1,721,005 research outputs found
Three-layer beams with interlayer slip and bi-linear interface law: an analytical solution
No full textOn micromechanics-based nonlocal modeling of elastic matrices weakened by voids
No full textWithin the mathematical modeling of the mechanical behavior of elastic composites, classical approaches usually treat the material as being macroscopically homogeneous with constant overall properties and develop constitutive equations relating suitable averages of microscopic stress and strain fields over a Representative Volume Element (RVE). As is well known, the application of such local approaches is limited to RVEs sufficiently large compared to the characteristic microstructural length of the material. In this paper the attention is focused on a specific class of elastic two-phase (matrix – heterogeneities) composites consisting of a matrix weakened by a random distribution of voids. The principal objective is to analyze the nonlocal effects of the internal microstructure of such weakened (“damaged”) materials (shape, orientation and distribution of voids) on their macroscopic mechanical properties. In order to do this, the accuracy of a standard local constitutive equation is analyzed by comparison with a nonlocal constitutive equation. From this comparison, quantitative estimates of the minimum RVE size of composite material for which the local model is sensible are also obtained. The formulation of nonlocal modeling here followed is that first developed by the second author together with Willis and more recently generalized by both the authors. Employing a generalization of the Hashin-Shtrikman variational formulation, these authors derived two micromechanics-based, completely explicit nonlocal constitutive equations relating the ensemble averages of stress and strain for random linear elastic two-phase composite materials consisting of an isotropic matrix containing isotropic heterogeneities. In particular, explicit results for the case of isotropic random distributions of heterogeneities (non-overlapping identical spheres and randomly-oriented spheroid-shaped inclusions/voids) resulting in isotropic macroscopic behavior were derived and further generalized to the case of transversely-isotropic distributions of heterogeneities (non-overlapping identical aligned spheroid-shaped inclusions/voids) resulting in more general transversely-isotropic macroscopic behavior. In order to apply the preceding theory to a wider range of practical applications for composites under consideration, including matrices weakened by voids of any shape, the preceding formulation is here specialized to the case of penetrable heterogeneities. From the comparison of previous results with the new set of results obtained, interesting conclusions will be drawn on the nonlocal effects of microstructure on the constitutive response of “damaged” materials
Effetti non locali nella risposta costitutiva di materiali compositi a microstruttura disordinata
No full textOggetto del lavoro è la stima della dimensione minima ammissibile per un elemento di volume rappresentativo di materiale composito, affinchè gli effetti non locali risultino trascurabili in una descrizione macroscopica del comportamento costituttivo. A tale scopo, si utilizza un modello non locale ottenuto sulla base di un approccio micromeccanico all'analisi della risposta di matrici al cui interno sia dispersa una distribuzione casuale di vuoti/inclusioni sferoidali. In particolare, vengono presentati alcuni risultati riferiti al caso di vuoti di forma diversa e per questi discussi i relativi effetti nonlocali
Descrizione anisotropa del danno in interfacce imperfette
No full textViene proposto un modello d’interfaccia imperfetta espresso in termini di trazioni e discontinuità di spostamento e basato su una descrizione al continuo del danno conseguente a stati di microfessurazione diffusa nell’interfaccia. Si considerano due micromeccanismi responsabili del comportamento macroscopico, le cui modalità di attuazione dipendono dalla condizione attuale dell’interfaccia: distacco e/o scorrimento con attrito tra le superfici opposte e propagazione del danno. Il modello dipende da cinque costanti e da tre variabili interne delle quali una, di tipo tensoriale, necessaria per descrivere il carattere anisotropo del danno ed altre due atte a descrivere il contatto monolatero attritivo. Con riferimento al caso particolare di interfacce non dilatanti, l’equazione costitutiva viene scritta in forma incrementale, finalizzata alla definizione di un elemento finito d’interfaccia da utilizzarsi in applicazioni numeriche
Correzione non locale alle proprietà elastiche globali di materiali compositi a microstruttura disordinata
No full textResponse of two-layer composite beams with interlayer slip and damaging interfaces
No full textBeams and columns made of different materials or reinforced with steel or composite elements are only some examples of two-layer structural systems. The combination of different elements improves the performances of the system but introduces weak elements such as interfaces. A perfect connection that retains relative displacements between the layers would allow a complete transmission of the stresses and ensure optimal performance in terms of global stiffness and strength. However, in practice, this is difficult to obtain, so that relative displacements between the layers can occur and only a partial composite action follows. As a consequence, the mechanical behavior of multi-layer composite beams depends not only on the geometrical and mechanical properties of the single layers but also on the nature of the bond between them. The optimal design of such composite systems needs to account for the response of interfaces and the progressive interface damaging as further global failure mechanism.
The problem of the equilibrium of multi-layer beams consisting of elastic layers elastically bonded has been the object of a large number of studies. Only a little attention has been focused on the nonlinear interfacial behavior. On the other hand, under loading conditions that generate interlaminar stresses flaws and defects due to manifacturing errors or impacts may propagate or, alternatively, mechanical shear devices such as nails and steel studs may yield. This leads to a further reduction of the degree of the connection between the layers and, as a consequence, of the global stiffness and strength of the system and even to its premature collapse when the layers are still elastic.
This work, trying to fill this gap, develops basic understanding of the essential features of such particular failure mechanism that affects the mechanical response and strength of structural composite elements, in order to optimize their design and performance in practical applications.
In the framework of a multi-scale treatment of the problem, composite beams are modelled as beams having a higher number of degrees of freedom than classical homogeneous beams and governed by additional compatibility and constitutive equations accounting for relative displacements between the layers. The analysis builds on previous works by the authors in which fundamental analytical solutions for two-layer beams with interlayer slip and non-proportional linear interface constitutive laws are obtained. The formulation is restricted to the analysis of bonds realized, for instance, by the use of nails for which the stiffness in the transverse direction can be assumed to be infinite, so that uplifts between the layers are not allowed and only slips between the layers in their longitudinal direction can occur.
According to classical elastic beam theory, each layer is modelled as an elastic Euler-Bernoulli beam. The connection in the longitudinal direction is modelled as a continuous distribution of shear tractions related to displacement discontinuities between the layers through a multi-linear law. Such a multi-linear law represents the evolution of the interfacial behavior during a loading process and allows simple analytical solutions for each its linear branch representing a regime the interface can undergo.
With reference to beams subjected to simple loading and constraining conditions, a complete simulation from damage initiation to ultimate failure of the damage process at the bond is conducted in order to investigate the mechanical response and the collapse of the system and to understand which parameters characterizing the interface law have the most influence on the global response of the composite system. Future developments deal with the interaction of this failure mechanism with failure mechanisms involving layer materials and the influence of such interaction on the global mechanical response
Analisi di lastre contenenti fessure interagenti
No full textL'evoluzione della frattura di lastre finite multi-fessurate viene simulata mediante un processo di carico incrementale in cui è assunto quale parametro di controllo la lunghezza delle fessure; possono così essere rilevate anche eventuali instabilità di tipo snap-back. Il problema è affrontato nell'ambito della Meccanica della Frattura Elastica Lineare, con riferimento a lastre di dimensioni finite contenenti distribuzioni ordinate o casuali di fessure interagenti in condizioni di carico, rispettivamente, di modo I e di modo misto. I relativi diagrammi carico-spostamento, compresi eventuali tratti instabili, sono tracciati utilizzando un codice di calcolo automatico basato sul Metodo degli Elementi di Contorno a Discontinuità di Spostamento
RVE size estimates for elastic matrices with spherically multi-layer inclusions
No full textA micromechanics-based nonlocal constitutive equation for a matrix containing a random distribution of homogeneous solid spheres is employed to analyze the case of spherically multi-layer inhomogeneous inclusions. The analysis builds on and generalizes previous papers focused on two-phase composites. In particular, it is shown how the task of the derivation of elastic properties for the inclusion phase can be make reasonable by replacing inhomogeneous inclusions with homogeneous spheres having equivalent elastic moduli. The constitutive equation is then used to explore nonlocal effects of layer distribution in the inclusions on the response of the composite material and derive quantitative estimates of the minimum RVE size over which a nonlocal correction to the standard local model is needed to provide a sensible description of the constitutive response of the material
Analytical solutions of three-layer beams with interlayer slip and step-wise linear interface law
No full textA new formulation to solve the equilibrium problem of three-layer beams with interlayer slip is proposed. Each layer is modelled as a linearly elastic Euler-Bernoulli beam. Connections between layers are assumed to be perfect in the transverse direction while to have finite stiffness in the longitudinal direction (only interlayer slips are allowed). Interface behaviors in the longitudinal direction are described through linear non proportional relationships relating shear traction and slip between two layers. A novel closed form solution is then obtained and explicit expressions for all static and kinematic variables are derived. This analytical solution can be employed to simulate the response of composite beams for different boundary and loading conditions generating interfacial tractions that induce an irreversible process of progressive interfacial debonding. A numerical example is considered to investigate the influence of a post-elastic interface behavior on the global response of the composite beam when the layers are still elastic
A Non-Associative Anisotropic Damage Model for Brittle Materials
No full textA micromechanically based anisotropic damage model for brittle materials having different tensile-compressive response is proposed. The material is modelled as an elastic isotropic matrix containing a statistically uniform distribution of growing microcracks. Under the simplifying assumption of non-interacting and self-similar propagating flat cracks, a friction-damage coupled model based on two tensor-valued internal variables, representing damage and frictional contact tractions, is derived. The use of a tensor-valued variable for damage, in particular, makes the model to be capable of describing the load-induced anisotropic response of brittle and quasi-brittle materials. In the framework of thermodynamics with internal variables, overall frictional sliding and crack growth criteria with associated flow rules are used to complement the model. The constitutive equations are then applied to analyze the material response to meaningful loading paths. In order to validate the model, limit strength domains for biaxial and triaxial stress states are derived as well
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