A multi-level interface model for damaged masonry

The aim of the present work is to propose a new micro-mechanical model in the context of the deductive approach used to derive interface models. This model, based on a previous study introduced previously by A. Rekik and F. Lebon, is used to reproduce the damage in masonry by combining structural analysis and homogenization methods. The focal point of this method is to assume the existence of a third material, called interphase, which is a mixture of the two principal constituents of masonry, brick and mortar, and that is the interface between them. This new element presents a low thickness, a low stiffness and a given damage ratio. The mechanical problem of masonry, initially a 3D problem, is solved numerically as a 2D problem using finite element methods. The properties of the interface brick-mortar material are obtained using three essentials steps. First of all, an exact homogenisation of a laminates is used to define a first homogeneous equivalent medium named HEM-1. After, the assumption of damaged material is taken into account by using the general framework given by M. Kachanov to evaluate the global behaviour of the damaged HEM-1 defining thus a second equivalent homogeneous medium noted HEM-2. The last step consists in using an asymptotic analysis technique which is performed to model HEM-2 as an interface or a joint. The properties of this joint are deduced from those of the HEM-2 material as proposed in former papers. Particularly, through the second homogenization are taken into account the variability of microcracks oriented family and simultaneously the opening-closure effects (unilateral behaviour). Numerically this interface is modelled with connector finite elements. Numerical results are compared to experimental ones available in the literature

Modelling Adhesion by Asymptotic Techniques

Chapter 6International audienceIn this chapter, a review of theoretical and numerical asymptotic studies on thin adhesive layers is proposed. A general mathematical method is presented for modelling the mechanical behavior of bonding and interfaces. This method is based on a simple idea that the adhesive film is supposed to be very thin; the mechanical problem depends strongly on the thinness of the adhesive. It is quite natural, mathematically and mechanically, to consider the limit problem, that is, the asymptotic problem obtained when the thickness and, possibly, the mechanical characteristics of the adhesive thin layer tend to zero. This asymptotic analysis leads to a limit problem with a mechanical constraint on the surface, to which the layer shrinks. The formulation of the limit problem includes the mechanical and geometrical properties of the layer. This limit problem is usually easier to solve numerically by using finite elements software. Theoretical results (i.e. limit problems) can be usually obtained by using at least four mathematical techniques: gamma-convergence, variational analysis, asymptotic expansions and numerical studies. In the chapter, some examples will be presented: comparable rigidity between the adhesive and the adherents, soft interfaces, adhesive governed by a non convex energy and imperfect adhesion between adhesive and adherents. Some numerical examples will also be given and, finally, an example of a numerical algorithm will be presented

Asymptotic analysis of an elastic thin interphase with mismatch strain

International audienceThis paper proposes the study of the equilibrium problem, where two elastic bodies are bonded to a thinelastic film under mismatchstrain conditions resulting in a state of residual stress. The asymptotic behavior of the film/adherent system is modeled as the film thickness tends to zero, using a method based on asymptotic expansions and energy minimization procedures. This method yields a family of non-local imperfect interface laws, which define a jump in the displacement and the traction vector fields. The amplitudes of the jumps turn out to be correlated with the state of residual stress and the elastic properties of the materials. As an example, the interface law is calculated at order zero in the case of a pure homogeneous mismatchstrain and a thin isotropic film consisting of Blatz-Ko material

Asymptotic behavior of a hard thin linear elastic interphase: an energy approach

International audienceThe mechanical problem of two elastic bodies separated by a thin elastic film is studied here. The stiffness of the three bodies is assumed to be similar. The asymptotic behavior of the film as its thickness tends to zero is studied using a method based on asymptotic expansions and energy minimization. Several cases of interphase material symmetry are studied (from isotropy to triclinic symmetry). In each case, non-local relations are obtained relating the jumps in the displacements and stress vector fields at order one to these fields at order zero

Stress based finite element methods for solving contact problems: comparisons between various solution methods

International audienceThis paper deals with numerical methods for solving unilateral contact problems with friction. Although these problems are usually defined in terms of the displacement, a stress based approach to the problem is developed here. The ‘‘equilibrium” finite elements method is therefore used. Using these elements make it possible to satisfy the local equilibrium condition a priori, but on the other hand, prescribed and contact forces have to be introduced using Lagrangian multipliers. The problem obtained is therefore a non-linear, constrained problem and the global system matrix is non-positive definite. Various solution algorithms are thus proposed and compared. Comparisons between the classical method and that developed here show that the stress formulation gives very satisfactory results in terms of the stresses

Asymptotic modeling of quasi-brittle interfaces

International audienceThis study deals with the damage modeling of quasi-brittle interfaces such as the mortar/brick interfaces present in masonry walls. For this purpose, a model is developed based on a bulk model presented by Gambarotta and Lagomarsino, which takes the damage to the mortar joint into account. A quasi-fragile damage interface model is introduced using an asymptotic technique. This model memorizes some of the geometrical and mechanical characteristics of the interface, such as the thickness, elastic coefficients, normal and tangential stress, and the damage variable. Numerical simulations are performed using the Gyptis finite element software: academic cases involving traction and shear loads are presented

Error estimation and mesh adaptation for Signorini-Coulomb problems using E-FEM

International audienceAn error estimator for modeling contact and friction problems is presented in this paper. This estimator is obtained by solving two contact with friction problems: the first problem is formulated, as classically, in terms of displacement fields, and the second one is obtained using a stress field formulation. With this approach, it is necessary to develop a stress (equilibrium) finite element method such as that presented in previous studies. This estimator is similar to that discussed in [11]. The efficiency of the error estimator is tested by applying it to some examples. Due to the non-associativity of the friction problem, the present estimator is not strictly a majorant of the error. However, in the case of the examples studied here, the value of the estimator was approximately that of a given reference error. A refinement strategy was therefore developed. This strategy is very robust, even in the presence of stress singularities. With a sufficiently fine initial mesh, this method was found to be very efficient

Imperfect interfaces as asymptotic models of thin curved elastic adhesive interphases

International audienceWe obtain a limit model for a thin curved anisotropic interphase adherent to two elastic media. Our method is based on asymptotic expansions and energy minimization procedures. The model of perfect interface is obtained at the first order, while an imperfect interface model is obtained at the next order. The conditions of imperfect contact, given in a parallel orthogonal curvilinear coordinate system, involve the interphase material properties, the first order displacement and traction vectors, and their derivatives. An example of implementation of the imperfect interface condition is given for a composite sphere assemblage