A generalized formulation for contact between beams

The currently available formulations for contact between beams are based on the identification of the minimal distance points along the beam axes, followed by some tuning in case of non-circular beam cross-sections. Up to now a suitable implementation within the framework of the Finite Element Method is available both for the frictionless and for the frictional case. The procedure requires the explicit computation of the virtual work contribution due to the contacts. In such a context for solving the problem with implicit schemes, the formulation has also to be consistently linearized. With this respect both the frictionless and the frictional formulation present severe problems. To overcome all the cited problems a generalized formulation is proposed, which deals with contact between circular beams. It has to be remarked that the contact problem is treated first in a completely generic framework, and only in a second step the results are particularized to the FE formulation. For such purpose the centroids of the beams in the 3-D space are considered as parametric functions. The framework for the consistent linearization is developed in a very rigorous and systematic way, providing evidence of the symmetry of the operators. The procedure is quite cumbersome, hence here only the most heavy part, related to the computation of all the fundamental geometrical terms involved, is presented

T-splines discretizations for large deformation contact problems

The isogeometric analysis (IGA) represents a new method of computational analysis that merges design and analysis into one model by using a unified geometric representation. NURBS (Non-Uniform Rational B-Splines) and T-Splines are the most widespread technologies in today’s CAD modelling tools and therefore are adopted as basis functions for analyses. In this work the isogeometric concept [1] is applied to study the large deformation multi-body contact problems, which still represent a significant challenge for the analysts in terms of robustness and stability of solutions. For this reason, the development of more efficient, fast and stable finite element contact discretizations is still a hot topic, especially due to the fact that engineering applications become more and more complex. Among the most important challenges that have to be met with respect to finite element discretization is the sensitivity of contact problem to the geometry accuracy. Non-smooth, C0-continuous finite element basis functions lead to convergence problems in the analysis of sliding contact and to highly oscillatory contact interactions even when convergence is achieved. Various contact smoothing techniques have been proposed in the literature to address this issue [2-6] which consider the smoothing of the master and slave surfaces as achieved by high-order finite element interpolation based on Lagrange, hierarchic, spline or NURBS interpolations. Within the isogeometric framework, a contact surface possessing C1 or higher continuity is easily achieved and significant advantages over conventional finite element descriptions have been demonstrated in the last years by applying NURBS based isogeometric discretizations [4-7] to frictionless and/or frictional multi-patch contact problems. A key problem of multivariate NURBS basis functions, in any case, is their rigid tensor product structure, which implies that refinement is a global process propagating throughout the domain. A possible way to improve the quality of contact results in terms of local pressures and global time-history curves with limited increase in the computational effort is represented by local refinement. This has been recently considered in [8] for frictionless contact applications by using analyis-suitable T-splines discretizations and here extended to large deformation Coulomb frictional contact problems. A Gauss-point-to-surface (GPTS) formulation is combined with the penalty method to treat the contact constraints in the discretized setting, as done in [9]. Using the Bèzier extraction, the suitable T-splines isogeometric discretizations are automatically generated for any analysis-suitable CAD geometry and easily incorporated into the finite element framework [10]. Some numerical examples show that the proposed contact formulation deliver accurate and robust predictions and demonstrate the potential of T-spline-based IGA to solve challenging contact problems in 2D and 3D

Interfacial stress analysis for thin plates bonded to curved substrates

This paper is focused on analytical and numerical modeling of the interface between a rigid substrate with simple curvature and a thin bonded plate. The interfacial behavior is modeled by independent cohesive laws in the normal and tangential directions. The analytical model makes use of appropriate simplifying assumptions. In the numerical model the interface is modeled by zero-thickness node-to-segment contact elements. In this paper the first results and comparisons between predictions of the two models are presented

The contact patch test for linear contact pressure distributions

It is well known that the classical one-pass node-to-segment algorithms for the enforcement of contact constraints fail the contact patch test. This implies that solution errors may be introduced at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method, but the situation is even worse with the penalty method. In a recent study, the authors proposed a modified one-pass node-to-segment algorithm which is able to pass the contact patch test also in conjunction with the penalty method. In a general situation, the pressure distribution transferred across a contact surface is non-uniform. Hence, even for a contact element which passes the contact patch test under a uniform distribution of the contact pressures, the transfer of a non-uniform state of stress may give rise to disturbances related to the discretization, which affect the accuracy of the analysis. This paper, following up to the previous study, develops an enhanced node-to-segment formulation able to pass a modified version of the contact patch test whereby a linear distribution of pressures has to be transmitted across the contact surface. The proposed formulation is illustrated and some numerical examples demonstrate the good patch test performance of the enhanced contact element

A debonding model for superficial reinforcements under inclined loading

This paper presents a numerical model of the interface between a quasi-brittle substrate and a thin elastic adherend subjected to mixed-mode loading. The interface is modeled by zero-thickness contact elements, which describe both debonding and contact within a unified framework using the node-to-segment contact strategy. Uncoupled cohesive interface constitutive laws are adopted in the normal and tangential directions. The formulation is implemented and tested using the finite element code FEAP. The model is able to predict the response of the bonded joint as a function of the main parameters, which are identified through dimensional analysis. The main objective is to compute the debonding load and the effective bond length of the adherend, i.e. the value of bond length beyond which a further increase of bond length has no effect on the debonding load, as functions of the peel angle

Mesomechanical modeling of debonding failures in FRP-strengthened structures

Debonding mechanisms in FRP-strengthened structures have been the subject of numerous investigations. Most of the modeling studies conducted thus far are based on the assumption of macroscopic relationships between local interfacial stresses and local relative displacements between FRP and substrate. Such laws are calibrated experimentally and incorporated in structural models with the purpose of determining macroscopic quantities of design interest. This approach presents a number of limitations, as macroscopic interfacial laws spatially homogenize complex damage and failure processes taking place at the lower scales. This paper proposes an alternative approach to the problem of FRP debonding, based on a mesomechanical analysis including explicit description of the interfacial geometry, and illustrates the first steps taken by the authors in this direction. The final goal is to be able to design and optimize the macroscopic interfacial behavior by tailoring the features at the lower scale. Also, a deeper understanding of mixed-mode interfacial failures is aimed at. The paper illustrates the basic idea, the main details about the current implementation, and preliminary numerical results

T-spline-based isogeometric treatment of mixed-mode debonding

In a context where adhesive-bonded joints are increasingly used in aerospace and automotive industries, prediction of interfacial and cohesive failure mechanisms is an important issue, that has to be treated both analytically and numerically. To this end, a successfull numerical tool dealing with failure prediction of adhesive joints is available in literature using standard low order finite elements relying on Lagrange polynomial bases. The two most popular numerical methods for the analysis are the Virtual Crack Closure Technique [1, 2] and interface elements with cohesive zone (CZ) laws [3, 4]. The numerical application of CZ models for debonding problems within finite element frameworks, however, usually suffer from unphysical stress oscillations at large stress gradients unless fine meshes discretize the fracture process zone ahead of the crack tip. An innovative framework where better geometrical accuracy is combined with higher and tailorable inter-element continuity is provided by isogeometric analysis, as here adopted to describe the interface damage mechanisms for adhesively-bonded interfaces in mixed-mode conditions. The debonding process along the adhesive interfaces are herein treated with CZ modeling by adopting “analysis-suitable” T-splines discretizations of the meshes. The interface is discretized with zero-thickness contact elements which encompass both contact and mixed-mode debonding within a unified framework, using a Gauss-point-to-surface formulation [5]. A coupled exponential cohesive interface constitutive law is then employed to treat the debonding phase, where all the components (I and II) of the traction vector depend on all the components of the interface separation. The methodology is explored for bi-dimensional composite-to-composite single-lap-joint specimens [6], composed of four composite substrate segments bonded by thin layers of adhesive (Figures 1a,b). The numerical results (see Figures 2a,b) show that mixed-mode CZ models combined with T-spline-based discretizations allow for a very accurate and robust treatment of debonding phenomena and are compared to standard linear and higher-order Lagrange interpolations