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In this Note we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a nonconvex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the augmented Lagrangian methods used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined buckling shapes. To cite this article: P. Alart, S. Pagano, C. R. Mecanique 330 (2002) 819–824. [Copyright &y& Elsevier]

This study is devoted to the effective elastic properties of nanoporous media containing spherical nanovoids. Nanocomposites materials are strongly dependent on their nanometric characteristic lengths. This size effect cannot be directly modeled using the classical homogenization schemes based on the Eshelby inclusion problem. However recent studies have extended the continuum mechanics and well-known micromechanical models to the nanoscale. In this paper, it is shown that these models can be replaced in a unified framework using the morphologically representative pattern-based approach of Stolz and Zaoui (1991) and therefore can be generalized to more complex microstructures. Following this approach, new bounds and estimates are derived. Two particular cases are treated: (i) the case of an ellipsoidal spatial distribution of the voids, (ii) the case of a biporous material containing both spherical nanovoids and randomly oriented spheroidal microvoids. The second case is typical of the microstructure of the irradiated uranium dioxide (UO 2 ). Thereby, the associated result could be used for determining the poro-elastic properties of these doubly voided materials. [ABSTRACT FROM AUTHOR]

By using ergodic theory of subadditive processes and variational convergence, we study the macroscopic behavior of a thin 3D composite made up of high-conductivity fibers that are randomly distributed according to a stochastic point process in a bounded open set of ${\mathbb R}^3$. The thickness of the body, the conductivity and the size of the cross sections of the fibers depend on a small parameter ɛ. The variational limit functional energy obtained when ɛ tends to 0 is deterministic and depends on two variables: one is the solution of a variational problem posed in a 2D bounded open set and describes the behavior of the medium; the other captures the limit behavior of suitably rescaled solutions in the fibers when the thickness and the size section become increasingly thin and the conductivity of the fibers becomes increasingly large. [ABSTRACT FROM AUTHOR]

The deformation of solid materials is nearly always accompanied with temperature variations, induced by intrinsic dissipation and thermomechanical coupling. Heat sources give precious information on the thermomechanical behaviour of materials. They can be indirectly observed from thermal measurements on the specimen boundary, obtained, e.g., via infrared thermography. To solve the inverse problem of identifying heat sources from such observations, a non-iterative algebraical method based on the reciprocity gap method is proposed. This approach, used elsewhere mainly for time-independent identification, is applied here to transient measurements. Under appropriate modelling assumptions the number of heat sources, their spatial locations and energies are retrieved, as demonstrated on numerical experiments where the robustness of the method to measurement noise is also studied. [ABSTRACT FROM AUTHOR]

Abstract: By combining variational convergence with ergodic theory of subadditive processes, we study the macroscopic behavior of a randomly fibered medium. The cross sections of the fibers are randomly distributed according to a stationary point process, their size is of order ε while the stiffness of the material in the matrix is of order . The variational limit functional energy obtained when ε tends to 0 is deterministic and non-local. [Copyright &y& Elsevier]

Abstract: A geomaterial called TexSol and composed of sand and wires was investigated by numerical experiments in order to determine its geometrical and mechanical parameters, such as tortuousness of the wire, anisotropy and characteristic length. This stage is essential for studying a material with an obvious non-local behavior. Investigations by discrete elements highlighted that the characteristic length was dependant on the loading level. These simulations provided access to variables that standard physical experiments cannot provide. Some parameters of a continuous model of TexSol were identified through discrete numerical experiments using a classic procedure. The other parameters were determined by finite element method updating. [Copyright &y& Elsevier]

Numerical experiments done on a two-dimensional stratified two-phase composite corroborate theoretical results on homogeneization of media capable of large deformations. [ABSTRACT FROM AUTHOR]

Abstract: We present a new model of adhesive bonded joints, encoding both gradient oscillations and gradient concentrations. By introducing a narrower notion of Young measure–varifold pair and a variational convergence of the energy functionals, we characterize the measure solutions of the model and give a microscopic description of the densities related to the classical formulation. [Copyright &y& Elsevier]

Abstract: Identification techniques solely based on displacement field measurements lack a stress scale and thus require a complementary information to be provided to complete the problem definition. Such a complementary test is proposed in this study, which is itself an identification designed for an unbounded two dimensional domain subjected to a normal point force on its boundary. A complex potential formulation is used to obtain a simple closed-form solution for the Poisson''s ratio and Lamé''s shear modulus. In order to evaluate the performance and robustness of this identification technique, the sensitivity to noise and error in grid positioning is investigated numerically. [Copyright &y& Elsevier]

In this Note we study a parameter identification problem associated with a two-dimensional mechanical problem. In a first part, the experimental technique of determining the displacement field is presented. The variational method proposed herein is based on the minimization of a separate convex functional which leads to the reconstruction of the elastic tensor and the stress field. These two reconstructed fields are continuous and piecewise linear on a triangulation of the two-dimensional problem. Some numerical and experimental examples are presented to test the performance of the algorithm. To cite this article: G. Geymonat et al., C. R. Mecanique 330 (2002) 403–408. [Copyright &y& Elsevier]

We studied the effective behavior of a composite made of a periodic distribution of inclusions linked to a matrix by a very thin layer, with the three components being of linear Kelvin-Voigt viscoelastic type. The effective behavior, derived by a rigorous mathematical homogenization method, is not of Kelvin-Voigt type but instead involves an additional fading memory term. The influence of various parameters of the composite were numerically analyzed through a finite elements method. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new micromechanical model for a collection of cohesive zone models embedded between each mesh of a finite element-type discretization. It aims to fully extend the previous linear results of Blal et al. (2012) [11] to the calibration of damageable cohesive parameters (cohesive peak stress, critical opening displacement, cohesive energy, etc). The main idea of the approach consists in replacing the underlying cohesive-volumetric discretization by an equivalent ‘matrix-inclusions’ composite. The overall behavior of this equivalent composite is estimated using homogenization schemes (Hashin–Shtrikman estimate and the modified secant method) and is given in a closed-form as function of both cohesive and bulk properties and the mesh density. In the particular case of a bilinear cohesive law a micromechanical damage model for quasi-brittle materials is derived. The corresponding local-to-global relationships are obtained for any overall triaxiality loading ratio. [Copyright &y& Elsevier]

In this study, criteria on the artificial compliance due to intrinsic cohesive zone models are presented. The approach is based on a micromechanical model for a collection of cohesive zone models embedded between each mesh of a finite element-type discretization. The overall elastic behaviour of this cohesive volumetric medium is obtained using homogenization techniques and is given in a closed-form as function of bulk properties of the relevant material and mesh parameters (the mesh type and size). Practical criteria are obtained for the calibration of the cohesive stiffnesses bounding the additional compliance inherent to intrinsic cohesive zone models by lower value. For isotropic planar discretizations (e.g. Delaunay mesh), a rigorous bound is derived whereas convenient estimates are given for non-isotropic discretizations (e.g. regular mesh). [ABSTRACT FROM AUTHOR]

Abstract: This Note presents criteria on the artificial compliance due to intrinsic cohesive zone models. A homogenized model is proposed for a collection of cohesive zones embedded between each mesh of a finite element-type discretization (cohesive-volumetric approach). The overall elastic behavior of this cohesive-volumetric medium is obtained as a function of the local properties and the mesh size. For an isotropic discretization, a criterion on the cohesive stiffnesses is derived: the additional compliance inherent to intrinsic cohesive zone models is bounded by lower value. [Copyright &y& Elsevier]