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In composite structures, the presence and growth of delamination mechanisms in static or fatigue loading conditions is of paramount interest and the American Society for Testing and Materials (ASTM) has adopted the three-points bend end-notched flexure test (3ENF) as the standard for measurement of mode II toughness. The drawback of the 3ENF test is the unstable crack growth and a modified version of the test, namely the four points bend end-notched flexure test (4ENF), has been proposed. The main advantage of the 4ENF over the 3ENF is that crack growth is stable under displacement control, but it can be strong influenced by the interlaminar frictional effects. The effect of frictional contact between the delamination surfaces has been initially analysed for the 3ENF test, whereas the evaluation of frictional effects on the 4ENF test has been proposed. Recently, the analytical solution of the mode II delamination toughness in the 4ENF test, with interlaminar friction, has been proposed. In the present paper, the analytical solution of the mode II delamination toughness, in presence of friction on the delamination surface, is proposed also for the 3ENF delamination tests. This solution is rigorously developed in the framework of Classical Beam Theory (CBT), under Bernoulli bending condition, and in the framework of linear elastic fracture mechanics. The frictional phenomenon is modelled as rigid perfectly-plastic with Mohr-Coulomb activation condition and non-associative flow rule. The mode II fracture energy is defined by the Griffith approach, by evaluating the energy release rate and the frictional dissipation. The results of the 3ENF and 4ENF mode II delamination toughness are compared for some values of the frictional coefficient.

Mechanical interfaces are theoretical and computational tools able to properly reproduce the progressive decohesion along predefined surfaces. Scientific literature is rich of interface models, developed under very different conctitutive framework, but mostly developed in small displacements, whereas a few of them assess the problem in a geometrically nonlinear setting. In the present contribution interface formulation is rigorously developed in the large displacements regime. The relevant cohesive interface constitutive relations are defined in the local reference with normal and tangential axes to the middle surface in the current configuration. The interface is defined as a zero thickness layer with the traction vector acting between the two connected surfaces. Membrane forces are assumed negligible and separation displacement is assumed to remain small, at least up to full debonding.

Mechanical interfaces are theoretical and computational tools able to properly reproduce then progressive delamination of composite structures. Scientific literature is rich of interface models, mostly developed in small displacements, whereas a few of them assess the problem in a geometrically nonlinear setting. In the present paper interface formulation is rigorously developed in a geometrically nonlinear setting, and the relevant interface constitutive relations are defined in the local reference with normal and tangential axes to the middle surface in the current configuration. The interface is defined as a zero thickness layer with tractions acting between the two connected surfaces. Membrane forces are assumed negligible and separation displacement is assumed to remain small, at least up to full debonding. Under this “constitutive” hypothesis rotational equilibrium is implicitly verified.

An Hellinger-Reissner (H-R) variational principle is proposed for stress gradient elasticity material models. Stress gradient elasticity is an emerging branch of non-simple constitutive elastic models where the infinitesimal strain tensor is linearly related to the Cauchy stress tensor and to its Laplacian. The H-R principle here proposed is particularized for a solid composed by several sub-domains connected by coherent interfaces, that is interfaces across the which both displacement and traction vectors are continuous. In view of possible stress-based finite element applications, a reduced form of the H-R principle is also proposed in which the field linear momentum balance equations are satisfied a-priori, the continuity condition of the displacements across the interfaces is relaxed and the analogous continuity condition of the traction is enforced as a side condition.

In many circumstances structural failure modes are driven by the formation and propagation of fractures. For instance in composite laminate structures one of the most worrying condition is delamination, which is an interlaminar progressive fracture. Fracture toughness is the material mechanical parameters which ensure fracture safe condition and it is also an essential parameter for performing nonlinear structural analysis, no matter if based on Fracture Mechanics or by means of Interface Cohesive theories. It is then of paramount relevance to evaluate the critical fracture energy by means of simple and reliable laboratory tests. Several tests are available for the direct determination of mode I and mode II fracture energies. If for mode I, fracture energy determination is nowadays well defined and the Double Cantilever Beam (DCB) test is normed and universally adopted, it is not the same for mode II fracture energy. The tests based on bending beams theory such as End Notched Flexure (ENF), End Loaded Split (ELS) test and Four Point End Notched Flexure (4ENF) are all widely used tests, which however for different reasons have not been fully accepted.

The paper is devoted to an interface constitutive modeling which couples a cohesive behavior, based on the damage mechanics theory, with a frictional one, defined in a non-associative plasticity framework. By means of a specific interpretation of the damage variable, the formulation follows the transition of the initial sound interface material layer, up to the fully cracked condition. The macrocrack surfaces have initial frictional properties and is subjected to degradation phenomena. Namely, the smoothing and breaking of surface asperities cause a progressive reduction of dilatancy effects and also of the frictional angle. These phenomena are modeled as uncoupled: dilatancy saturation is assumed to occur when relevant internal variable reach a limit value; frictional strength reduction is assumed to occur as effect of an oligocyclic process, which takes place during the plastic sliding between the macrocrack surfaces. The constitutive model is developed in a fully compliance with thermodynamic principles. Some numerical branch tests are presented in order to show the main features of the proposed model. Finally, computational efficiency is verified by comparing the results of a FE applications with available experimental data

This paper deals with finite element dynamic analysis of prestressed cables with uncertain pretension subjected to deterministic excitations. The theoretical model addressed for cable modeling is a two-dimensional finite-strain beam theory, which allows us to eliminate any restriction on the magnitude of displacements and rotations. The dynamic problem is formulated by referring the motion to the inertial frame, which leads to a simple uncoupled quadratic form for the kinetic energy. The effect of the externally applied stochastic pretension is approximately described by means of an uncertain 'axial' component of stress resultant, which is assumed constant along the cable in its dead load configuration. The so-called improved perturbation approach is employed to solve this stochastic problem, obtaining two coupled systems of nonlinear deterministic ordinary differential equations, governing the mean value and deviation of response. An efficient and accurate iterative procedure is proposed to obtain the solution of these equations. In order to investigate the influence of random pretension on structural response, few numerical applications are presented and results are discussed.

A special weak-form shakedown is studied for elastic-plastic internal-variable material models with nonlinear hardening, damageable elastic moduli and damageable yield surface, in the hypothesis of ductile damage, (i.e. damage induced by plastic strains), but the precise evolutive law of damage being left unspecified. Sufficient weak-form shakedown theorems are presented, one static and another kinematic, each assessing whether eventually plastic deformations cease together with their consequences, including ductile damage. A two-sided delimitation is provided, within which the weak-form shakedown safety factor can be located. An upper bound to the post-transient damage for a particular isotropic damage model is also proposed. A simple numerical application is presented.

Internal variable elastic-plastic-damage, or elastic-damage, material models endowed with free energy are considered. Referring to a structure of such a material subjected to loads varying inside a given domain, the classical notion of (elastic) shakedown is widened to signify that the structure eventually responds to the loads in an elastic manner after certain (finite) amounts of plastic strain and/or damage have been produced. For structures fulfilling an ad-hoc D-stability requisite, an extended shakedown theorem is presented as a generalization of the classical Melan theorem to nonlinear elasticity and damage - besides nonlinear hardening. For common materials exhibiting linear elastic behaviour for constant damage, the extended Melan theorem saves its classical format, but the elastic stress response to the loads must be a damaged response computed on the basis of a trial time-independent damage field; more particularly, in the case of elastic-damage materials, no self-stresses are considered. The impending inadaptation collapse modes at the shakedown limit are studied under periodic loads showing that reverse damage is not allowed and thus either damage ceases after some transient phase or it continues afterwards in a ratchetting collapse mode until fracture occurs. The greater computational difficulties posed by the extended Melan theorem are observed and a few numerical applications are presented.