A damage interface model with cohesive-frictiona continuous transition

Failure modelling of friction stir welded joints in tensile tests

XFEM approach to nonlinear analysis of composite structures

Adhesive inter-laminar and cohesive inner-layer damage mechanisms for composite materials

Extended finite element method for cohesive-frictional delamination processes

Constitutive modelling of cemented granular materials with transitions from cohesive to frictional behaviour

Interazione fra fluido e struttura nell’analisi sismica di dighe in calcestruzzo

Interlaminar decohesion and inner-layer damage in composite structures

Un approccio agli elementi finiti alla indentazione di film sottili

A thermodynamically consistent CZM for low-cycle fatigue analysis

A cohesive zone model for low-cycle fatigue analysis is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variable. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the damage activation condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behavior without any fatigue degradation for low levels loading conditions.

Material Internal Frictional Dissipation Modelling

This presentation is concerned with a first introductory study devoted to internal frictional dissipation modelling of cracked materials. The problem is set as periodic Representative Volume Element (RVE) with oriented cracks diffused in the bulk material. As first stage, useful for moderate loading levels, cracks are considered fixed and stable at certain position and are modelled as perfect frictional mechanical interface with unilateral contact features. Analyses on cyclic material response are discussed for 2D problems. A second type of analyses is performed considering a further cohesion strength and a crack propagation criteria, which are typical of interface damage mechanical approac…

Cyclic Delamination Analysis: Experimental and Cohesive-Frictional interface Finite Element Modelling

EFFETTO DELL’ATTRITO NELL’AVANZAMENTO DELLA DELAMINAZIONE PER MODO II DI CARICO

Il lavoro valuta l’influenza della dissipazione energetica dovuta agli effetti attritivi che si sviluppano all’interfaccia tra le lamine di provini sollecitati a Modo II di carico. Sono state effettuate diverse prove sperimentali su compositi in fibra di vetro e resina epossidica soggetti a condizioni di carico cicliche e valore medio crescente, tali da mantenere le lamine del composito in continua aderenza. Al fine di valutare l’incidenza dell’attrito interlaminare nella delaminazione per Modo II, i risultati delle prove sperimentali sono stati riprodotti per mezzo di analisi agli elementi finiti utilizzando il programma di calcolo FEAP (con codice sorgente aperto), nel quale è stato imple…

Multiple Surface Cracking and Debonding Failure for Thin Thermal Coatings

Abstract A mechanical analysis of thin films of quasi-brittle materials used as thermal coatings for superalloy substrate is proposed. The study considers a bi-material element subjected to uniform tension formed by a thin layer of quasi-brittle material (typically a ceramic) bonded on an elastic substrate. The bounding between the coating film and the substrate is realized by a very thin primer which mechanically modeled as a zero thickness cohesive frictional interface. The analysis is developed by a non-linear finite element simulation in which, in order to consider damage size effects, a non-local isotropic damage model is adopted for the quasi-brittle coating. The results of the analys…

Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions

The dynamic dam-fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under the assumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements, which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transient analysis of fluid-structure system. Comp Struct 1979;10:383-93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element for the dynamic analysis of fluid-solid system. Int J Numer Methods Eng 1983;19:1657-68]. The irrotational condition for inviscid fluids is imposed by the penalty method and con…

Cohesive-frictional interface model with oligocyclic degradation of surfaces roughness

The present work is devoted to the constitutive modelling, through the classical interface kinematical formulation, of the mechanical behaviour of the internal adhesive layers, connecting different bodies. The proposed interface constitutive model couples a cohesive behaviour with a frictional one and it is able to follow the transition from the sound condition to the fully cracked one by means of a specific interpretation of the damage variable. In the fully cracked condition, the dilatancy exhaustion and the frictional strength degradation are also modelled.

A Thermodynamically Consistent CZM for Low-Cycle Fatigue Analysis

A cohesive zone model for low-cycle fatigue analysis is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variable. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the damage activation condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behavior without any fatigue degradation for low levels loading conditions.

A computational framework for low-cycle fatigue in polycrystalline materials

Abstract A three-dimensional framework for low-cycle fatigue analysis of polycrystalline aggregates is proposed in this work. First, a cohesive law coupling plasticity and damage is developed for modelling cycle-by-cycle degradation of material interfaces up to complete de-cohesion and failure. The law may model both quasi-static degradation under increasing monotonic load and degradation under cyclic loading, through a coupled plasticity-damage model whose activation and flow rules are formulated in a thermodynamically consistent framework. The proposed interface laws have been then implemented and coupled with a multi-region boundary element formulation, with the aim of analysing low-cycl…

Dam-reservoir interaction in the seismic analysis of gravity dams

Two-Scale Interface Element for Modelling Fracture Propagation under Cyclic Loading

A frictional interface model for the propagation of cohesive fracture under cyclic loading

The paper presents an extension of a recent presented mechanical interface model, [1-2], for the description of the smooth cohesive/frictional transition along potentially active cohesive fracture surfaces. The model presented includes the description of internal frictional dissipative mechanisms which are active under combined compressive/sliding loading in either the cohesive process zone, or in the fully fractured interface portion. Moreover, always under compressive/sliding loading conditions, frictional dissipation mechanisms can also develop in the undamaged (or sound) portion of the interface, justified by the circumstance that also at the virgin state in the bonding surface are pres…

Un modello di interfaccia elasto-danneggiativo con effetti termo-meccanici

Numerical and Experimental Analysis of the Frictional Effects on 4ENF Delamination Tests Performed on Unidirectional CFRP

Abstract Progressive delamination in composite materials under static or fatigue loading condition are, in many structures, one of the predominant cause of failure. In the paper, an accurate study of quasi-static delamination growth under mode II loading condition is conducted. Several experimental tests are performed on composite laminates consisting of unidirectional carbon/epoxy layers. Four-point end-notched flexure (4ENF) test is employed in order to characterize the mode II interlaminar fracture toughness. The R-curve is obtained by means of optical and numerical determination of crack tip position. The energy release rate and the crack length are calculated through experimental deter…

Non associative damage interface model for mixed mode delamination and frictional contact

Abstract The present paper proposes a new interface constitutive model based on the non-associative damage mechanics and frictional plasticity. The model is developed in a thermodynamically consistent framework, with three independent damage variables. The non associative flow rules drive the concurrent evolution of the three damage variables. The interface model provides two independent values for the mode I fracture energy and the mode II fracture energy and it is able to accurately reproduce arbitrary mixed mode fracture conditions. The model can also take into account the presence of frictional effects both at the fully debonded zones and at the partially debonded ones. The experimental…

Effects of the indentation process on fatigue life of drilled specimens: optimization of the distance between adjacent holes

The generation of permanent compressive stresses around the holes is recognized as a valuable mean to delay the onset and propagation of the defects and to extend the fatigue life of the mechanical components. In the work, a bilateral indentation process, performed on each side of the component, is widely used in order to create a residual circumferential stress field around the area to be drilled and that persists after the drilling operation. In order to evaluate the process parameters and to identify optimal geometric solutions, several static and fatigue tests are conducted on AW 6082-T6 aluminum alloy specimen where two holes are created. In particular, experimental tests on only drill…

Effect of the indentation process on fatigue life of drilled specimens

Design and manufacture of mechanical elements are strongly influenced by the evaluation of the residual stresses due to their effects on the material strength. This paper presents numerical and experimental results performed on AW 6082-T6 aluminum alloy drilled specimens when the hole is created after a bilateral indentation process. The plastic deformation induced by the indenters creates a compressive residual stress field around the hole, which persists after the drilling operation. Several numerical analysis have been carried out in ANSYS APDL explicit solver for different indentation depths and hole diameters in order to evaluate the compressive circumferential stresses, optimal proces…

Incremental Delamination Processes under Cyclic Loading

A Cohesive-Frictional Interface Model with Frictional Properties Degradation

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 …

Hybrid equilibrium element with high-order stress fields for accurate elastic dynamic analysis

In the present article the two-dimensional hybrid equilibrium element formulation is initially developed, with quadratic, cubic, and quartic stress fields, for static analysis of compressible and quasi-incompressible elastic solids in the variational framework of the minimum complementary energy principle. Thereafter, the high-order hybrid equilibrium formulation is developed for dynamic analysis of elastic solids in the variational framework of the Toupin principle, which is the complementary form of the Hamilton principle. The Newmark time integration scheme is introduced for discretization of the stress fields in the time domain and dynamic analysis of both the compressible solid and qua…

Nonlocal Interface Mechanical Model

The paper presents a nonlocal elastic damage-frictional interface model. The reason to introduce nonlocal mechanical features inside the constitutive relations is justified by the fact that there are several circumstances, in which the interface displays inside an extended process zone with microstructural spatial interactions. Typically, spatial bridging mechanical effects can be effectively modeled by integral (strongly nonlocal) stress-strain relations. The paper develops an elastic nonlocal model with local isotropic damage and the relations are constructed following a thermodynamical consistent approach.

A symmetric nonlocal damage theory

The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid's boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present app…

Cohesive delamination and frictional contact on joining surface via XFEM

In the present paper, the complex mechanical behaviour of the surfaces joining two different bodies is analysed by a cohesive-frictional interface constitutive model. The kinematical behaviour is characterized by the presence of discontinuous displacement fields, that take place at the internal connecting surfaces, both in the fully cohesive phase and in the delamination one. Generally, in order to catch discontinuous displacement fields, internal connecting surfaces (adhesive layers) are modelled by means of interface elements, which connect, node by node, the meshes of the joined bodies, requiring the mesh to be conforming to the geometry of the single bodies and to the relevant connectin…

Mixed Mode Delamination Analysis by a Thermodynamically Consistent Cohesive Interface Model with Independent Mode I and Mode II Fracture Energies

Abstract In the present paper a new thermodynamically consistent cohesive interface model is proposed; it based on a predefined Helmhotz free energy with a single scalar damage variable and produces two independent fracture energies, in pure mode I and pure mode II debonding conditions. The proposed model can also take in to account the frictional effects with a smooth transition of the mechanical behaviour, from the initial cohesive one of the sound material, to the frictional one of the fully debonded interface. The cohesive-frictional behaviour is based on the mesoscale geometric interpretation of the scalar damage variable, which distinguish sound and debonded fractions of a representat…

Frictional effect in mode II delamination: Experimental test and numerical simulation

Abstract The present paper proposes an experimental and a numerical analysis of the frictional effect on the mode II delamination. Frictional stresses between the crack edges can absorb and dissipate significant energy contributions in the delamination zones, especially under cyclic loading conditions. The experimental tests are performed for a set of unidirectional End-Notched Flexure (ENF) composite specimens, which are subjected to fatigue loading law with increasing mean value. The numerical analyses are performed considering a cohesive–frictional constitutive model, which is able to reproduce the transition of the interface behavior from the sound elastic condition to the fully cracked…

Analytical Solution of the 4ENF Test with Interlaminar Frictional Effects and Evaluation of Mode II Delamination Toughness

The present paper proposes an analytical solution of the four points bend end-notched flexure test (4ENF) with frictional contact between the delamination surfaces. The analytical solution was developed in the framework of the classic Euler-Bernoulli bending beam theory with orthotropic linear elastic constitutive behavior. The frictional contact was modeled as rigid-perfectly plastic with the Mohr-Coulomb activation function and the nonassociative flow rule. The elastic solution of the partially cracked beam subjected to the four points bending test with frictional contact was developed, and the Mode II delamination toughness was analytically determined by means of the Griffith approach, a…

An elastic-damage nonlocal interface model

A nonlocal elastic damage interface model is proposed

A Model for Low-Cycle Fatigue in Micro-Structured Materials

A microscale formulation for low-cycle fatigue degradation in heterogeneous materials is presented. The interface traction-separation law is modelled by a cohesive zone model for low-cycle fatigue analysis, which is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variables. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the static failure condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behaviour without any fatigue degradation for low levels of cyclic tra…

Analisi numerico-sperimentale sull’influenza dell’attrito nella delaminazione in Modo II

An elastic-damage interface model with thermo-mechanical coupled effects

A microplane model for plane-stress masonry structures

Publisher Summary For a refined nonlinear finite element analysis of masonry structures, an accurate constitutive model that is able to reproduce the desired phenomenological material features is required. Constitutive models for quasi-brittle materials, as plain concrete, have been proposed in the chapter, which allow to reproduce the very complex response in the two- or three-dimensional state of stress. Usually, the constitutive relations proposed are based on some appropriate extensions of elastic-plastic continuum models and more recently on continuum damage models. It has been observed that for these tensorial-based constitutive relations to be effective often require a large number o…

Hybrid equilibrium elements for accurate stress analysis

It is widely recognized that displacement elements produce poor stress fields, which do not satisfy strong equilibrium conditions. In several fields of computational mechanics, such as cohesive crack propagation and cohesive delamination, stress fields drive all the nonlinear phenomena and very fine meshes have to be employed in order to avoid numerical instabilities. In fact, inter-element equilibrium condition is generally not satisfied and stress fields can abruptly change between adjacent elements, producing strong inconvenient in crack propagation analysis. In the present paper hybrid stress elements are proposed as alternative to standard finite element for linear and non linear analy…

Effective reference and current integration for large displacement interface

The most common interface formulations proposed in literature are generally based on the restrictive hypothesis of small strains and small displacements and, even though their application to geometrically nonlinear problems is of paramount interest, only few contributions are available in literature. Motivations are probably due to the difficulties encountered on such formulation, as already mentioned by several authors. A pioneering formulation is the finite displacement three-dimensional interface developed by Ortiz and Pandolfi in [1], where normal and tangential traction components are evaluated with respect to the middle surface in the current configuration, producing a non-symmetric g…

A Computational Two-Scale Approach to Nonlinear Analysis of Etherogeneous Composite Structures

Elimination of spourious kinematic modes in hybrid equilibrium element

It is widely recognized that displacement based elements produce solution with poor stress fields, which do not satisfy equilibrium equations. In several fields of computational mechanics, such as cohesive crack propagation and cohesive delamination, stress fields drive all the nonlinear phenomena and very fine meshes have to be employed in order to avoid numerical instabilities. Inter-element equilibrium condition is generally not satisfied and the stress field can abruptly change between adjacent elements, producing numerical instabilities in non linear analysis. Finite element formulation based on stress fields satisfying locally equilibrium condition are known in literature since 1964 b…

Nonlocal Elastic-Damage Interface Mechanical Model

The paper presents a nonlocal extension of the elastic-damage interface mechanical model, which is able to describe the effects of the spatially extended microstructure on the decohesion (or fracture) process along a surface. The key feature of the proposed model is an integral constitutive relation between tractions and displacement jumps at the interface. The presence of an integral kernel brings in the model an internal length measure, which characterizes the transition from the microscale, dominated by heterogeneities and discontinuous media, to the mesoscale, characterized as an enhanced homogenized continuum with nonlocal features. The motivations and the fields of applications of the…

An Interface Mechanical Model with a Cohesive to Frictional Transition

A thermodynamically consistent mechanical interface model is presented. The model is based on the interface damage mechanic theory applied in a special fashion such that the interface damage variable is also used as a parameter which drives the continuous and smooth transition from the sound initial cohesive state to the final fully fractured frictional state. Interface damage activation and fictional sliding are promoted by a damage activation function and a Coulomb frictional yielding function. The main features of the model are discussed in details and some numerical results for the material response are shown in monotonic and cyclic loading regimes.

Integration of finite displacement interface element in reference and current configurations

In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two i…

A symmetric tangent stiffness approach to cohesive mechanical interfaces in large displacements

The present article proposes a formulation for a cohesive interface element in large displacement conditions. Theoretical and computational aspects, useful for an effective and efficient finite element implementation, are examined in details. A six-node (or higher) isoparametric interface element for two dimensional cohesive fracture propagation problems is developed. The element operators are consistently derived by a variational approach enforced in the current configuration, where a current frame is defined with axes tangential and normal to the middle line of the interface opening displacement gap. Under the constitutive assumption of small value of the modulus of the vector product bet…

Mode I failure modeling of friction stir welding joints

This paper analyzes mechanical response by finite element method up to the decohesion failure in fracture mode I for joints of friction stir welding (FSW) of an aluminum alloy. It first describes experimental investigations on specimens with FSW embedded, subjected to uniform traction and local punch tests used to characterize local elastic and plastic material parameters. The heterogeneity of the mechanical properties induced by the FSW process is taken into account for the elastic-plastic finite element simulation. The growing damage and the opening failure of the welding zone are described by the adoption of a cohesive interface model with specific mechanical properties.

A thermodynamically consistent cohesive-frictional interface model for mixed mode delamination

Abstract A new interface constitutive model based on damage mechanics and frictional plasticity is presented. The model is thermodynamically consistent, it is able to accurately reproduce arbitrary mixed mode debonding conditions and it is proved that the separation work is always bounded between the fracture energy in mode I and the fracture energy in mode II. Analytical results are given for proportional loading paths and for two non-proportional loading paths, confirming the correct behavior of the model for complex loading histories. Numerical and analytical solutions are compared for three classical delamination tests and frictional effects on 4ENF are also considered.

Hybrid Equilibrium Finite Element Formulation for Cohesive Crack Propagation

Equilibrium elements have been developed in hybrid formulation with independent equilibrated stress fields on each element. Traction equilibrium condition, at sides between adjacent elements and at sides of free boundary, is enforced by use of independent displacement laws at each side, assumed as Lagrangian parameters. The displacement degrees of freedom belongs to the element side, where an extrinsic interface can be embedded. The embedded interface is defined by the same stress fields of the hybrid equilibrium element and it does not require any additional degrees of freedom. The extrinsic interface is developed in the consistent thermodynamic framework of damage mechanics with internal …

Restraining approach for the spurious kinematic modes in hybrid equilibrium element

The present paper proposes a rigorous approach for the elimination of spurious kinematic modes in hybrid equilibrium elements, for three well known mesh patches. The approach is based on the identification of the dependent equations in the set of inter-element and boundary equilibrium equations of the sides involved in the spurious kinematic mode. Then the kinematic variables related to the dependent equations are reciprocally constrained and, by application of master slave elimination method, the set of inter-element equilibrium equations is reduced to full rank. The elastic solutions produced by means of the proposed approach verify the homogeneous, the inter-element and the boundary equi…

Fatigue crack growth of new FML composites for light ship buildings under predominant mode II loading condition

The use of light but strong materials is largely studied in various area of the shipbuilding, this because the need of reducing the weight, and especially the weight of all the structures above the main deck assume primary importance for the stability. Traditionally in fast boats like fast ferries, hydrofoils, patrol boats, the typical materials are Aluminum alloy or composites, both those materials have advantages and disadvantages, but the new development of technologies made possible to combine them, in order to have a new material, combining the advantages of both, in terms of fatigue resistance, firefighting characteristics. In this paper, predominant mode II fatigue delamination tests…

Cohesive–frictional interface constitutive model

AbstractIn the framework of numerical analysis of joined bodies, the present paper is devoted to the constitutive modeling, via an interface kinematic formulation, of mechanical behaviour of internal adhesive layers. The proposed interface constitutive model couples a cohesive behaviour, based on the damage mechanics theory, with a frictional one, defined in a non-associative plasticity framework. Namely, the interface formulation follows the transition of the adhesive material from the sound elastic condition to the fully cracked one. This formulation is able to model, by means of a specific interpretation of the damage variable and in a relevant mathematical setting, the interface interme…

Elimination of spurious kinematic modes in hybrid equilibrium elements

Hybrid stress elements are proposed as alternative to standard finite elements for linear and non linear analysis. Hybrid stress formulation is developed in a rigorous mathematical setting and an original approach for elimination of spurious kinematic modes is presented. Hybrid equilibrium method is compared to classical displacement based method by linear elastic analysis of some well known structural examples.

Shakedown Analysis by Elastic Simulation

Shakedown analysis of elastic plastic structures is widely credited as a valuable analytical/numerical tool for design purposes. For complex structures and loading conditions, e. g. for fast breeder nuclear reactor plants, full inelastic analysis is rarely performed, practically never within the early stages of the design advancement and the inherent decision process. The essential information therein needed can in fact be obtained, at moderate computational costs, by application of the shakedown methods and rules, at least within some limits related to the present developments of shakedown theory and its applicability to practical engineering problems, see e. g. Ponter et al. (1990), Carte…

Hybrid equilibrium element with interelement interface for the analysis of delamination and crack propagation problems

This article proposes a formulation for the analysis of delamination and fracture propagation problems at the interelement interface, with perfect adhesion at the pre-failure condition and with linear softening at the post-failure regime. The proposed formulation is based on the hybrid equilibrium element (HEE) model, with stress fields which strongly verify the homogeneous equilibrium equations and interelement equilibrium equations. The HEE can easily model high-order stress fields and can implicitly model the initially rigid behavior of an extrinsic interface at the element sides. The interface model is defined as a function of the same degrees of freedom of the HEE (generalized stresses…

Cohesive-frictional interface in an equilibrium based finite element formulation

The Hybrid Equilibrium Element (HEE) formulation, with quadratic stress field is defined in the class of statically admissible solutions, which implicitly satisfy the homogeneous equilibrium equations. The inter-element equilibrium condition and the boundary equilibrium condition are exactly imposed by considering a quadratic displacement fields at the element sides, as an interfacial Lagrangian variable, in a classical hybrid formulation. The displacement degrees of freedom are independently defined for each element side, where a cohesive-frictional interface can be embedded. The embedded interface is defined by the same stress fields of the hybrid equilibrium element and it does not requi…

Nonlocal interface mechanical models

The paper presents a nonlocal elastic damage-frictional interface model. The reason to introduce nonlocal mechanical features inside the constitutive relations is justified by the fact that there are several circumstances, in which the interface displays inside an extended process zone with microstructural spatial interactions. Typically, spatial bridging mechanical effects can be effectively modeled by integral (strongly nonlocal) stress-strain relations. The paper develops an elastic nonlocal model with local isotropic damage and the relations are constructed following a thermodynamical consistent approach.

An extrinsic interface developed in an equilibrium based finite element formulation

Abstract The phenomenon of delamination in composite material is studied in the framework of hybrid equilibrium based formulation with extrinsic cohesive zone model. The hybrid equilibrium formulation is a stress based approaches defined in the class of statically admissible solutions. The formulation is based on the nine-node triangular element with quadratic stress field which implicitly satisfy the homogeneous equilibrium equations. The inter-element equilibrium condition and the boundary equilibrium condition are imposed by considering independent side displacement fields as interfacial Lagrangian variable, in a classical hybrid formulation. The hybrid equilibrium element formulation is…

Inter-Element Crack Propagation with High-Order Stress Equilibrium Element

The present contribution proposes a formulation based on the use of hybrid equilibrium elements (HEEs), for the analysis of inter-element delamination and fracture propagation problems. HEEs are defined in terms of quadratic stress fields, which strongly verify both the homogeneous and inter-element equilibrium equations and they are employed with interfaces, initially exhibiting rigid behavior, embedded at the elements’ sides. The interface model is formulated in terms of the same degrees of freedom of the HEE, without any additional burden. The cohesive zone model (CZM) of the extrinsic interface is rigorously developed in the damage mechanics framework, with perfect adhesion at the pre-…

Analisi agli elementi finiti di crolli e tecniche di decostruzione per strutture intelaiate in C.A.

Multiple Crack Localization and Debonding Mechanisms for Thin Thermal Coating Films

Experimental tests, carried out on small scale alloy specimens covered on one side with a thin thermal coating, have shown complex failure mechanisms. The failure mechanisms observed are due to the competition between two fracture mechanisms. The two mechanisms are: (i) Vertical tensile coating surface cracks and (ii) debonding shear decohesion mechanisms along the interface between the coating and the substrate. The present paper analyzes the mechanical problem of the nonlinear behavior thin film on a stiff substrate adopting a computational approach. Namely, incremental 2D nonlinear finite element simulations. The stiff superalloy substrate is modeled as a thermo-elastic material. The coa…