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International audience; A general theoretical and numerical framework for the strength and mass optimisation of variable-stiffness composite laminates (VSCLs) is presented in this work. The optimisation is performed in the context of the first-level problem of the multi-scale two-level optimisation strategy (MS2LOS) for VSCLs. Both the failure load maximisation problem (subject to a constraint on the mass) and the mass minimisation one (with a constraint on the VSCL strength) are solved for two benchmark structures. The effect of the presence of a constraint on the maximum tow curvature is also investigated. The solutions are searched by means of a deterministic algorithm by considering different scenarios in terms of the VSCL macroscopic behaviour: the orthotropy type and shape, the direction of the main orthotropy axis and the thickness of the laminate are tailored either globally (uniform over the structure) or locally. The polar method is used to represent the point-wise elastic response of the VSCL at the macroscopic scale. The distributions of the polar parameters and of the thickness are described through B-spline entities: their properties are exploited in computing physical and geometrical response functions of the VSCL as well as their gradient. The VSCL strength at the macroscopic scale is assessed using a laminate-level failure criterion in the space of polar parameters. Numerical results show considerable improvements with respect to both quasi-homogeneous isotropic structures and an optimised VSCL solution taken from the literature obtained by using the design approach based on lamination parameters. These results confirm the effectiveness of the proposed strategy and the great potential of VSCLs.

A consistent energy-based cohesive zone model to simulate the mode I delamination behaviour of Fully-Uncoupled Multi-Directional (FUMD) laminates is presented in this study. The proposed energy-based approach allows determining a more general constitutive response of the cohesive interface to better match the experimental results. The constitutive behaviour of the interface is implemented in a standard finite elements (FE) code by means of a user-defined subroutine. To perform the simulations, FE models of a Double Cantilever Beam (DCB) specimen are developed with standard and multidirectional interfaces. The results of the simulations are compared to the experimental ones in terms of force–displacement curves and crack front shape to assess the effectiveness of the proposed model. The comparison shows that the numerical simulations can closely replicate the opening delamination behaviour of DCB specimens during propagation and, in particular, they capture quite well the shape of the delamination fronts with some differences: numerical delamination fronts are characterised by a curvature lower than the one of the experimental counterparts, especially towards the specimen edges. Simulations carried out for different initial delamination lengths confirmed that the delamination changes its front shape at the very beginning of the propagation, then the front remains unaltered. The length of the transition zone for the shape of the delamination front has been found to be much lower than the specimen width.

In this paper, a multi-scale modeling approach is proposed to determine the undamped natural frequencies of lattice structures (LSs) and the related mode shapes. At the macroscopic scale, the LS is modeled as an equivalent homogenized medium whose elastic properties are determined through the strain energy-based homogenization technique. The accuracy of the finite element (FE) model of the homogenized continuum (denoted as low-fidelity FE model) in predicting the undamped natural frequencies and the associated modes is assessed by comparing them to those provided by a high-fidelity FE model of the real architecture of the LS (wherein all the geometrical features of the LS are explicitly modeled). In this context, the influence of the number of representative volume elements (RVEs) to be considered at the macroscopic scale on the relative error on the natural frequencies, resulting from both FE models of the LS, is investigated. Moreover, the influence of the geometrical imperfections induced by the additive manufacturing technology on the accuracy of the low-fidelity FE model is also investigated. These analyses are carried out for different topologies of LS taken from the literature. Results highlight that the accuracy of the low-fidelity FE model in predicting the undamped natural frequencies and their related mode shapes mainly depends upon the LS RVE topology and on the number of RVEs considered at the macroscopic scale.

International audience; In the present work, a physically-based finite element model simulating the compression moulding process of cork-based agglomerates is presented. The goal is the prediction of the pre-stress state due to the process and its influence on the macroscopic mechanical properties of the agglomerate. An ad-hoc algorithm simulating the mould filling phase (based on a generalised Voronoi's tesselation algorithm which is paired with a 2D physics engine) as well as the moulding compression phase is presented. A numerical campaign is conducted to show the effectiveness of the modelling strategy and to assess the influence of packing density on the behaviour of the agglomerate. For all considered cases, the stress-strain and time dependent density curves of the agglomerate show that a high packing density configuration, resulting from a proper selection of particles size mixing, allows obtaining higher tangent moduli than that of natural cork with a lower material density.

The recent development of new manufacturing techniques of composite structures, e.g., additive manufacturing (AM) techniques, allows for going beyond the classical design rules, thus leading the designer to find innovative and more efficient solutions like the variable angle-tow (VAT) composites. VAT composites allow taking advantage from the benefits related to the curvilinear fibre path in the most effective way, though their utilisation unavoidably implies an increased complexity of the design process. In fact, VAT composites are characterised by a large number of design variables involved at different scales. Accordingly, a dedicated multi-scale optimisation approach able to integrate both mechanical and technological requirements (to ensure the manufacturability of the solution) must be developed. In this work, the multi-scale two-level (MS2L) optimisation strategy for VAT laminates is used, for the first time, to design a VAT laminate by taking into account the manufacturing requirements related to the fused filament fabrication (FFF) and continuous filament fabrication (CFF) processes. To show the effectiveness of the MS2L strategy in terms of manufacturability of the optimised solutions, a prototype of the VAT plate is realised by developing an ad hoc CAD model interfaced with the CFF machine. The realised prototype matches very well the optimum fibre path resulting from the MS2L strategy and the importance of including technological constraints within the design process is highlighted.

The accurate representation of the 3D stress fields at the bonded areas of adhesive joints is essential for their design and strength evaluation. In the present study, higher-order beam models deve...

This work deals with the optimum design of variable angle-tow (VAT) composites in the theoretical framework of B-Spline surfaces. The design problem is formulated as a constrained optimisation problem in the context of the multi-scale two-level (MS2L) optimisation methodology. The proposed approach aims at optimising all parameters characterising the VAT laminate at each pertinent scale (mesoscopic and macroscopic ones). In particular, this study focuses on the first level of the MS2L optimisation strategy that aims at determining, at the VAT laminate macroscopic scale, the optimum distribution of the laminate mechanical properties over the structure. At this stage, the behaviour of the VAT composite is described by means of the polar formalism and the spatial distribution of the polar parameters is represented through a set of suitable B-Spline surfaces. The expression of the gradient of objective and constraint functions is determined in a closed form by exploiting the properties of the B-Spline surfaces. Moreover, the effect of the discrete variables tuning the shape of the B-Spline surfaces (mainly the number of control points) on the quality of the optimum solution is investigated. The effectiveness of the proposed approach is tested through some meaningful benchmarks taken from literature.

The present study aims at describing the debonding phenomenon of a particle embedded in an elastic matrix. Two types of fracture mechanics approaches are developed and compared in this context. The phenomenon is analytically described using a finite fracture mechanics approach, while numerical simulations are performed using a cohesive zone model to describe the decohesion process. Both methods rely on two mechanical parameters: the interface strength, σmaxand the fracture energy, Gc, of the interface. Both modelling approaches produce results that show larger particles tend to debond before smaller ones although noticeable differences are observed, especially concerning the relationship between the critical load and the particle radius: in the framework of the FFM, the critical load is inversely proportional to the square root of the particle radius, while when using CZM, the critical load is inversely proportional to the particle radius.

International audience; This work presents a new strategy for dealing with blending requirements in the composite structures design. Firstly, new analytical expressions of blending constraints, in the polar parameters space, are derived. Secondly, a dedicated numerical strategy for the recovery of blended stacking sequences is presented. The proposed approach is implemented in the framework of the multi-scale two-level optimisation strategy (MS2LOS) for composite laminates design. The theoretical aspects of this work are supported by the application of the proposed methodology to a numerical benchmark taken from the literature. The results obtained by means of the MS2LOS based on the polar formalism outperform those reported in the literature.

cellular scale level, the cell behaviour, especially its migration, is affected by the specificities of the surface of the substrate, such as the stiffness of the surface and its roughness topography. The latter has been shown to have a great impact on various cell mechanisms, such as the cell adhesion, migration, or proliferation. In fact, the mere presence of micro roughness leads to an improvement of those mechanisms, with a better integration of the implants. However, the phenomena behind those improvements are still not clear. In this paper, we propose a three-dimensional (3D) model of a single cell migration using a Cellular Potts (CP) model to study the influence of the surface topography on cell motility. To do so, various configurations were tested, such as: (i) a substrate with a random roughness, (ii) a substrate with a rectangular groove pattern (parallel and perpendicular to the direction of motion), (ii) a substrate with a sinusoidal groove pattern. To evaluate the influence of the surface topography on cell motility, for each configuration, the cell speed and shape as well as the contact surface between the cell and the substrate have been quantified. Our numerical results demonstrate that, in agreement with the experimental observations of the literature, the substrate topography has an influence on the cell efficiency (i.e. cell speed), orientation and shape. Besides, we also show that the increase of the contact surface alone in presence of roughness is not enough to explain the improvement of cell migration on the various rough surfaces. Finally, we highlight the importance of the roughness dimension on cell motility. This could be a critical aspect to consider for further analyses and applications, such as surface treatments for medical applications. This work has been funded by RNC Santé of Arts et Métiers, supporting the first author through a PhD scholarship

This paper proposes an experimental study whose goal is to validate the concept of Fully-Uncoupled Multi-Directional (FUMD) specimens for delamination tests. In order to reduce the likelihood of delamination jump, a glass/epoxy UD-fabric composite was used to fabricate double cantilever beam specimens. Mode I tests were performed with standard UD specimens and with FUMD specimens having the following delamination interfaces: 0 ° //0 ° , 0 ° //15 ° , 0 ° //30 ° , 0 ° //45 ° and -45 ° //45 ° . Delamination fronts after the tests were observed by means of ultrasonic C-scans. By comparison with the UD specimens, it is shown that FUMD sequences are able to promote a fairly symmetric and flat delamination front. Analysis of the rotations of such specimens during the test confirms that they do exhibit an uncoupled mechanical behaviour. Critical energy release rate is found to be dependent on interface plies mismatch angle, but not on global stiffness of the specimens.

Architected cellular materials (ACMs) with a periodic micro-structure are often employed in high-performance components obtained through additive manufacturing (AM) technologies due to their high specific strength and stiffness. ACMs are also used in thermal applications, where their high surface-to-mass ratio can be conveniently exploited to enhance heat transfer. In this work, a numerical approach to predict the effective thermal conductivity (ETC) of ACMs obtained by AM is proposed. The model is based on a general numerical homogenisation scheme and an explicit description of the representative volume element (RVE) of the ACM. Numerical analyses have been conducted on 31 RVEs geometries: results show that the macroscopic ETC of ACMs strongly depends on the relative density and the geometrical features of the RVE. Moreover, starting from the database of RVEs geometries, seven configurations are chosen to design graded ACMs through a computer-aided design-compatible topology optimisation method based on non-uniform rational basis spline hyper-surfaces to represent the pseudo-density field, and on the well-known solid isotropic material with penalisation (SIMP) approach. In particular, the penalisation law used in the SIMP method is replaced by a physically-based penalisation scheme obtained by interpolating the results of the homogenisation for each RVE topology and a suitable post-processing phase is developed to recover the distribution of the graded ACM over the structure from the results of the optimisation process. The effectiveness of the proposed approach is shown on 2D and 3D benchmark problems taken from the literature.

In this work, a multi-scale optimisation strategy for the preliminary design of composite structures involving design requirements at different scales, is presented. Such a strategy, denoted as GL-MS2LOS, has been formulated by integrating a dedicated global-local (GL) modelling approach into the multi-scale two-level optimisation strategy (MS2LOS). The GL-MS2LOS aims at proposing a very general formulation of the design problem, without introducing simplifying hypotheses and by considering, as design variables, the full set of geometric and mechanical parameters defining the behaviour of the composite structure at each pertinent scale. By employing a GL modelling approach, most of the limitations of well-established design strategies based on analytical or semi-empirical models are overcome. The effectiveness of the presented GL-MS2LOS is proven on a meaningful study case: the least-weight design of a composite fuselage barrel of a wide-body aircraft undergoing various loading conditions and subject to requirements of different nature. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm to perform the optimisation. Refined local FE models are created only for critical regions of the structure, automatically detected during the global analysis, and linked to the global one thanks to the implementation of a sub-modelling approach. The whole process is completely automated and, once set, it does not need any further user intervention. The general nature of the GL-MS2LOS allows finding an optimised configuration characterised by a weight saving of 40% when compared to an optimised aluminium solution obtained through a similar GL optimisation strategy. Project PARSIFAL (Prandtlplane ARchitecture for the Sustainable Improvement of Future AirpLanes), Grant Agreement n.723149.

International audience; The tensile load at debonding onset between stiff particles and a soft matrix is predicted with the coupled criterion which combines a stress and an energy conditions. A finite element model of a representative volume element is implemented in order to consider the influence of the size of the particles, the particle volume fraction, mixed mode conditions at the interface and the presence of residual stresses. It is also shown how this approach can be used in order to analyze experimental data for the identification of the interfacial fracture parameters.

International audience; In this paper, a procedure to obtain fully uncoupled multi-directional stacking sequences for delamination specimens is outlined. For such sequences, in-plane, membrane-bending and torsion–bending coupling terms are null (in closed-form solution in the framework of classical laminated plate theory) for the entire stack and for both its halves, which form two arms in the pre-cracked region of a typical delamination specimen. This is achieved exploiting the superposition of quasi-trivial quasi-homogeneous stacking sequences, according to appropriate rules. Any pair of orientations of the plies embedding the delamination plane can be obtained. To assess the effectiveness of the proposed approach, a fully uncoupled multi-directional sequence is designed and compared to other relevant sequences proposed in the literature. Finite element simulations of double cantilever beam test are performed using classic virtual crack closure technique and a revised state-of-the-art virtual crack closure technique formulation too. Some interesting conclusions regarding proper design of multidirectional stacks for delamination tests are drawn. Moreover, the results confirm the suitability of fully uncoupled multi-directional sequences for delamination tests. Thanks to their properties, these sequences might lay the foundations for the development of standard test procedures for delamination in angle-ply interfaces.

International audience; In this work, a design strategy for optimising thin-walled structures based on a global-local finite element (FE) modelling approach is presented. The preliminary design of thin-walled structures can be stated in the form of a constrained non-linear programming problem (CNLPP) involving requirements of different nature intervening at the different scales of the structure. The proposed multi-scale optimisation (MSO) strategy is characterised by two main features. Firstly, the CNLPP is formulated in the most general sense by including all design variables involved at each pertinent scale of the problem. Secondly, two scales (with the related design requirements) are considered: (a) the structure macroscopic scale, where low-fidelity FE models are used and (b) the structure mesoscopic scale (or component level), where more accurate FE models are involved. In particular, the mechanical responses of the structure are evaluated at both global and local scales, avoiding the use of approximated analytical methods. The MSO is here applied to the least-weight design of an aluminium fuselage barrel of a wide-body aircraft. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm. Refined local FE models are created only for critical regions of the structure, automatically detected during the global analysis, and linked to the global one, thanks to the implementation of a sub-modelling approach. The whole process is completely automated, and once set, it does not need any further user intervention.; In this work, a design strategy for optimising thin-walled structures based on a global-local finite element (FE) modelling approach is presented. The preliminary design of thin-walled structures can be stated in the form of a constrained non-linear programming problem (CNLPP) involving requirements of different nature intervening at the different scales of the structure. The proposed multi-scale optimisation (MSO) strategy is characterised by two main features. Firstly, the CNLPP is formulated in the most general sense by including all design variables involved at each pertinent scale of the problem. Secondly, two scales (with the related design requirements) are considered: i) the structure macroscopic scale, where low-fidelity FE models are used; ii) the structure mesoscopic scale (or component-level), where more accurate FE models are involved. In particular, the mechanical responses of the structure are evaluated at both global and local scales, avoiding the use of approximated analytical methods. The MSO is here applied to the least-weight design of an aluminium fuselage barrel of a wide-body aircraft. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm. Refined local FE models are created onlyfor critical regions of the structure, automatically detected during the global analysis, and linked to the global one thanks to the implementation of a sub-modelling approach. The whole process is completely automated and, once set, it does not need any further user intervention.

Selective Laser Melting process represents an interesting opportunity in the biomedical field to fabricate customized implants. However, the surface roughness of components obtained through additive manufacturing is a major limitation and affects the surface wettability. In the present work, chemical etching is adopted to deal with such an issue. To do so, the effects of chemical etching parameters (such as immersion time and composition of the solution) on the surface roughness, weight loss and wettability is analyzed. Different samples (obtained through different printing orientations) are considered. The tests show that the roughness and the wetting of the surfaces are improved thanks to chemical etching. As a major result, the most influencing parameters on surface wetting are two: the roughness and the material properties (which vary with samples depth). The first author is grateful to ENSAM Fundation for supporting this research work through the RNC Santé of Arts et Métiers Science and Technology engineering school. Specimens were produced on the Futurprod Additive Manufacturing Plateform of I2M Institute (Bordeaux, France).

This work focuses on the analysis of the micro and macroscopic mechanical response of particle-reinforced composites. A particular attention is paid to the influence of two fundamental design parameters, i.e. the particles shape and their volume fraction (up to very high values ranging from 0 to almost 0.8), on the overall mechanical response of the structure as well as on the resulting elastic symmetry of the material. The strain energy-based homogenisation technique of periodic media is here applied to a 2D finite element model of a representative volume element of the composite. Different algorithms are developed to generate, with a good level of accuracy, the real microstructure of the composite material characterised by circular as well as polygonal particles. Moreover, for each studied configuration, a link between the geometrical parameters of the microstructure (particles shape, size, distribution, and volume fraction) and the size of the representative volume element is also provided in order to properly describe the constitutive behaviour of the composite at the macroscopic scale. The numerical results are compared with analytical models taken from the literature to prove on the one hand the limitations of the analytical approaches and on the other hand the effectiveness of the proposed numerical models.

In this work a multi-scale two-level (MS2L) optimisation strategy for optimising VAT composites is presented. In the framework of the MS2L methodology, the design problem is split and solved into two steps. At the first step the goal is to determine the optimum distribution of the laminate stiffness properties over the structure (macroscopic scale), while the second step aims at retrieving the optimum fibres-path in each layer meeting all the requirements provided by the problem at hand (mesoscopic scale). The MS2L strategy has been improved in order to integrate all types of requirements (mechanical, manufacturability, geometric, etc.) within the first-level problem. The proposed approach relies on: (a) the polar formalism for describing the behaviour of the VAT laminate, (b) the iso-geometric surfaces for describing the spatial variation of both the laminate stiffness properties (macro-scale) and the layers fibres-path (meso-scale) and (c) an hybrid optimisation tool (genetic and gradient-based algorithms) to perform the solution search. The effectiveness of the MS2L strategy is proven through a numerical example on the maximisation of the first buckling factor of a VAT plate subject to both mechanical and manufacturability constraints.

International audience; In this paper, a general numerical homogenisation scheme coupled with an efficient mod-elling strategy for predicting the effective thermoelastic properties of cork-based agglomerates is presented. In order to generate a realistic representation of the geometry anddistribution of particles for the representative volume element (RVE) of the agglomerateat the mesoscopic scale, a general parametric model based onthe Voronoi’s tesselation(VT) has been developed. However, the classical algorithm for VT has been enhanced byadding a full parametrization of the RVE. The grains composing the RVE are generatedby considering the full set of design variables involved at this scale, i.e. the material prop-erties of the constitutive phases (grains and matrix) and the main geometric parametersrelated to the grain (volume fraction, average diameter, geometric and material orienta-tions). Numerical results show that the macroscopic effective thermoelastic properties ofthe cork-based agglomerate are strongly affected by the previous parameters in perfectagreement with experimental results available in literature.

This work deals with the problem of the optimum design of a sandwich panel made of carbon-epoxy skins and a metallic cellular core. The proposed design strategy is a multi-scale numerical optimisation procedure that does not make use of any simplifying hypothesis to obtain a true global optimum configuration of the system. To face the design of the sandwich structure at both meso and macro scales, a two-level optimisation strategy is employed: at the first level the goal is the determination of the optimum shape of the unit cell of the core (meso-scale) together with the material and geometric parameters of the laminated skins (macro-scale), while at the second level the objective is the design of the skins stacking sequence (skin meso-scale) meeting the geometrical and material parameters provided by the first-level problem. The two-level strategy is founded on the polar formalism for the description of the anisotropic behaviour of the laminates, on the NURBS basis functions for representing the shape of the unit cell and on the use of a genetic algorithm as optimisation tool to perform the solution search. To prove its effectiveness, the multi-scale strategy is applied to the least-weight design of a sandwich plate subject to constraints of different nature: on the positive-definiteness of the stiffness tensor of the core, on the admissible material properties of the laminated faces, on the local buckling load of the unit cell, on the global buckling load of the panel and geometrical as well as manufacturability constraints related to the fabrication process of the cellular core.

International audience; This work deals with the problem of predicting the temperature-dependent equivalent elastic properties of cork-based composites by investigating the influence of the variability related to the material properties of natural cork. A dedicated numerical homogenisation approach based on the strain energy of periodic and a-periodic media has been developed to this purpose. The proposed methodology is based, on the one hand, on an efficient modelling strategy capable to generate 2D and 3D finite element models which closely emulates the realistic meso-structure of the agglomerate. On the other hand, the strategy makes use of the Monte Carlo algorithm to study the influence of the variability in model inputs on the equivalent elastic behaviour of the cork-based composite at different temperatures. Firstly, the effectiveness of the modelling strategy in representing a realistic meso-structure of the agglomerate, in terms of geometry, has been evaluated by comparing the numerical results to digital images of real cork-based composites. Secondly, the homogenisation strategy has been applied to a realistic configuration of cork agglomerate. Numerical results show that the greater the temperature the lower the overall stiffness of the agglomerate, according to natural cork trends, but the variability related to the macroscopic equivalent elastic properties of the agglomerate is considerably lower than that affecting the elastic behaviour of the natural cork, which represents a positive result concerning the use of cork agglomerates in industrial applications.

The objective of the present study is to describe the progressive debonding of inclusions in particle or fibre reinforced composites. To do so, the mean-field homogenisation scheme of Mori-Tanaka is enriched to take into account imperfect interfaces. The interfaces are modelled by a bilinear Cohesive Zone Model (CZM) taking into account normal and tangential effects. Results obtained with this new mean-field homogenisation scheme are compared to 2D FE-based numerical simulations that are used as reference results. The effects of inclusions volume fraction and size are also observed.

International audience; This paper focuses on the analytical formulation of a tensorial laminate-level failure criterion. The criterion is formulated and expressed in the framework of the first-order shear deformation theory (FSDT) in order to take into account the influence of the transverse shear stresses on the failure mechanisms. More precisely the most common polynomial ply-level failure criteria (expressed under a unified matrix formulation) are considered and reformulated at the laminate level. The proposed unified formulation relies on the utilisation of the polar formalism gener- alised to the FSDT framework. Through this approach all the considered criteria can be formulated in terms of tensor invariants. Furthermore, thanks to the polar representation, an important theoretical result is proven: the existence of a set of analytical relationships between the laminate strength and stiffness invariants.

International audience; The importance of lightweight structures in many fields of engineering is well known since long time. The innovations in technological processes based on material addiction allow pushing the design towards challenging geometries and associated structural properties. Engineered materials like lattice structures can be theoretically used to modify the local material properties and strength with minimization of the mass of components; in practice, several issues are still to be solved in stabilization of additive processes and achieving repeatable structures able to pass qualification procedures. At this purpose, dedicated experimental and design methods like those reported in this paper are needed.

International audience; Quasi-trivial (QT) sequences have largely proven to be an extremely powerful tool in the design and optimisation of composites laminates. In this paper new interesting properties of this class of stacks are derived. These properties allow to obtain QT sequences by superposing (according to some prescribed rules) any number of QT elementary stacks. In this way, QT solutions with arbitrary large number of plies can be readily obtained, overcoming the computational issues arising in the search of QT solutions with huge number of layers. Moreover, a general version of the combinatorial algorithm to find QT stacks is proposed in this work. It is also proven that the previous estimation of the number of QT solutions, for a given number of plies and saturatedgroups, is not correct because a larger number of solutions has been found in this study.

In this paper we deal with the problem of determining on the one hand the effective elastic properties of particulate-polymer composite materials and on the other hand the actual degree of symmetry of the resulting homogenised material. This twofold purpose has been accomplished by building a 2D as well as a 3D finite element model of the heterogeneous material and by using the strain-energy based numerical homogenisation technique. Both finite element models are able to reproduce with a good level of accuracy the real microstructure of the composite material by considering a random distribution of both particles and air bubbles (that are generated by the fabrication process). To assess the effectiveness of the proposed models, we present a numerical study to determine the effective elastic properties of the composite along with a comparison with the existing analytical and experimental results taken from literature and a sensitivity analysis in terms of the spatial distribution of the particles of the unit cell. Numerical results show that both models are able to provide the equivalent elastic properties with a very good level of accuracy when compared to experimental results and that the particulate-reinforced polymer composite could show, depending on the particles volume fraction and arrangement, an isotropic or a cubic elastic symmetry.

International audience; In this work the authors propose a new paradigm for the optimum design of variable angle tow (VAT) composites. They propose a generalisation of a multi-scale two-level (MS2L) optimisation strategy already employed to solve optimisation problems of anisotropic structures characterised by a constant stiffness distribution. In the framework of the MS2L methodology, the design problem is split into two sub-problems. At the first step of the strategy the goal is to determine the optimum distribution of the laminate stiffness properties over the structure, while the second step aims at retrieving the optimum fibres-path in each layer meeting all the requirements provided by the problem at hand. The MS2L strategy relies on: a) the polar formalism for describing the behaviour of the VAT laminate, b) the iso-geometric surfaces for describing the spatial variation of the stiffness properties and c) an hybrid optimisation tool (genetic and gradient-based algorithms) to perform the solution search. The effectiveness of the MS2L strategy is proven through a numerical example on the maximisation of the first buckling factor of a VAT plate subject to both mechanical and manufacturability constraints.

The strength optimisation of orthotropic materials is an open problem. The majority of the studies conducted on strength optimisation of anisotropic materials have been performed with the help of a phenomenological failure criterion that describe the conditions to obtain a limit state identified with the ultimate strength of the material. This paper is a study concerning the bidimensional linear case. Our approach concerns the formulation of a failure criterion through tensors invariants, in order to reduce the optimisation variables to only one: the orientation of material properties of the continuum. Finally, the analytical approach is introduced in order to minimise the failure index and results obtained with the use of three different failure criteria that are compared in order to understand the role of the three formulations with respect to the strength's behaviour. Copyright © 2012 John Wiley & Sons, Ltd.

International audience; In this paper, we deal with the problem of optimizing the anisotropy distribution of a laminated structure in order to maximize, simultaneously, its stiffness and strength. For these two objectives, two functionals are considered: the compliance as a measure of the plate stiffness and a laminate-level failure index as a measure of the strength. To solve this optimization problem we used a two-step hierarchical strategy: in the first step the aim is to find the best distribution of the stiffness and strength anisotropic tensors of an equivalent homogenized plate, while in the second one the objective is to find at least one laminate lay-up satisfying the optimal properties obtained as result of the first step. The polar formalism has been used to represent both the stiffness and strength tensors and allowed us to find analytical solutions to the local minimizations of the two functionals. A test case is finally presented to show the effectiveness of the proposed strategy.

International audience; This work deals with the problem of the optimum design of a sandwich panel. The design process is based on a general two-level optimisation strategy involving different scales: the meso-scale for both the unit cell of the core and the constitutive layer of the laminated skins and the macro-scale for the whole panel. Concerning the meso-scale of the honeycomb core, an appropriate model of the unit cell able to properly provide its effective elastic properties (to be used at the macro-scale) must be conceived. To this purpose, in this first paper, we present the numerical homogenisation technique as well as the related finite element model of the unit cell which makes use of solid elements instead of the usual shell ones. A numerical study to determine the effective properties of the honeycomb along with a comparison with existing models and a sensitive analysis in terms of the geometric parameters of the unit cell have been conducted. Numerical results show that shell-based models are no longer adapted to evaluate the core properties, mostly in the context of an optimisation procedure where the parameters of the unit cell can get values that go beyond the limits imposed by a 2D model.

In this study, an indentation failure analysis of sandwich composite plates via several higher-order theories is presented. The unified formulation by Carrera is adopted in order to derive displacement based or mixed, refined theories based on an equivalent single layer approach or a layerwise one. In this manner, out-of-plane normal and transverse shear stresses responsible for the indentation failure can be accurately described. A closed form, Navier-type solution is assumed. Simply supported plates made of fibre-reinforced polymeric skins and foam cores are investigated. The side-to-thickness ratio, a/ h, and the indenter side dimension are considered as analysis parameters. The effect of skins' lamination and thickness is also investigated. Failure indentation is described in terms of failure loading value and failure position. The variation of displacement and stress fields near the indentation area are also presented. The accuracy of the proposed theories is assessed towards Pagano's three-dimensional exact solution. The obtained results show that higher-order models are required to accurately describe the indentation failure of sandwich plates.

A failure analysis of composite plates accounting for localized loadings is presented in this work. A unified formulation is adopted to derive classical, higher order, layerwise, and mixed theories. A closed form, Navier-type solution is assumed. Simply supported, cross-ply laminates are investigated. Plates are subjected to a stepwise loading, an off-centric localized one and a localized moment. First-ply failure loading and index are obtained via several failure criteria. The influence of the side-to-thickness ratio is accounted for investigating thin and very thick plates. Symmetric and asymmetric stacking sequences are investigated. The accuracy of the proposed theories is assessed. On the basis of the obtained results, it can be concluded that higher order models are required for a correct failure analysis in which the three-dimensional stress state attributable to the localized loadings is accurately described.

A linear static analysis of composite beams is presented in this work. Simply supported, cross-ply laminated beams are examined. Beams with different values of length-to-thickness ratio subjected to bending loadings are considered. Carrera’s Unified Formulation is adopted to derive several hierarchical theories. The kinematic field is imposed above the cross-section via a N-order polynomials approximation of the displacements unknown variables. The governing equations and boundary conditions are variationally obtained through the Principle of Virtual Displacements. A closed form, Navier-type solution is adopted. Thanks to this formulation, quasi three-dimensional strain and stress fields can be obtained. Classical beam models, such as Euler–Bernoulli’s and Timoshenko’s, are obtained as particular cases. Results are validated in terms of accuracy and computational costs towards three-dimensional FE models implemented in the commercial code ANSYS. Numerical investigations show that good results are obtained as long as the appropriate expansion order is used.

The object of this study is the development of a novel class of stacking sequencesfor the design of multidirectional polymer matrix laminated composite specimens for interlaminar fracture toughness (or delamination) tests. These sequences allow to obtain multidirectional specimens that, in the framework of Classic Laminated Plate Theory, have a thermo-elastic behaviour that closely matches that of unidirectional specimens: they are completely free from elastic couplings and they do not develop laminate-level thermally-induced deformations due to the curing process. Furthermore, they allow to test delamination interfaces between plies of any desired orientation. Because of their properties, they were labelled Fully-Uncoupled Multi-Directional (FUMD).In order to design these layups, Quasi-Trivial (QT) solutions were exploited.Firstly, an algorithm for the creation of a database of such solutions was conceived and implemented.Thanks to it, more and longer QT solutions were found than in previous studies.Then, analytical rules were established allowing to obtain new QT solutions from the superposition of known ones.These criteria allow to obtain QT sequences of any desired length, thus overcoming existing computational limitations arising when searching for QT solutions using the algorithm.Combining QT solutions with a few basic laminate design principles and the superposition criteria, FUMD stacking sequences are designed.In order to assess the properties of delamination specimens obtained with FUMD layups, a Finite Element model of a Double Cantilever Beam specimen was developed and used to compare the behaviour of a FUMD layup with that of other sequences proposed in relevant literature on the topic of delamination in multidirectional laminates.By means of the standard and of a revised Virtual Crack Closure Technique formulations, Energy Release Rate distributions and modal partitions of the specimens were evaluated.It emerged that the FUMD layup resulted in an optimal behaviour of the specimen.Eventually, a mode I interlaminar fracture toughness experimental campaign was performed.FUMD Double Cantilever Beam specimens were fabricated, along with with unidirectional ones.A UD-fabric material was used to reduce the likelihood of delamination migration.Rotations of the specimens arms and the shape of the delamination fronts were studied in order to assess the capability of the specimens to yield the correct mechanical behaviour for mode I delamination testing.For both aspects, FUMD specimens yielded results similar to those obtained with unidirectional specimens.With respect to interlaminar fracture toughness, specimens with identical delamination interface yielded similar values, even if their global stiffness was different.On the other hand, different interfaces led to different interlaminar fracture toughness, related to different fracture behaviours.While this work represents a preliminary study and further research is clearly required, FUMD delamination specimens have shown a good potential, and they may stand out as a viable solution for interlaminar fracture toughness tests.Possibly, they could be considered for an extension of the scopes of existing standard test methods to multidirectional laminates and interfaces.; Le sujet de cette étude est le développement de séquences d’empilement pour la conception d'éprouvettes multidirectionnelles en matériaux composite à matrice polymère destinées à des essais de délaminage.Ces séquences permettent d’obtenir des éprouvettes multidirectionnelles qui, dans le cadre de la théorie classique des stratifiés, montrent un comportement thermoélastique qui reproduit celui des composites unidirectionnels : elles sont complètement libres de tout type de couplage élastique et ils ne développent pas des déformations résiduelles dues au cycle de cuisson.Par ailleurs, ces empilements permettent de tester n’importe quelle interface de délaminage.La conception de ces empilements est basée sur les solutions Quasi-Triviales (QT).Un algorithme pour la création d’une base de données de ces solutions a été conçu et implémenté.Grace à cela, un nombre plus grand de solutions QT et des solutions QT avec un nombre plus grand de plis que dans des études précédentes ont été trouvées.Ensuite, des critères analytiques permettant d’obtenir de nouvelles solutions à partir de la superposition des solutions connues ont été établis.Ces critères permettent d’obtenir des séquences QT avec n’importe quel nombre de couches.En combinant les solutions QT, les principes usuels de conception des stratifiés et les critères de superposition, les séquences d’empilement Fully-Uncoupled Multi-Directional (FUMD) ont été obtenues.Pour évaluer les propriétés des éprouvettes de délaminage obtenues avec ces séquences, un modèle Éléments Finis d’une éprouvette Double Cantilever Beam (DCB) a été développé pour comparer le comportement d’une séquence FUMD à celui d’autres séquences proposées dans la littérature pour les essais de délaminage.En utilisant la méthode de refermeture (Virtual Crack Closure) dans ses formulations originale et révisée, les distributions du taux de restitution d’énergie (Energy Release Rate) et ses partitions modales ont été évaluées.La séquence FUMD démontre les meilleurs résultats.Finalement, une campagne expérimentale de caractérisation du délaminage en mode I a été menée.Des éprouvettes DCB avec des séquences FUMD ont été conçues et fabriquées.Des plis tissés déséquilibrés ont été utilisés pour réduire la probabilité de changement de plan de délaminage.Les rotations des bras des éprouvettes et la forme du front du délaminage ont été étudiés pour évaluer la capacité des éprouvettes à garantir un comportement mécanique optimal lors du test de délaminage en mode I.Les résultats obtenus avec les éprouvettes FUMD sont proches de ceux obtenus avec les éprouvettes unidirectionnelles.En ce qui concerne l'énergie de rupture, les éprouvettes ayant la même interface de délaminage ont montré des valeurs très proches, même si leur rigidité était sensiblement différente.Par ailleurs, la caractérisation d'interfaces différentes a abouti à des énergies de rupture différentes, résultants des modes de ruptures non identiques.Ce travail ne représente qu'une étude préliminaire et des recherches complémentaires sont nécessaires.Néanmoins les éprouvettes de délaminage FUMD ont démontré un bon potentiel, et sont intéressantes pour les essais de délaminage.

Ceramics have extensively been used for ballistic protection in the last decades. The combination of their mechanical properties makes them very interesting for armouring. Indeed, they exhibit a high hardness, large compression strength, high stiffness and low density. Ceramic armouring plates are commonly manufactured through a sintering process, where ceramic powders are pressed at high temperatures. This manufacturing process tends to limit the size and shape of components and imparts high costs. On the other hand, moulding using a polymer matrix composite provides an alternative process for developing lower cost parts whilst accommodating increased complexity of geometry and size.However, the mechanical behaviour of such a material is not completely known and depends on multiple design parameters: the mechanical properties of the phases, their volume fraction, the size and spatial distributions of the particles, and the adhesion between the components. The objective of the thesis is to evaluate the influence of the main morphological parameters on the overall mechanical properties, emphasising the influence of the particle/matrix adhesion. To do so, both numerical and experimental multiscale analyses of the material under quasi-static and dynamic loadings were carried out.More precisely, static and dynamic properties of the particle-reinforced composite have been determined for different combinations of the design variables. In particular, attention has been dedicated to the particle/matrix decohesion mechanism. Cohesive zone models (CZM) and Finite Fracture Mechanics (FFM) approaches were used to model this phenomenon and a strong effect of the particle size on debonding was observed., Les matériaux céramiques présentent généralement des propriétés mécaniques très intéressantes pour la réalisation de blindages. Ce sont des matériaux très durs et pourtant légers. Les plaques de blindages en céramique sont classiquement mises en forme par pressage à haute température de poudres, ce qui limite la taille et la forme des réalisations tout en impliquant un coût élevé. Une alternative pour produire ces pièces est le moulage d’un composite constitué de particules de céramiques dans une matrice époxy. Ce procédé permet de réduire le coût des pièces tout en autorisant des géométries plus complexes et des dimensions plus importantes.Le comportement mécanique de ce type de matériau dépend de multiples paramètres de conception : propriétés mécaniques des constituants (matrice polymère et particules céramiques), proportion volumique des deux phases, taille et distribution spatiale des particules ou encore l’adhésion entre les constituants. L’objectif de la thèse est d’évaluer l’influence de ces paramètres sur les propriétés d’usage du matériau. Pour ce faire, une analyse multi-échelle du matériau sous sollicitations quasi-statique et dynamique est réalisée.Plus précisément, les propriétés statiques et dynamiques du composite à renforts particulaires ont été déterminées pour différentes combinaisons de ces paramètres de conception. En particulier, le mécanisme de décohésion particule/matrice a été spécifiquement étudié. Les approches de Modèles de Zone Cohésive (CZM) et de Mécanique de la Rupture Finie (FFM) ont été utilisées pour modéliser ce phénomène et un fort effet de taille des particules a été observé.

The object of this study is the development of a novel class of stacking sequencesfor the design of multidirectional polymer matrix laminated composite specimens for interlaminar fracture toughness (or delamination) tests. These sequences allow to obtain multidirectional specimens that, in the framework of Classic Laminated Plate Theory, have a thermo-elastic behaviour that closely matches that of unidirectional specimens: they are completely free from elastic couplings and they do not develop laminate-level thermally-induced deformations due to the curing process. Furthermore, they allow to test delamination interfaces between plies of any desired orientation. Because of their properties, they were labelled Fully-Uncoupled Multi-Directional (FUMD).In order to design these layups, Quasi-Trivial (QT) solutions were exploited.Firstly, an algorithm for the creation of a database of such solutions was conceived and implemented.Thanks to it, more and longer QT solutions were found than in previous studies.Then, analytical rules were established allowing to obtain new QT solutions from the superposition of known ones.These criteria allow to obtain QT sequences of any desired length, thus overcoming existing computational limitations arising when searching for QT solutions using the algorithm.Combining QT solutions with a few basic laminate design principles and the superposition criteria, FUMD stacking sequences are designed.In order to assess the properties of delamination specimens obtained with FUMD layups, a Finite Element model of a Double Cantilever Beam specimen was developed and used to compare the behaviour of a FUMD layup with that of other sequences proposed in relevant literature on the topic of delamination in multidirectional laminates.By means of the standard and of a revised Virtual Crack Closure Technique formulations, Energy Release Rate distributions and modal partitions of the specimens were evaluated.It emerged that the FUMD layup resulted in an optimal behaviour of the specimen.Eventually, a mode I interlaminar fracture toughness experimental campaign was performed.FUMD Double Cantilever Beam specimens were fabricated, along with with unidirectional ones.A UD-fabric material was used to reduce the likelihood of delamination migration.Rotations of the specimens arms and the shape of the delamination fronts were studied in order to assess the capability of the specimens to yield the correct mechanical behaviour for mode I delamination testing.For both aspects, FUMD specimens yielded results similar to those obtained with unidirectional specimens.With respect to interlaminar fracture toughness, specimens with identical delamination interface yielded similar values, even if their global stiffness was different.On the other hand, different interfaces led to different interlaminar fracture toughness, related to different fracture behaviours.While this work represents a preliminary study and further research is clearly required, FUMD delamination specimens have shown a good potential, and they may stand out as a viable solution for interlaminar fracture toughness tests.Possibly, they could be considered for an extension of the scopes of existing standard test methods to multidirectional laminates and interfaces., Le sujet de cette étude est le développement de séquences d’empilement pour la conception d'éprouvettes multidirectionnelles en matériaux composite à matrice polymère destinées à des essais de délaminage.Ces séquences permettent d’obtenir des éprouvettes multidirectionnelles qui, dans le cadre de la théorie classique des stratifiés, montrent un comportement thermoélastique qui reproduit celui des composites unidirectionnels : elles sont complètement libres de tout type de couplage élastique et ils ne développent pas des déformations résiduelles dues au cycle de cuisson.Par ailleurs, ces empilements permettent de tester n’importe quelle interface de délaminage.La conception de ces empilements est basée sur les solutions Quasi-Triviales (QT).Un algorithme pour la création d’une base de données de ces solutions a été conçu et implémenté.Grace à cela, un nombre plus grand de solutions QT et des solutions QT avec un nombre plus grand de plis que dans des études précédentes ont été trouvées.Ensuite, des critères analytiques permettant d’obtenir de nouvelles solutions à partir de la superposition des solutions connues ont été établis.Ces critères permettent d’obtenir des séquences QT avec n’importe quel nombre de couches.En combinant les solutions QT, les principes usuels de conception des stratifiés et les critères de superposition, les séquences d’empilement Fully-Uncoupled Multi-Directional (FUMD) ont été obtenues.Pour évaluer les propriétés des éprouvettes de délaminage obtenues avec ces séquences, un modèle Éléments Finis d’une éprouvette Double Cantilever Beam (DCB) a été développé pour comparer le comportement d’une séquence FUMD à celui d’autres séquences proposées dans la littérature pour les essais de délaminage.En utilisant la méthode de refermeture (Virtual Crack Closure) dans ses formulations originale et révisée, les distributions du taux de restitution d’énergie (Energy Release Rate) et ses partitions modales ont été évaluées.La séquence FUMD démontre les meilleurs résultats.Finalement, une campagne expérimentale de caractérisation du délaminage en mode I a été menée.Des éprouvettes DCB avec des séquences FUMD ont été conçues et fabriquées.Des plis tissés déséquilibrés ont été utilisés pour réduire la probabilité de changement de plan de délaminage.Les rotations des bras des éprouvettes et la forme du front du délaminage ont été étudiés pour évaluer la capacité des éprouvettes à garantir un comportement mécanique optimal lors du test de délaminage en mode I.Les résultats obtenus avec les éprouvettes FUMD sont proches de ceux obtenus avec les éprouvettes unidirectionnelles.En ce qui concerne l'énergie de rupture, les éprouvettes ayant la même interface de délaminage ont montré des valeurs très proches, même si leur rigidité était sensiblement différente.Par ailleurs, la caractérisation d'interfaces différentes a abouti à des énergies de rupture différentes, résultants des modes de ruptures non identiques.Ce travail ne représente qu'une étude préliminaire et des recherches complémentaires sont nécessaires.Néanmoins les éprouvettes de délaminage FUMD ont démontré un bon potentiel, et sont intéressantes pour les essais de délaminage.