Giorgio Zavarise

Contact with friction between beams in 3‐D space

In 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 effectiveness of the method. Copyright

ON CONTACT BETWEEN THREE-DIMENSIONAL BEAMS UNDERGOING LARGE DEFLECTIONS

Contact 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 Newtons method.

A segment-to-segment contact strategy

In this 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.

A method for solving contact problems

In 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.

Numerical simulation of wear-mechanism maps

Abstract Wear-mechanism maps for different materials, actually steel on steel, are being modeled with FEM. A microthermo-mechanical approach has been used in order to model accurately the macroscopic phenomena of wear. A plastic law for the normal micromechanical contact of asperities has been implemented in FEAP and a slight modification, based on experimental results, is proposed. For the three mechanisms modeled, good correlation between the numerical results of wear and those found in literature has been obtained for a pin-on-disk configuration. The flash temperatures reached in the contact interface have been also studied and fair good agreement with literature is achieved.

A superlinear convergent augmented Lagrangian procedure for contact problems

The numerical solution of contact problems via the penalty method yields approximate satisfaction of contact constraints. The solution can be improved using augmentation schemes. However their efficiency is strongly dependent on the value of the penalty parameter and usually results in a poor rate of convergence to the exact solution. In this paper we propose a new method to perform the augmentations. It is based on estimated values of the augmented Lagrangians. At each augmentation the converged state is used to extract some data. Such information updates a database used for the Lagrangian estimation. The prediction is primarily based on the evolution of the constraint violation with respect to the evolution of the contact forces. The proposed method is characterised by a noticeable efficiency in detecting nearly exact contact forces, and by superlinear convergence for the subsequent minimisation of the residual of constraints. Remarkably, the method is relatively insensitive to the penalty parameter. This allows a solution which fulfils the constraints very rapidly, even when using penalty values close to zero.

Thermomechanical contact : a rigorous but simple numerical approach

Abstract A contact element which deals with mechanical and thermal fields is presented. The geometrically linear formulation leads to an algorithm which is on the 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 the addition of the contact algorithm to any finite element code.

A unified interface constitutive law for the study of fracture and contact problems in heterogeneous materials

A unified interface constitutive law for the description of contact and decohesion at bi-material interfaces is proposed. To this aim, a synthesis of the nonlinear models pertaining to Fracture and Contact Mechanics is presented. The issues pertinent to the implementation within the FE discretization framework are also discussed in detail. Finally, a numerical example of fatigue modeling at the mesoscopical level in a fiber-reinforced composite is provided.

Modeling a multistrand SC cable with an electrical DC lumped network

The paper presents a procedure for the numerical computation of the global interstrand resistances measured between strands of superconducting multistrand cables. The procedure is based on a geometrical reconstruction of the cable strands geometries, which are used to generate an electrical equivalent DC lumped network. In this network, the strands are represented by ideal short circuits and the geometrical points of contact between the strands correspond to lumped conductances. The network is completed with a suitable arrangement of connections between strands and DC power supplies. The network equations are then solved numerically and the strand currents are evaluated together with the interstrand voltages. The accuracy of the procedure is discussed through a comparison with experimental results.

A consistency assessment of coupled cohesive zone models for mixed-mode debonding problems

Due to their simplicity, cohesive zone models (CZMs) are very attractive to describe mixed-mode failure and debonding processes of materials and interfaces. Although a large number of coupled CZMs have been proposed, and despite the extensive related literature, little attention has been devoted to ensuring the consistency of these models for mixed-mode conditions, primarily in a thermodynamical sense. A lack of consistency may affect the local or global response of a mechanical system. This contribution deals with the consistency check for some widely used exponential and bilinear mixed-mode CZMs. The coupling effect on stresses and energy dissipation is first investigated and the path-dependance of the mixed-mode debonding work of separation is analitically evaluated. Analytical predictions are also compared with results from numerical implementations, where the interface is described with zero-thickness contact elements. A node-to-segment strategy is here adopted, which incorporates decohesion and contact within a unified framework. A new thermodynamically consistent mixed-mode CZ model based on a reformulation of the Xu-Needleman model as modified by van den Bosch et al. is finally proposed and derived by applying the Coleman and Noll procedure in accordance with the second law of thermodynamics. The model holds monolithically for loading and unloading processes, as well as for decohesion and contact, and its performance is demonstrated through suitable examples.