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A novel thermodynamically consistent cohesive-frictional model for the analysis of interface degradation and failure under either monotonic quasi-static loading or cyclic loading in low-cycle fatigue problems is proposed. Starting from the definition of a suitable Helmholtz energy density function, a phenomenological interface model is developed in the framework of plasticity and damage mechanics. In particular, a coupled plasticitydamage activation function is defined and employed together the consistent evolution rules to capture the evolution of damage and plasticity under the action of the external loads. Due to the specific features of such threshold and flow rules, the initiation and accumulation of damage under monotonic increasing loads is captured and accompanied by negligible plastic evolution, allowing to approximate pure damage-based cohesive laws. On the other hand, coupling associative plasticity and damage evolution allows linking the interface degradation in low-cycle fatigue processes to plastic hysteresis, on the basis of the phenomenological assumption that no infinite plastic flows may happen without microstructural transformation leading to loss of load bearing capability. The model also embodies a smooth transition from an initially cohesive to a residual frictional interface behaviour, governed by a Coulomb frictional activation function. The developed formulation has been implemented and assessed for individual interfaces, highlighting consistent phenomenological behaviour. It has been then applied to the analysis of delamination and de-bonding in composite test cases, showing accuracy against experimental data and confirming its potential.

An extended Ritz formulation for the analysis of buckling and post-buckling behaviour of cracked composite multilayered plates is presented. The formulation is based on: (i) the First-order Shear Deformation Theory to model the mechanics of the multilayered plate; (ii) the von Karman’s theory to account for geometric non-linearities ; (iii) the use of an extended set of approximating functions able to model the presence of an embedded or edge crack and to capture the crack opening fields as well as the global behaviour within a single cracked domain. The numerical results of the buckling analyses and the equilibrium paths in the post-buckling regime are compared with the results from finite elements simulations , confirming the accuracy and potential of the formulation.

In the present work, families of equivalent singe layer and layer-wise models for the static and free vibrations analysis of magneto-electro-elastic multilayered plates are developed. The models are defined in the framework of a unified formulation, which offers a systematic approach for generating refined plate theories through suitable expansions of the through-the-thickness components of the relevant fields, considering the expansion order as a free parameter. The key features of the developed formulation are: a) the condensation of the electric and magnetic description into the mechanical representation, based on the quasi-static electric-magnetic approximation, which allows to reduce the computation of the analysis for both layer-wise and equivalent single layer models; b) the employment of the Reissner Mixed Variational Theorem, in which the displacements and transverse stress components are used as primary variables, thus allowing the explicit fulfilment of the transverse stress interface equilibrium. The proposed methodology is assessed by generating different layer-wise and equivalent single layer models for the analysis of thick magneto-electro-elastic plates and comparing their solution against available three-dimensional analytic results.

A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficient for numerical implementation. Useful general relationships for the computation of derivatives of various order of the fundamental solutions are presented. Furthermore, no particular treatment is needed for mathematically degenerate cases. The fundamental solutions of the Laplace equation and isotropic elastic solids are exactly retrieved as special cases. Numerical results are presented to demonstrate the accuracy of the approach for isotropic elastic, generally anisotropic elastic, transversely isotropic and generally anisotropic piezo-electric and magneto-electro-elastic materials.

In this study, a two-dimensional multi-region framework, based on the use of the Virtual Element Method (VEM), is developed for computational materials homogenization and applied to different classes of widely employed heterogeneous materials. The VEM has recently emerged as a powerful generalisation of the Finite Element Method capable of dealing with very general polygonal mesh elements, including non-convex or highly distorted elements. Such features are appealing for the treatment of problems whose analysis domains present complex or statistical morphological features, which would generally require careful and time-consuming mesh/data preparation and regularization. In this work, the lowest-order VEM for two-dimensional elastostatics is employed for the homogenization of polycrystalline materials and unidirectional fibre-reinforced composites. In both cases, artificial micro-morphologies are usually generated resorting to automatic algorithms aimed at approximating/reproducing the statistical microscopic features of real materials. In such a context, the likely presence of morphological irregularities, and subsequent mesh distortions, usually requires caution and the employment of sophisticated mesh regularization procedures. The study demonstrates how the inherent features of the VEM can be conveniently exploited for such classes of problems, as the method allows the relaxation of the requirements on the mesh quality, yet providing accurate numerical results.

An original finite element formulation for the analysis of large deflections in magneto-electro-elastic multilayered plates is presented. The formulation is based on an equivalent single-layer model in which first order shear deformation theory with von Karman strains and quasi-static behavior for the electric and magnetic fields are assumed. To obtain the plate model, the electro-magnetic state is firstly determined and condensed to the mechanical primary variables, namely the generalized displacements. In turn, this result is used to obtain laminate effective stiffness coefficients that allow to express the plate mechanical stress resultants in terms of the generalized displacements and applied electro-magnetic boundary conditions only, taking the magneto-electro-elastic couplings into account. The weak form of the mechanical equilibrium equations is then written and used to express the finite element matrices. Numerical results obtained by implementing an isoparametric four-node MITC finite element are presented to validate the approach and show its features and potentiality. The proposed modeling strategy and the corresponding finite element formulation can take advantage of the solution tools available for the mechanics of classical multilayered plates leading to the straightforward integration of magneto-electro-elastic plate finite elements into existing codes. © 2013 Elsevier Ltd.

In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as three-dimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the traction-separation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incremental-iterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo- and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads.

A fast boundary element method for the analysis of three-dimensional solids with cracks and adhesively bonded piezoelectric patches, used as strain sensors, is presented. The piezoelectric sensors, as well as the adhesive layer, are modeled using a 3D state-space finite element approach. The piezoelectric patch model is formulated taking into account the full electro-mechanical coupling and embodying the suitable boundary conditions and it is eventually expressed in terms of the interface variables, to allow a straightforward coupling with the underlying host structure, which is modeled through a 3D dual boundary element method, for accurate analysis of cracks. The technique is computationally enhanced, in terms of memory storage and solution time, using the hierarchical format in conjunction with a GMRES solver. An original strategy retaining the advantages of the fast hierarchical solution without increasing the implementation complexity to take into account the piezoelectric patches is proposed for the solution of the final system. The presented work is a step towards modeling of structural health monitoring systems.

In this work, a two-scale approach to degradation and failure in polycrystalline materials is proposed. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modeled using a three-dimensional boundary element formulation in which the presence of damage is formulated through an initial stress approach to account for the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modeled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighborhood of the selected points. A three-dimensional grain-boundary formulation is used to simulate intergranular degradation and failure in the microstructure, whose morphology is generated using the Voronoi tessellations. Intergranular degradation and failure are modeled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVEs as periodic boundary conditions, while overall macro-stresses are obtained as volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. To avoid pathological damage localization at the macro-scale, integral non-local counterparts of the strains are employed. A multiscale processing algorithm is described. Two multiscale simulations are performed to demonstrate the capability of the method.