A damage interface model with cohesive-frictiona continuous transition

Failure modelling of friction stir welded joints in tensile tests

Dynamic shakedown of structures under repeated seismic loads

Elastic, perfectly plastic structures are considered under the action of repeated short-duration exitations of seismic type acting in an unknown time sequence, but belonging to a given polyhedral excitation domain. The basic excitations (vertices of the polyhedron) are chosen as discrete-spectrum waves each with frequencies coincident with the first natural frequencies of the structure, and amplitudes related to the ground features and earthquake intensity (according to the Kanai and Tajimi filter model) in such a way that every admissible excitation-obtained as a linear convex combination of the basic ones-has a maximum power not exceeding a given value. In the framework of unrestricted dy…

A thermodynamically consistent nonlocal formulation for damaging materials

A thermodynamically consistent nonlocal formulation for damaging materials is presented. The second principle of thermodynamics is enforced in a nonlocal form over the volume where the dissipative mechanism takes place. The nonlocal forces thermodynamically conjugated are obtained consistently from the free energy. The paper indeed extends to elastic damaging materials a formulation originally proposed by Polizzotto et al. for nonlocal plasticity. Constitutive and computational aspects of the model are discussed. The damage consistency conditions turn out to be formulated as an integral complementarity problem and, consequently, after discretization, as a linear complementarity problem. A n…

Erratum to: Letter to the Editor [Engineering Fracture Mechanics 2003 (70) 1219-21]

Erratum and Corrections

XFEM approach to nonlinear analysis of composite structures

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

A thermodynamic approach to nonlocal plasticity and related variational principles

Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, …

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…

Fluid-structure interaction approach with smoothed particle hydrodynamics and particle-spring systems

This paper presents a novel three-dimensional fluid-structure interaction (FSI) approach, where the meshless smoothed particle hydrodynamics (SPH) method is used to simulate the motion of incompressible fluid flows, whilst structures are represented by a simplified approach based on particle-spring systems. The proposed FSI technique allows to use independent spatial-temporal resolutions for the fluid and structural computational domains. The particle-spring elastic constants are calibrated and relationships with the mechanical material properties, Young's modulus and Poisson's ratio, are determined. Fluid and structure computational domains are separated by interfaces made of triangular el…

A mechanical approach to fractional non-local thermoelasticity

In recent years fractional di erential calculus applications have been developed in physics, chemistry as well as in engineering elds. Fractional order integrals and derivatives ex- tend the well-known de nitions of integer-order primitives and derivatives of the ordinary di erential calculus to real-order operators. Engineering applications of these concepts dealt with viscoelastic models, stochastic dy- namics as well as with the, recently developed, fractional-order thermoelasticity [3]. In these elds the main use of fractional operators has been concerned with the interpolation between the heat ux and its time-rate of change, that is related to the well-known second sound e ect. In othe…

Non-stationary spectral moments of base excited MDOF systems

The paper deals with the evaluation of non-stationary spectral moments of multi-degree-of-freedom (MDOF) line systems subjected to seismic excitations. The spectral moments of the response are evaluated in incremental form solution by means of an unconditionally stable step-by-step procedure. As an application, the statistics of the largest peak of the response are also evaluated.

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…

Shakedown Under Thermomechanical Loads

A shakedown theory for elastic–perfectly plastic structures subjected to thermomechanical loads varying within a given range is outlined under the assumption of temperature-dependent yield stress, but temperature-independent elastic moduli and thermal expansion coefficient are considered. Inertia and creep effects, along with thermal coupling phenomena, are considered negligible. A nonstandard constitutive model is used in which a central role is played by the yield function-assumed convex in the stress–temperature space. The inherent flow mechanism obeys the normality rule and includes, beside the standard plastic strain rates, an extra scalar variable work conjugate of the temperature, co…

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.

Dam-reservoir interaction in the seismic analysis of gravity dams

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

Nonlocal Elastic-Damage Models

A theory of nonlocal isotropic damage for elastic quasi-brittle materials is presented under the assumption of isothermal conditions and small deformations. Key ingredients of this theory are a self-adjoint (regularization) operator which transforms a local field into a related nonlocal one while preserves uniform fields and a free energy which depends on the strain and (linearly) on the nonlocal damage variable, as well as on an (scalar) internal variable accounting for the damage hardening. The relevant thermodynamic restrictions on the constitutive equations are obtained by means of two alternative procedures, one based on the principle of virtual power and the other on the concept of “n…

An approach to elastic shakedown based on the maximum plastic dissipation theorem

ELASTIC-PERFECTLY PLASTIC SOLID STRUCTURES are considered subjected to combined loads, superposition of permanent (mechanical) loads and cyclically variable loads, the latter being specified to within a scalar multiplier. The classical maximum dissipation theorem is used to derive known results of the shakedown theory, as well as a few apparently novel concepts: the shakedown limit load associated with a given (noninstantaneous) collapse mode, the mixed upper bound to the shakedown safety factor, and the mixed static-kinematic formulation of the shakedown safety factor problem. The shakedown load boundary surface is also investigated and a number of its notable features are pointed out. A s…

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

A method to transform a nonlocal model into a gradient one within elasticity and plasticity

Abstract A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kerne…

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…

A Thermodynamic Plasticity Formulation with Local and Nonlocal Internal Variables

In order to obtain the elastic response of nonhomogeneous materials, it is often sufficient to adopt an implicit homogenization technique which allows one to treat the material as an equivalent continuum medium. For large stress concentration or for accurate small scale studies this widely applied technique may show some limit and a more refined analysis might be required involving nonlocal elastic effects, see e.g. Kroner (1967), Eringen et al. (1977).

A non-local model of fractional heat conduction in rigid bodies

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent s…

Incremental Delamination Processes under Cyclic Loading

Discussion: “Chaotic Motion of an Elastic-Plastic Beam” (Poddar, B., Moon, F. C., and Mukherjee, S., 1988, ASME J. Appl. Mech., 55, pp. 185–189)

Discussion on caotic motion of a pinned beam subjected to pulse loading

Shakedown of Structures Accounting for Damage Effects

Shakedown theory for elastic-plastic-damage materials is exposed. Two kinds of shakedown are considered: i) Enlarged shakedown (or simply shakedown), in which both plastic deformations and damage eventually cease, after which the structural response is purely elastic; ii) Weak-form shakedown, in which plastic deformations eventually cease together with their consequences (including ductile damage), not necessarily damage from other sources (which are however escluded by assumption). An (enlarged) shakedown static-type theorem is given for a class of D-stable structures. Sufficient theorems of weak-form shakedown are provided, i.e. a static-type one (quite similar to that of Hachemi and Weic…

Shakedown Problems for Material Models with Internal Variables

The classical shakedown theory is reconsidered with the objective of extending it to a quite general constitutive law for rate-insensitive elastic-plastic material models endowed with dual internal variables and thermodynamic potential. The statical and kinematical shakedown theorems, the corresponding approaches to the shakedown load multiplier problem and a deformation bounding theorem are presented and discussed with a view of further developments.

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…

Mathematical Programming Methods for the Evaluation of Dynamic Plastic Deformations

Dynamic plastic deformation can be evaluated with two accuracy levels, nemely either by a full analysis making use of a step-by-step procedure, or by a simplified analysis making use of a bounding technique. Both procedures can be achieved by means a unified mathematical programming approach here presented. It is shown that for a full analysis both the direct and indirect methods of linear dynamics coupled with mathematical programming methods can be successfully applied, whereas for a simplified analysis a convergent bounding principle, holding both below and above the shakedown limit, can be utilized to produce an efficient linear programming-based algorithm.

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…

Consistent shakedown theorems for materials with temperature dependent yield functions

The (elastic) shakedown problem for structures subjected to loads and temperature variations is addressed in the hypothesis of elastic-plastic rate-independent associative material models with temperature-dependent yield functions. Assuming the yield functions convex in the stress/temperature space, a thermodynamically consistent small-deformation thermo-plasticity theory is provided, in which the set of state and evolutive variables includes the temperature and the plastic entropy rate. Within the latter theory the known static (Prager's) and kinematic (König's) shakedown theorems - which hold for yield functions convex in the stress space - are restated in an appropriate consistent format…

A thermodynamically consistent formulation of nonlocal and gradient plasticity

A nonlocal integral approach to elastic-damage interface modelling

An elastic-damage nonlocal interface model

A nonlocal elastic damage interface model is proposed

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

A constitutive framework based on elastic and internal energy degradation

A general constitutive framework is presented capable of representing different irreversible deformation modes, like plasticity, elastic damage, complex evolution of the hardening properties and the induced coupling effects. The formulation can be framed in the generalized standard material models with internal variables and multiple dissipative activation functions. The formulation is thermodynamically consistent and the state laws, the structure of the dissipation and of the activation functions are all derived complying with the principles of thermodynamics. The generalized flow rules are derived under the hypothesis of generalized associativity. The main aspect of the proposed model is …

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…

An elastic interface model with nonlocal integral damaging effects

Thermodynamically consistent residual-based gradient plasticity theory and comparison

A gradient plasticity theory for small deformations is presented within the framework of nonlocal continuum thermodynamics. The second principle (Clausius–Duhem inequality), enriched by an additional term named energy residual, is employed in conjunction with the concepts of insulation condition and locality recovery condition, in order to derive all the pertinent restrictions upon the constitutive equations. These include the expressions of the energy residual and of the plastic dissipation density, as well as the PDEs governing the gradient kinematic and isotropic hardening of the material, together with the related higher-order boundary conditions for both the fixed and the moving bounda…

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.

A theoretical link between gradient and nonlocal elasticity models, including higher order boundary conditions

The paper presents a recently developed rational derivation of the strain gradient elasticity model from the nonlocal (or integral) model. This kind of derivations are generally recovered just by an expansion into a Taylor series of the nonlocal strain field up to a certain order, and then operating the integration (or averaging) over the spatial interaction domain. The latter procedure is fully consistent when the analysis is performed over an unbounded domain, but when a classical bounded domain is analyzed it lacks in reproducing the so-called higher-order boundary conditions. In the present contributions the complete derivation is achieved employing an extended version of the Principle …

Shakedown of Structures Subjected to Dynamic External Actions and Related Bounding Techniques

The shakedown theory for dynamic external actions is expounded considering elastic-plastic internal-variable material models endowed with hardening saturation surface and assuming small displacements and strains as long with negligible effects of temperature variations on material data. Two sorts of dynamic shakedown theories are presented, i.e.: i) Unrestricted dynamic shakedown, in which the structure is subjected to (unknown) sequences of short-duration excitations belonging to a known excitation domain, with no-load no-motion time periods in between and for which a unified framework with quasi-static shakedown is presented; and ii) Restricted dynamic shakedown, in which the structure is…

A thermodynamics-based formulation of gradient-dependent plasticity

Abstract A nonlocal thermodynamic theoretical framework is provided as a basis for a consistent formulation of gradient-dependent plasticity in which a scalar internal variable measuring the material isotropic hardening/softening state is the only nonlocal variable. The main concepts of this formulation are: i) the ‘regularization operator’, of differential nature, which governs the relation between the above nonlocal variable and a related local variable (scalar measure of plastic strain) and confers a unified character to the proposed formulation (this transforms into a formulation for nonlocal plasticity if the regularization operator has an integral nature); ii) the ‘nonlocality residua…

A Linear Programming Method for Bounding Plastic Deformations

A method for providing upper and lower bounds to plastic deformations is presented, which has the feature of being applicable both below and above the structure shakedown limit. The bounds provided are expressed in terms of some fictitious plastic strains obeying relaxed yielding laws, whose evaluation is made by means of a suitable LP-based algorithm.

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.

Some observations on the regularizing field for gradient damage models

Gradient enhanced material models can potentially preserve well-posedness of incremental boundary value problems also after the onset of strain softening. Gradient dependent constitutive relations are rooted in the assumption that some scalar or tensor field, which appears in the yield function, has to be enriched by adding a term involving its second-order gradient field. For gradient-dependent plasticity this term is universally accepted to be the equivalent plastic strain. For gradient-dependent damage models different choices have been presented in the literature. They all possess the desired regularization of the solution, but they are not identical as regards the structural response. …

A thermodynamically consistent gradient plasticity theory and comparisons with other formulations

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…

A nonlocal damage interface model

Energy-Residual-Based approach to gradient plasticity

The “energy-residual-based approach” mentioned in the title consists in a thermodynamically consistent procedure for the formulation of a phenomenological plasticity model of either strain gradient, or nonlocal (integral) type. The authors have developed this procedure on the last ten years. It seem therefore appropriate to present an update of this theory at this forum. For brevity we shell limit ourselves to strain gradient plasticity.

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…

Theorems of restricted dynamic shakedown

Abstract Dynamic shakedown for a rate-independent material with internal variables is addressed in the hypothesis that the load values are restricted to those of a specified load history of finite or even infinite duration, thus ruling out the possibility—typical of classical shakedown theory—of indefinite load repetitions. Instead of the usual approach to dynamic shakedown, based on the bounded plastic work criterion, another approach is adopted here, based on the adaptation time criterion. Static, kinematic and mixed-form theorems are presented, which characterize the minimum adaptation time (MAT), a feature of the structure-load system, but which are also able to assess whether plastic w…

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.

Mode superposition methods in dynamic analysis of classically and non-classically damped linear systems

Mode-superposition analysis is an efficient tool for the evaluation of the response of linear systems subjected to dynamic agencies. Two well-known mode-superposition methods are available in the literature, the mode-displacement method and the mode-acceleration method. Within this frame a method is proposed called a dynamic correction method which evaluates the structural response as the sum of a pseudostatic response, which is the particular solution of the differential equations, and a dynamic correction evaluated using a reduced number of natural modes. The greater accuracy of the proposed method with respect to the other methods is evidenced through extensive numerical tests, for class…

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…

Dynamic shakedown of structures with variable appended masses and subjected to repeated excitations

Elastic shakedown for discrete, or finite-element discretized, structures subjected to combinations of static and time-variable loads is addressed in the hypothesis of elastic-perfectly plastic material behavior. The static load is conceived as the weight of an additional mass appended to the structure, whereas the time-variable load is conceived as an unknown sequence of excitations belonging to a specified domain, with intervals between subsequent excitations during which the structure is considered as being motionless. It is shown that, in the plane of the static and time-variable load parameters, the structure's dynamic shakedown domain is nonconvex and that its boundary curve generally…

Una interfaccia elasto-danneggiativa arricchita con termini gradiente

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…