Stéphane Pagano

Identification of mechanical properties by displacement field measurement: a variational approach

We study a parameter identification problem associated with a two-dimensional mechanical problem. In the first part, the experimental technique of determining the displacement field is briefly presented. The variational method proposed herein is based on the minimization of either a separately convex functional or a convex functional that 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 domain. Some numerical and experimental examples are presented to test the performance of the algorithms.

Local energy analysis of high-cycle fatigue using digital image correlation and infrared thermography

This paper presents the first results provided by an experimental set-up developed to estimate locally the terms of the energy balance associated with the high-cycle fatigue (HCF) of DP 600 steel. The experimental approach involves two quantitative imaging techniques: digital image correlation and infrared thermography. First, a variational method is used to derive stress fields from the displacement fields. Patterns of deformation energy per cycle can then be determined on the basis of stress and strain data. Second, a local form of the heat equation is used to derive separately the thermoelastic and dissipative sources accompanying HCF. Energy balances show that around 50 per cent of the deformation energy associated with the mechanical hysteresis loop is dissipated while the rest corresponds to stored energy variations.

Artificial compliance inherent to the intrinsic cohesive zone models: criteria and application to planar meshes

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).

Identification of transient heat sources using the reciprocity gap

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.

Numerical modelling of reinforced geomaterials by wires using the non smooth contact dynamics

In Civil Engineering soils may be reinforced by different structures. Wires will interest us. Mixed sand and wire, known as TexSol, may be modelled as a continuous medium with classical behaviour laws [6] or with more sophisticated ones taking into account remote interactions [1]. Our approach consists of a discrete model based on the Non Smooth Contact Dynamics. Different choices have been tested on some numerical examples to exhibit at the macroscopic scale the influence of the local models of interaction [5]. First of all we make some numerical tests to compare the mechanical behaviour of a TexSol and a sand sample. Then, we compute in both samples the stress tensors of the wires and the sand in order to understand the role of each component. Our final goal is to define a micro-macro approach and a homogenized realistic behaviour law; if this study is only a first step, it is essential.

An inverse method applied to the determination of deformation energy distributions in the presence of pre-hardening stresses

This paper presents an experimental procedure to estimate the deformation energy distribution within plane samples submitted to mechanical loading. This procedure combined a digital image correlation (DIC) technique giving in-plane displacement fields with an identification method that separately provided fields of material properties and stress distributions developed during the loading. The method was first applied to simulated data to characterize the capabilities of the image processing. Finite element computations were first performed on a complex structure using a standard linear kinematical hardening model to generate multistage loadings leading to heterogeneous displacements and distributions of deformation energy. Loads and displacements were then used as inputs to check the robustness of the image processing by comparing the identified deformation energy fields with the computed ones. The procedure was then applied to experimental data. Tests were conducted under conditions similar to the numerical tests. The identification of a linear kinematical hardening model gave deformation energy patterns showing a good agreement with the simulated results, even in the presence of residual stresses induced by a pre-hardening.

Elastic characterization of wood by Resonant Ultrasound Spectroscopy (RUS): a comprehensive study

The main principle of Resonant Ultrasound Spectroscopy (RUS) measurement method is to excite a sample and to deduce its elastic constants from its free mechanical resonant frequencies. The goal of this paper is to propose an application of RUS in the case of wood cubic samples by: (1) using frequencies and mode shapes (or vibration patterns) of the free resonant modes in an iterative numerical procedure to solve the inverse problem for identifying components of the stiffness tensor of the sample’s material, (2) finding the limits and optimizing the robustness of the identification procedure in the case of wood and (3) applying it to a large density range of wood samples. Specific continuous waves have been used as excitation signal in order to experimentally determine the free resonant frequencies and mode shapes of the sample in a faster way by means of Scanning Doppler Vibrometer measurements. Afterward, the stiffness tensor was derived by solving iteratively an inverse problem. The gain of using the mode shapes in the inverse identification procedure is demonstrated to be particularly necessary for wood, especially for pairing each measured frequency with its corresponding theoretically predicted one, as viscoelastic damping causes the resonant peaks to overlap and/or disappear. A sensitivity analysis of each elastic constant on the measured resonant frequencies has thus been performed. It shows that, in its current state of development, not all of the elastic constants can be identified robustly and a modified identification procedure is thus proposed. This modified procedure has been applied successfully to wood samples with a large density range, including softwood and hardwood, and particularly non-homogeneous wood species or with specific anatomical features.

DC Solutions of Postbuckling Problems

In this paper 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 non convex 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 classical augmented Lagrangian method used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined postbuckling shapes and to microbuckling in a cellular structure.

Un algorithme de décomposition convexe pour l'étude de structures en alliage à mémoire de forme Application aux manchons de raccordement

ABSTRACT We present, in this paper, a theoretical and numerical modelisation of the coupling sleeves. The model takes into account shape memory alloys behavior, thermomechanics couplings and frictional contact. The numerical solution is based on a convex difference algorithm associated with two fixed point algorithms for thermal and frictional problems.

Convex Difference Algorithm and Applications to Some Mechanical Problems

The splitting of functional into two convex functions provides a specific algorithm to determine the local minima. This approach is applied to two mechanical problems with non convex potentials: the modeling of shape memory alloys and the buckling of thin beams.