces. Here, we report a reformulation of Kirchhoff shells using the theory of moving frames. This reformulation permits us to treat the deformation and the geometry of the shell as two separate entities. The structure equations which represent the familiar torsion and curvature free conditions (of the ambient space) are used to combine deformation and geometry in a compatible way. From such a perspective, Kirchhoff type theories have non-classical features which are similar to the equations of defect mechanics (theory of dislocations and disclinations). Using the proposed framework, we solve a boundary value problem and thus demonstrate, to an extent, the importance of moving frames.

We propose a construction of fatigue laws from cohesive forces models in the case of a crack submitted to a mode I cyclic loading. Taking the cumulated opening as the memory variable and the surface energy density associated with Dugdale’s model, we explicitly construct the fatigue law which gives the crack growth rate by cycle dℓ/dN in terms of the stress intensity factor K I . In particular, we recover a Paris law with an exponent 4, i.e., dℓ/dN = C K 4 , when K I is small, the coefficient C being explicitly expressed in terms of the material parameters. Furthermore, the law can be applied in the full range of values of K I and can be extended to non simple cycles.

A dynamic model to predict crack growth phenomena in z-pinned reinforced composite structures is proposed. The formulation is based on a novel technique, which is able to couple Fracture Mechanics concepts with a strategy based on a moving mesh methodology. The former is utilized to predict the crack growth, whereas the latter defines the way to take into account the geometry changes on the basis of the invoked fracture parameters. The presence of the z-pins is simulated by means of a large-scale bridging approach, introducing along the delaminated interfaces normal and tangential traction forces depending on the dynamic characteristics of the pull-out mechanism. In order to evaluate the fracture parameters, which govern the crack evolution, the J-integral decomposition procedure is utilized, providing new expressions in the framework of a large-scale bridging crack growth. A numerical modeling based on the finite element procedure is implemented and comparisons with experimental results are reported to validate the proposed formulation. Moreover, a parametric study is developed to investigate the influence of z-pins on the crack growth mechanisms.

Modeling the formation and evolution of microstructure in phase transforming materials presents challenges to traditional continuum mechanics approaches. This is mainly because they do not account for effects arising from the discreteness of the underlying lattice. Such effects can be described by non-classical approaches based on discrete particle models. We study the propagation of an austenite-martensite phase boundary using a Frenkel–Kontorova model. The model is based on a one dimensional chain of atoms on the phase boundary under the influence of a temperature dependent substrate potential. Using this model we derive the kinetic relation as a function of temperature.

We conduct systematic dynamic experiments on the martensite reorientation in different samples of the single crystal Ni–Mn–Ga Ferromagnetic Shape Memory Alloy (FSMA) driven by a high-frequency magnetic field and a compressive stress. It is found that the output reversible strain strongly depends on the loading frequency, with the maximum output strain up to 6 % at the resonance frequency; and this resonance frequency can be changed by modifying the setting of the compressive stress (the pre-stress level). That provides an alternative way to control/design the system’s optimal working frequency range, besides modifying the spring stiffness and sample geometry. On the other hand, temperature rise accompanies the high-frequency field-induced strain because of the energy dissipation of the martensite twinning and eddy current, which depend on both the frequency and the sample geometry. With these results, some guidelines for improving the FSMA engineering designs are given and some challenging issues for further theoretical study such as the magneto–thermal–mechanical coupling are pointed out.

The article presents a numerical finite element study of fluid leakage in concrete. Concrete cracking is numerically modelled in the framework of a macroscopic probabilistic approach. Material heterogeneity and the related mechanical effects are taken into account by defining the elementary mechanical properties according to spatially uncorrelated random fields. Each finite element is considered as representative of a volume of heterogeneous material, whose mechanical behaviour depends on its own volume. The parameters of the statistical distributions defining the elementary mechanical properties thus vary over the computational mesh element-by-element. A weak hydro-mechanical coupling assumption is introduced to represent the influence of cracking on the variation of transfer properties: it is assumed that the mechanical cracking of a finite element induces a loss of isotropy of its own permeability tensor. At the elementary level, an experimentally enhanced parallel plates model is used to relate the local crack permeability to the elementary crack aperture. A Monte Carlo-like approach allows to statistically validate the numerical method. The self-consistency of the proposed modelling strategy is finally explored through the numerical simulation of the hydro-mechanical splitting test, recently proposed by authors to evaluate the real-time evolution of the transfer properties of a concrete sample under loading.

In this paper we consider masonry bodies undergoing loads that can be represented by vector valued measures, and prove a result which is an appropriate formulation to this context of the static theorem of the limit analysis. As applications, we study the equilibrium of panels that are subjected both to distributed loads and concentrated forces, and determine equilibrated tensor valued measures. Then, by using an integration procedure for parametric measures, we explicitly calculate equilibrated stress fields that are represented by integrable functions. The obtained solutions are discussed.