Jean-François Caron

Model of multilayered materials for interface stresses estimation and validation by finite element calculations

Abstract The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called multiparticle models of multilayered materials (M4). The first one can be considered as a stacking sequence of Reissner–Mindlin plates (five kinematic fields per layer), while the second is a membranar superposition (two fields per layer plus a global one). These simplified models are able to provide finite values of interfacial stresses, even on the free edges of a structure. The current paper consists of validating the M4 by a finite element analysis through describing the stress fields in both a (0,90) s laminate in tension (free-edge problem) and a transversally microcracked (0,90) s laminate. A comparison of the various energy contributions helps yield a mechanical perspective: it appears possible to define an interply energy as well as a layer energy, these energies expressing the FE 3D reality.

Software application for evaluating interfacial stresses in inelastic symmetrical laminates with free edges

Abstract Authors propose herein a software application called DEILAM, which is able to evaluate the free edge effects in multilayered inelastic structures that essentially bear tensile loads. The inelastic behavior of both layers and interfaces are take into account. The program therefore involves inelastic strain fields in the layers and fields of displacement discontinuities at the interfaces. These inelastic fields, such as thermal strains or interface sliding, are assumed to be known by the user. For evaluating the 3D interfacial stresses, the program uses an approximate model that models the laminate by a superposition of Reissner plates coupled by interfacial stresses. Calculations show that no singularities exist for the model even at the edge and results converge quickly. Calculations are validated by comparing the results with finite element calculations and with Pagano’s local model. Analysing the maximum values of the interfacial stresses for some examples, the authors then show how the software can help predict the place where delamination might appear. Since delamination is a critical failure mode that often takes place at free edges, this program with a delamination criterion involving the maximum interfacial stresses can prove to be an important tool in composite structure design.

Un nouveau modèle de plaque multicouche épaisse

Resume On propose un nouveau modele de plaques multicouches bien adapte pour le calcul des structures soumises a dimportants efforts tranchants. Les hypotheses du modele portent directement sur les deformations 3D. Les contraintes verifient exactement lequilibre avec les efforts exterieurs sauf pres des bords libres. La loi de comportement 3D est respectee. Un schema iteratif permet la resolution du probleme. Une comparaison avec des calculs aux elements-finis est presentee.

Modelling the kinetics of transverse cracking in composite laminates

Abstract A micromechanical model of transverse cracking in composite laminates under monotonie loading is proposed. To compute stresses, we simplify the problem and use a uniaxial model, often called a shear-lag analysis, which allows an analytical determination of the stress fields. In the model the laminate is discretised into cells including potential cracks. The initial strengths of these cells are randomly distributed according to a law which is experimentally identified from a series of tests on unidirectional samples taking into account the size effects. Then, by using a single series of tests, we can simulate the transverse cracking of 90 ° plies in any kind of laminate. The predictions of the simulations are validated on [02,902]s carbon/epoxy composite specimens. We have observed and counted cracks during experimental tension tests and compared them with simulations. We observe good agreement between predictions of the model and experimental results.

Modelling of fatigue microcracking kinetics in crossply composites and experimental validation

Abstract We describe a micromechanical model of transverse cracking in [ α ,90 p ] sym composite laminates under fatigue loading. Several features are recalled which have been the subject of another article. These concern static aspects (such as stress fields, strength distributions, etc.) and have permitted us to predict the number of cracks created during the first cycle of loading. This paper presents the principles of the fatigue model and also proposes several experimental aspects concerning the identification of parameters and validation of the model. A micromechanical hypothesis is suggested, which is based on a physical interpretation of damage to predict the reduction in residual strength of 90° plies during fatigue loading. The model is incremental and allows us to describe in a simple but non-linear way the increase of damage in the 90° plies of a [ α ,90 p ] s laminate. We then include this fatigue aspect in our more general tool which describes a static description of the transverse cracking kinetics of a [ α ,90 p ] sym composite. The predictions of the simulations are validated on [0 2 ,90 2 ] s carbon/epoxy specimens. We have observed and counted cracks during experimental tension–tension tests and compared the results with simulations. We observe good agreement between predictions of the model and experimental results.

Optimization of gridshell bar orientation using a simplified genetic approach

Gridshells are defined as structures that have the shape and rigidity of a double curvature shell but consist of a grid instead of a continuous surface. This study concerns those obtained by elastic deformation of an initially flat two-way grid. This paper presents a novel approach to generate gridshells on an imposed shape under imposed boundary conditions. A numerical tool based on a geometrical method, the compass method, is developed. It is coupled with genetic algorithms to optimize the orientation of gridshell bars in order to minimize the stresses and therefore to avoid bar breakage during the construction phase. Examples of application are shown.

Critère d'initiation de délaminage dans les stratifiés☆

Resume A partir dun modele multiparticulaire de materiaux multicouches original qui permet de calculer analytiquement les efforts de cisaillement et darrachement au niveau des interfaces dun empilement quelconque, les auteurs proposent un critere en contrainte maximale de cisaillement dinterface. Le critere rend compte des effets depaisseurs constates experimentalement. Les idees sont validees par des essais sur deux types dempilement.

Un modèle de stratifiés

Resume Un modele multiparticulaire appele M4-5n est propose pour letude des materiaux multicouches presentant des deformations elastique et anelastiques dans les couches et des discontinuites des deplacements aux interfaces entre les couches. Le modele est construit a partir de la formulation variationnelle dHellinger–Reissner. Les champs anelastiques jouent le role de variables detat dans le modele.

Interface behaviour in laminates with simplified model

This paper focuses on the mechanical definition of the interface in the composite laminates. The chosen point of view is reduced to a multiparticle model vision of the interface (as for the shear-lag analysis). First, we describe several of such multiparticle models, and detail our own proposal, using a Reissner variational principle. We propose then a general expression for the interface behaviour in laminates which involves more than the two close ply stiffnesses and the stresses at the considered interface. By studying the specific case of a [0,90]s, we can compare to over formula found in literature and to a finite element approach. We examine also the stress fields shape, and the stiffness reduction versus crack density, provide by the analysis. We discuss therefore the validity of the classical interface stiffness concept used in a more general framework, for example, for laminates different from the academic [0,90]s.

A 4-degree-of-freedom Kirchhoff beam model for the modeling of bending–torsion couplings in active-bending structures

Gridshells are lightweight structures made of interconnected slender beams. Due to large displacements, high interaction between the beams, and bending–torsion coupling, modeling gridshells requires specific non-linear numerical tools to reach convergence within a reasonable time. In this article, the development of such a tool is presented. It is based on the Kirchhoff beam theory and uses the dynamic relaxation method. First, from Kirchhoff’s equations, the internal forces and moments acting on a beam are obtained. Once this mathematical work is done, the dynamic relaxation method is used in order to get the static equilibrium configuration of the beam. This new approach is tested on several examples and validated for slender beams with arbitrary rest-state configuration and cross sections. In particular, results for ribbons with high bending–torsion coupling are presented. Finally, this process enables the fast and precise modeling of gridshells including bending–torsion coupling.