186,665 research outputs found
Application of augmented lagrangian techniques for nonlinear constitutive laws in contact interfaces
No full textThe use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm
On contact between three-dimensional beams undergoing large deflections
No full textContact between three-dimensional beams which undergo large motions is considered. To formulate the associated constraint conditions the point of contact has to be detected within the beam. Once this is known the contact constraint has to be formulated for a given beam discretization and the associated contribution to the weak form has to be developed. Also, consistent linearization of the contact contribution is derived, which is needed within Newton's metho
A segment-to-segment contact strategy
No full textthis paper, a method is proposed to define the geometrical contact constraints. Within this treatment one has the possibility to define locally the contact parameters for an accurate treatment of contact constraints. Local values of the geometrical variables can be determined at the integration points, hence the method permits to integrate contact constitutive laws along contact segments.
The weak form for this new formulation is developed. Furthermore, also the consistent linearization is carried out. Finally a technique is proposed to reduce the large number of terms involved. In this case, an almost consistent tangent stiffness is determined. @ 1998 Elsevier Science Ltd. All rights reserved
Numerical modelling of intergranular fracture in polycrystalline materials and grain size effects
No full textABSTRACT. In this paper, the phenomenon of intergranular fracture in polycrystalline materials is investigated
using a nonlinear fracture mechanics approach. The nonlocal cohesive zone model (CZM) for finite thickness
interfaces recently proposed by the present authors is used to describe the phenomenon of grain boundary
separation. From the modelling point of view, considering the dependency of the grain boundary thickness on
the grain size observed in polycrystals, a distribution of interface thicknesses is obtained. Since the shape and
the parameters of the nonlocal CZM depend on the interface thickness, a distribution of interface fracture
energies is obtained as a consequence of the randomness of the material microstructure. Using these data,
fracture mechanics simulations are performed and the homogenized stress-strain curves of 2D representative
volume elements (RVEs) are computed. Failure is the result of a diffuse microcrack pattern leading to a main
macroscopic crack after coalescence, in good agreement with the experimental observation. Finally, testing
microstructures characterized by different average grain sizes, the computed peak stresses are found to be
dependent on the grain size, in agreement with the trend expected according to the Hall-Petch law.
SOMMARIO. In questo articolo, il fenomeno della frattura intergranulare nei material policristallini è studiato
mediante un approccio di meccanica della frattura non lineare. Il modello non locale di frattura coesiva per
interfacce con spessore finito recentemente proposto dai presenti autori è impiegato per descrivere il fenomeno
di separazione ai bordi di grano. Da un punto di vista modellistico, considerando la dipendenza dello spessore
dei bordi di grano dalla dimensione del grano stesso, si è ottenuta una distribuzione delle proprietà meccaniche
delle interfacce. Essendo la forma ed i parametri del modello non locale della frattura coesiva dipendenti dallo
spessore dell'interfaccia, si ottiene una distribuzione di energie di frattura come conseguenza della variabilità
statistica della microstruttura del materiale. Usando tali dati si conducono simulazioni di meccanica della frattura
su elementi di volumi rappresentativi (RVE) in 2D e si determinano le rispettive curve di tensionedeformazione.
La frattura è il risultato di un insieme di microfessure diffuse che danno luogo alla propagazione
di una fessura macroscopica principale, in ottimo accordo con quanto osservato sperimentalmente. Infine,
testando microstrutture dotate di diversi diametri medi dei grani, si osserva come le tension
Thermomechanical contact - a rigorous but simple numerical approach
No full textA contact element which deals with mechanical and thermal fields is presented. The geometrically linear formulation leads to an algorithm which is on one hand very simple to code, but on the other hand very efficient and yields deep insight into the real physical behaviour of contact conductance. The presented formulation permits to add the contact algorithm to any finite element code
Contact with friction between beams in 3-D Space
No full textIn this paper a formulation to deal with friction between straight beams undergoing large displacements in 3-D space is proposed. The detection of the contact point and the computation of the amount of sliding are carried out using a completely symmetric treatment between the two contacting beams. Starting from the virtual work equation the consistent linearization of the frictional contact contribution is computed and the complete equation set is arranged in matrix form suitable for FE implementation. Some numerical examples are added to show the eectiveness of the method
A nonlocal cohesive zone model for finite thickness interfaces – Part II: FE implementation and application to polycrystalline materials
No full textNumerical aspects of the nonlocal cohesive zone model (CZM) presented in Part I are discussed in this companion paper. They include the FE implementation of the proposed nonlocal CZM in the framework of zero-thickness interface elements and the numerical treatment of the related nonlocality. In particular, a Newton–Raphson method, combined with a series expansion to obtain tentative values for the cohesive tractions, is used to efficiently compute the tangent stiffness matrix and the residual vector of the interface elements. Then, numerical applications to polycrystalline materials are proposed, focusing on the constitutive modelling of the finite thickness interfaces between the grains. It will be shown that the parameters of the nonlocal CZM (shape, peak stress, fracture energy) depend on the thickness of the interface. The CZM is able to produce statistical distributions of Mode I fracture energies consistent with those assumed a priori in stochastic fracture mechanics studies. The statistical variability of fracture parameters, originating from the natural variability of the interface thicknesses, has an important influence on the crack patterns observed from simulated tensile tests. Finally, we show that the relation between interface thickness and grain size can be used to explain the grain-size effects on the material tensile strength. In particular, considering a sublinear relation between the interface thickness and the grain diameter at the microscale, the nonlocal CZM is able to recover the Hall–Petch law. Therefore, the proposed model suggests that an inverse relation between the interface thickness and the grain size would lead to an inversion of the Hall–Petch law as well. This new interpretation seems to be confirmed by experimental data at the nanoscale, where the inversion of the Hall–Petch law coincides with the anomalous increase of the interface thickness by reducing the grain size
A method for solving contact problems
No full textIn this paper a further method is presented to solve problems involving contact mechanics. The basic idea is related to a special modification of the unconstrained functional to include inequality constraints. The modification is constructed in such a way that minimal point of the unconstrained potential can be exactly shifted to the constraint limit. Moreover, the functional remains smooth and the admissible range of the solution is not restricted. The solution search process with iterative techniques takes advantage from these features. In fact, due to a better control of gap status changes, a more stable solution path with respect to other methods is usually obtained.
The characteristics of the method are evidenced and compared to other classical techniques, like penalty and barrier methods. The finite element discretization of the proposed method is included and some numerical applications are shown
A nonlocal cohesive zone model for finite thickness interfaces - Part I: mathematical formulation and validation with molecular dynamics
No full textA nonlocal cohesive zone model is derived taking into account the properties of finite thickness interfaces. The functional expression of the stress–separation relationship, which bridges the gap between continuum damage mechanics and nonlinear fracture mechanics, depends on the complex failure phenomena affecting the material microstructure of the interface region. More specifically, the shape of the nonlocal cohesive zone model is found to be dependent on the damage evolution. On the other hand, damage is in its turn a function of dissipative mechanisms occurring at lower length scales, such as dislocation motion, breaking of interatomic bonds, formation of free surfaces and microvoids, that are usually analyzed according to molecular dynamics. Hence, the relationship intercurring between the parameters of the damage law and the outcome of molecular dynamics simulations available in the literature is also established. Therefore, the proposed nonlocal cohesive zone model provides also the proper mathematical framework for interpreting molecular dynamics-based stress–separation relationships that are typically nonlocal, since they always refer to a finite number of atom layers
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