Andrei Constantinescu

Inverse problems in elasticity

This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.

An energetic approach in thermomechanical fatigue for silicon molybdenum cast iron

Abstract The purpose of this paper is to define a low cycle fatigue criterion in order to predict the failure of engineering structures. The major problem in defining a predictive fatigue criterion is that it should be applicable for structures submitted to complex multiaxial thermo-mechanical loadings but should be identifiable from simple experiments on specimens. After a short critical review of the principal criteria used in low cycle fatigue it will be shown that the dissipated energy per cycle permits a correlation of isothermal and anisothermal results obtained on silicon molybdenum cast iron in the case of specimens and also on structures.

Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap

This paper considers the identification problem of a linear crack in a body of finite extension within the framework of linear two-dimensional elastodynamics. In a series of prior papers in electricity, elasticity or acoustics, it has been proved using the reciprocity gap that three different series of adjoint wave fields determine in closed-form solution the normal of the plane of the crack, the position of the plane and finally the complete crack extension. The work developed next within the framework of linear elastodynamics defines a novel instantaneous reciprocity gap as the instantaneous work done by the adjoint tractions on the crack opening displacement. This quantity is then used to identify linear cracks in a two-dimensional problem. It is shown using a numerical example that a unique family of planar shear waves permits the identification of the normal, position and a convex hull of a linear crack through simple interpretations of the instantaneous reciprocity gap. This method is more general in the sense that it applies to three-dimensional problems as well.

On the identification of elastoviscoplastic constitutive laws from indentation tests

This paper addresses the identification of the parameters of a nonlinear constitutive law from indentation tests. The identification problem is considered as a constrained minimization problem and the gradient is computed using the adjoint state method, in spite of the difficulties of the underlying contact problem. This provides a general framework to perform optimization in some problems involving contact conditions and nonlinear material behaviour. The case of a Maxwell viscoelastic and a Norton-Hoff elastoviscoplastic constitutive law are treated extensively and a series of numerical identification examples are shown.

On the identification of elastic moduli from displacement-force boundary measurements

This paper addresses an identification problem for a linear elastic anisotropic body. We suppose that we can measure the displacement distribution on the boundary of an elastic body induced by a known applied static load. This represents a partial knowledge of the Dirichlet to Neumann data map. From such displacement-force boundary data pairs we reconstruct the interior distribution of the elastic moduli by minimizing an error-functional based on the constitutive equation. The decomposition of this error-functional using ‘eigenelastic moduli’ and ‘eigentensors’ will indicate the limitation of identification in the anisotropic case and will be the key point in the process of minimization. Numerical results for cubic material symmetry are finally used to validate the feasibility of the proposed method.

On the determination of elastic coefficients from indentation experiments

The main result of this paper is the extension of the adjoint state method to variational inequalities. This is done for the Signorini contact problem (Kikuchi N and Oden J T 1988 Contact Problems in Elasticity: a Study of Variational Inequalities and Finite Element Methods (Philadelphia: SIAM)) and used for the identification of elastic coefficients from an indentation test. The result is obtained by two independent approaches based on the penalized and respectively, mixed formulations of the direct problem, a Signorini contact problem. An important and astonishing result is that the obtained adjoint problem is a linear problem with Dirichlet boundary conditions. This is expected for problems described with variational equalities (Bui H D 1993 Introduction Aux Problemes Inverses en Mecanique des Materiaux (Paris: Eyrolles) (Engl. Transl. (Boca Raton, FL: CRC Press)), Lions J L 1968 Controle Optimal des Systemes Gouvernes par des Equations aux Derivees Partielles (Dunod)), but is a new result for problems described with variational inequalities. As an application, the elastic coefficients of an isotropic body have been identified from the knowledge of a displacement-force curve measured during an indentation test. The efficiency of the method is illustrated on numerical examples for the identification of a bimaterial and a functional gradient material.

Toward ALISP : A proposal for automatic language independent speech processing

The models used in current automatic speech recognition (or synthesis) systems are generally relying on a representation based on phonetic symbols. The phonetic transcription of a word can be seen as an intermediate representation between the acoustic and the linguistic levels, but the a priori choice of phonemes (or phone-like units) can be questioned, as probably non-optimal. Moreover, the phonetic representation has the drawback of being strongly language-dependent, which partly prevents reusability of acoustic resources across languages. In this article, we expose and develop the concept of ALISP (Automatic Language Independent Speech Processing), namely a general methodology which consists in inferring the intermediate representation between the acoustic and the linguistic levels, from speech and linguistic data rather than from a priori knowledge, with as little supervision as possible. We expose the benefits that can be expected from developing the ALISP approach, together with the key issues to be solved. We also present preliminary experiments that can be viewed as first steps towards the ALISP goal.

Mechanical model of the inspiratory pump

The inspiratory pump (inspiratory muscles and the rib cage) translates inspiratory commands in alveolar ventilation by applying expanding forces to the lungs. Its functioning is of paramount importance to the physiology of breathing and of many pathological situations. Major difficulties in studying its function in relationship with its structure arise from the extremely complex geometrical disposition of its active and passive elements. We herein describe a two-compartment model of the inspiratory pump, with model parameters identification derived from actual measurements obtained by magnetic resonance imaging in normal humans. The equations governing the model are presented. Numerical simulations validate the model by showing a behaviour similar to physiological observations. This opens the possibility of predicting the behaviour of the respiratory system during diseases involving changes in its mechanical or geometrical characteristics.

Fatigue of Metallic Stents: From Clinical Evidence to Computational Analysis.

The great success of stents in treating cardiovascular disease is actually undermined by their long-term fatigue failure. The high variability of stent failure incidence suggests that it is due to several correlated aspects, such as loading conditions, material properties, component design, surgical procedure, and patient functional anatomy. Numerical and experimental non-clinical assessments are included in the recommendations and requirements of several regulatory bodies and they are thus exploited in the analysis of stent fatigue performance. Optimization-based simulation methodologies have been developed as well, to improve the fatigue endurance of novel designs. This paper presents a review on the fatigue issue in metallic stents, starting from a description of clinical evidence about stent fracture up to the analysis of computational approaches available from the literature. The reported discussion on both the experimental and numerical framework aims at providing a general insight into stent lifetime prediction as well as at understanding the factors which affect stent fatigue performance for the design of novel components.

Harnessing Photochemical Shrinkage in Direct Laser Writing for Shape Morphing of Polymer Sheets

Structures that change their shape in response to external stimuli unfold possibilities for more efficient and versatile production of 3D objects. Direct laser writing (DLW) is a technique based on two-photon polymerization that allows the fabrication of microstructures with complex 3D geometries. Here, it is shown that polymerization shrinkage in DLW can be utilized to create structures with locally controllable residual stresses that enable programmable, self-bending behavior. To demonstrate this concept, planar and 3D-structured sheets are preprogrammed to evolve into bio-inspired shapes (lotus flowers and shark skins). The fundamental mechanisms that control the self-bending behavior are identified and tested with microscale experiments. Based on the findings, an analytical model is introduced to quantitatively predict bending curvatures of the fabricated sheets. The proposed method enables simple fabrication of objects with complex geometries and precisely controllable shape morphing potential, while drastically reducing the required fabrication times for producing 3D, hierarchical microstructures over large areas in the order of square centimeters.