We propose a method for designing inflatable shells made of superimposed quasi-inextensible membranes sealed according to specific welding patterns. The shapes of the patterns are defined on unit triangular cells and allow us to locally control the contraction of the cells from rest to inflated configuration. By paving the patterns on the surface of the structure and properly grading their parameters, we are able to generate inflatables of prescribed deployed shapes through metric frustration.Our triangular cells exhibit isotropic contraction. Our inverse design algorithm can thus leverage conformal parametrization to compute local contraction ratios that are converted to pattern geometries. Key to our approach is to define the arrangement of the patterns using an unstructured triangulation of the target surface. Compared to more traditional arrangements laid out on regular grids, our approach allows us to easily cut or segment the structure without visible seams and to decrease the contraction range necessary to reproduce a given surface, thus enlarging our design space. Additionally, unstructured arrangements lead to inflatable structures whose cells conform to the boundary of the target surface and therefore better covers it.We demonstrate the capabilities of our approach in simulation and by fabricating various prototypes, made of one or multiple components.

Effective models for slender structures derived from well-known plate (or shell) theories are justified within the limit of a small thickness, and may therefore prove limited for intermediate slenderness. On the other hand, direct 3D simulation of such structures is sub-optimal because it does not take advantage of the presence of small dimensions in some directions and is sometimes too costly and ill-conditioned. In this context, the Proper Generalized Decomposition (PGD) method, a model order reduction method based on a modal representation of the solution with separation of variables, makes it possible to obtain a 3D solution with 2D resolution complexity. In this work, an analysis of the links between the PGD reduced order model and the solution provided by plate theory is carried out using asymptotic expansion. It is shown that, in the limit of large slenderness, the first mode of the PGD exhibits Kirchhoff-Love type kinematics, but only corresponds to the asymptotic solution in very special cases of loading and boundary conditions. To capture the asymptotic solution, a new PGD strategy is introduced consisting of computing the first two modes simultaneously. We also demonstrate that the PGD is subject to shear locking, and we show how to deal with it. Numerical experiments are provided, demonstrating the interest of this approach and confirming the theoretical analysis.

Inflatable pads, such as those used as mattresses or protective equipment, are structures made of two planar membranes sealed according to periodic patterns, typically parallel lines or dots. In this work, we propose to treat these inflatables as metamaterials.By considering novel sealing patterns with 6-fold symmetry, we are able to generate a family of inflatable materials whose macroscale contraction is isotropic and can be modulated by controlling the parameters of the seals. We leverage this property of our inflatable materials family to propose a simple and effective algorithm based on conformal mapping that allows us to design the layout of inflatable structures that can be fabricated flat and whose inflated shapes approximate those of given target freeform surfaces.

The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion equation and establish such results in arbitrary dimensions, by using a straightforward adaptation of the classical arguments used for the homogenization of highly oscillatory problems posed on fixed (non-thin) domains. We next consider the linear elasticity problem, which raises challenging difficulties in its full generality. Under some classical assumptions on the symmetries of the elasticity tensor, the problem can be split into two independent problems, the membrane problem and the bending problem. Focusing on two-dimensional problems, we show that the membrane case can actually be addressed using a careful adaptation of classical arguments. In the bending case, the scheme of the proof used in the membrane and diffusion cases can however not be straightforwardly adapted. In that bending case, we establish the desired strong convergence results by using a different strategy of proof, which seems, up to our knowledge, to be new.

Determining the membrane, bending, and shear stiffness of cross-laminated timber (CLT) and innovative panels requires advanced finite element computations and homogenization techniques based on thin and thick plate theories. These computations may not be easily implemented by engineers. To address this issue, this paper implements and makes accessible a machine-learning model that directly predicts the linear elastic properties of CLT and innovative panels. First, a large database of plate stiffness moduli is built from finite element computations taking into account microstructural characteristics such as the layers’ thicknesses, board width, gaps width, longitudinal modulus of elasticity, and longitudinal and rolling shear stiffness moduli of timber. Second, three approximations are built and investigated: closed-form solutions, an artificial neural network trained on the database, and another artificial neural network that uses the closed-form solutions as prior knowledge before being trained on the data. The results demonstrate the superiority of artificial neural networks with prior knowledge and a very satisfying accuracy for engineering applications. The root mean square percentage error (RMSPE) values range from 0.23% to 3.01%, and the maximum absolute percentage error (MaxAPE) values range from 1.12% to 20%.

There are very few examples of architectured materials producing significant strain-gradient effects in elastostatics. In the present paper, we generate for the first time new microstructures featuring these effects from topological optimization of two-dimensional periodic media. The optimized shape functionals depend on the first and second-order homogenized tensors, obtained from a two-scale asymptotic expansion homogenization scheme. The optimization method applied here relies on the recently rigorously derived topological derivative of the second-order homogenized tensor, measuring the strain-gradient sensitivity with respect to a small circular inclusion at the microscopic level endowed with different material property from the background. This previous theoretical work allows an accurate numerical implementation.

La construction de coques minces en béton est coûteuse en matériaux et en main d’œuvre à cause de la fabrication du coffrage qui génère une vaste quantité de déchets. Ces éléments non réutilisables ont un impact négatif sur l’ACV de la construction. Ces difficultés expliquent en partie pourquoi la construction de coques minces est devenue rare à la fin du XXème siècle malgré l’indéniable qualité architecturale qu’elles confèrent aux espaces créés. Cette recherche a pour objectif de modéliser et concevoir un nouveau système de coffrage économe en moyens, pour préfabriquer des éléments surfaciques en béton à partir de structures gonflables. Contrairement à des exemples historiques proposant des gonflables à simple peau, nous proposons de liaisonner deux membranes selon un motif. Composé de courbes, le motif est conçu afin qu’une fois les membranes gonflées, la métrique du plan varie de manière non uniforme et génère une surface en trois dimensions selon le theorema egregium de Gauss. Le dessin du motif d’assemblage est guidé par un outil numérique capable de simuler précisément une forme gonflée en 3D à partir d’un motif de soudure en 2D. Cette méthode de fabrication serait automatisable et transposable à plus grande échelle. L’article décrira les principes géométriques et l’outil de simulation numérique. Nous présenterons une application, la fabrication d’un coffrage gonflable et la construction d’une coque mince en béton.

The principles of origami design have proven useful in a number of technological applications. Origami tessellations in particular constitute a class of morphing metamaterials with unusual geometric and elastic properties. Although inextensible in principle, fine creases allow origami metamaterials to effectively deform non-isometrically. Determining the strains that are compatible with coarse-grained origami kinematics as well as the corresponding elasticity functionals is paramount to understanding and controlling the morphing paths of origami metamaterials. Here, within a unified theory, we solve this problem for a wide array of well-known origami tessellations including the Miura-ori as well as its more formidable oblique, non-developable and non-flat-foldable variants. We find that these patterns exhibit two universal properties. On one hand, they all admit equal but opposite in-plane and out-of-plane Poisson's ratios. On the other hand, their bending energy detaches from their in-plane strain and depends instead on the strain gradient. The results are illustrated over a case study of the self-equilibrium geometry of origami pillars.

Since the success of bone regenerative medicine depends on scaffold morphological and mechanical properties, numerous scaffolds designs have been proposed in the last decade, including graded structures that are suited to enhance tissue ingrowth. Most of these structures are based either on foams with a random pore definition, or on the periodic repetition of a unit cell (UC). These approaches are limited by the range of target porosities and obtained effective mechanical properties, and do not permit to easily generate a pore size gradient from the core to the periphery of the scaffold. In opposition, the objective of the present contribution is to propose a flexible design framework to generate various three-dimensional (3D) scaffolds structures including cylindrical graded scaffolds from the definition of a UC by making use of a non-periodic mapping. Conformal mappings are firstly used to generate graded circular cross-sections, while 3D structures are then obtained by stacking the cross-sections with or without a twist between different scaffold layers. The effective mechanical properties of different scaffold configurations are presented and compared using an energy-based efficient numerical method, pointing out the versatility of the design procedure to separately govern longitudinal and transverse anisotropic scaffold properties. Among these configurations, a helical structure exhibiting couplings between transverse and longitudinal properties is proposed and permits to extend the adaptability of the proposed framework. In order to investigate the capacity of common additive manufacturing techniques to fabricate the proposed structures, a subset of these configurations is elaborated using a standard SLA setup, and subjected to experimental mechanical testing. Despite observed geometric differences between the initial design and the actual obtained structures, the effective properties are satisfyingly predicted by the proposed computational method. Promising perspectives are offered concerning the design of self-fitting scaffolds with on-demand properties depending on the clinical application.

Construction of concrete shells is expensive and generates wastes from the fabrication of formworks. Being non-reusable, these elements have a negative impact on the life-cycle assessment of the construction. The purpose of this research is to design and build a new inexpensive formwork system made of inflatable structures for precast and thin concrete shells construction. By sealing two membranes according to a pattern, this system allows the construction of complex inflated shapes. The sealing pattern is designed such that, once inflated, the planar metric becomes not uniform and generates a 3D surface following Gauss’s Theorema Egregium, a classical result of differential geometry. This design of the seal pattern is guided by a numerical tool capable of accurately predicting the inflated shape. The simulations are compared to physical models made of fabrics, before manufacturing inflatable formwork prototypes in composite membranes from about 1 to three metres wide. Support is set up to pour concrete on the inflatable formwork without damaging it for reuse. The resulting thin concrete shell and its fabrication method are eligible for wider-scale application in the AEC industry.

This paper presents an architectured material featuring significant strain-gradient effects and called pantographic material. It is easy to fabricate, being a plate made of a single and continuous linear elastic material containing voids. The pattern consists of triangles connected by thin junctions and arranged in such a way that two floppy strain modes are present. A homogenization scheme based on the two-scale asymptotic expansion is suggested, keeping only significant strain-gradient contributions in the homogenized energy through an adequate projection. The predictions from the homogenization scheme are validated against a full-scale simulation and yield very good L2 error estimates whereas the classical first-gradient homogenization fails. Furthermore, the relative position of the unit cell in the full-scale computation does not have a significant influence on the quality of the prediction. Finally, with an adequate choice of scalings between the scale separation and the junction thinness, it is possible to ensure that strains as well as displacements in compliant junctions remain bounded while preserving macroscopic strain-gradient effects.

The Asymptotic Expansion Load Decomposition higher-order beam model is based on the classical two-scale asymptotic expansion in the linear elasticity framework.It was successively extended to eigenstrains and to plasticity in small deformations in different papers. The present paper offers a comprehensive and consistent presentation of our approach applied to civil engineering applications.

The multiscale elasticity model of solids with singular geometrical perturbations of microstructure is considered for the purposes, e.g., of optimum design. The homogenized linear elasticity tensors of first and second orders are considered in the framework of periodic Sobolev spaces. In particular, the sensitivity analysis of second order homogenized elasticity tensor to topological microstructural changes is performed. The derivation of the proposed sensitivities relies on the concept of topological derivative applied within a multiscale constitutive model. The microstructure is topologically perturbed by the nucleation of a small circular inclusion that allows for deriving the sensitivity in its closed form with the help of appropriate adjoint states. The resulting topological derivative is given by a sixth order tensor field over the microstructural domain, which measures how the second order homogenized elasticity tensor changes when a small circular inclusion is introduced at the microscopic level. As a result, the topological derivatives of functionals for multiscale models can be obtained and used in numerical methods of shape and topology optimization of microstructures, including synthesis and optimal design of metamaterials by taking into account the second order mechanical effects. The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

An original experimental setup, dedicated to the measurement of the dynamic response of structures, is presented. Called the Robotized Laser Doppler Vibrometer (RLDV), it consists in the assembly of a fixed point Laser Doppler Vibrometer (LDV) on a 6-axis industrial robot arm. This allows to measure the 3D velocity on the surface of objects with a wide range of shapes and sizes. In comparison with commercially available solutions, it represents an affordable and versatile tool. First, the motivations and the new challenges associated to the use of a robot arm to do such experiments are discussed. Second, the different strategies implemented to overcome these difficulties are developed. A software solution is proposed. By the use of a virtual model of the experimental setup, the measurement procedure can be designed and simulated in order to preview robot motion and avoid collisions. With a small number of parameters, the good proceeding of the measurement can be insured on a fine measurement mesh. The software is completed by an interface that allows for the setting of the signal acquisition parameters. At the end, all the procedure is automated and long measurements can be achieved with a reduced supervision. To illustrate the proposed setup, an experimental application is developed. The 3D modal shapes of a curved beam are measured and compared with numerical predictions, showing an excellent correlation.

The present paper introduces a new elastoplastic beam model for reinforced concrete based on a higher-order beam model previously developed (Int J Numer Methods Eng. https://doi.org/10.1002/nme.5926 , 2018 ). Steel and concrete are both defined as elastoplastic materials. The beam model represents the concrete body whereas rebars are given a specific discretization. A Rankine criterion is used for concrete in both tension and compression, and a closed-form solution for the local projection of the trial stress on the yield surface is formulated. Steel rebars are modelled with 1D bar elements and added to the global stiffness of the concrete beam model. The kinematics of the higher-order beam model is enriched by a systematic method with displacement modes. This extension of the kinematics leads to local accuracy and yields results comparable to 3D computations. The present reinforced concrete model is validated through a set of case studies. Implemented within the software programs of the company Strains Engineering, the objective is to develop a fast computing and efficient model that can be directly used by engineers.

Various forms of timber hollow structural profiles have either been proposed in the literature or are already commercially available. Tests performed on Circular Hollow Section (CHS) beams showed failure modes not usually encountered in timber structures. For relatively thin-walled profiles, a sudden failure in the compression zone, with the opening of the cross-section, was observed. To confidently use and market CHS timber products, design rules considering all possible failure modes must be developed. This paper presents a Finite Element (FE) model of CHS timber beams which captures all experimentally observed failure modes. Cohesive zone elements were used to model the quasi-brittle failure modes of the timber material. The model was validated against ten experimental tests performed on CHS of three different cross-sectional slenderness and manufactured from juvenile hardwood Gympie messmate (Eucalyptus cloeziana) rotary peeled veneers. The model was found to accurately capture the measured structural behaviour and resulted in an average experimental-to-predicted bending capacity ratio of 1.02. The model was also used to explain the mechanisms leading to the sudden compressive failure mode. A parametric study was finally performed on 72 CHS beams of different cross-sectional slenderness. Results showed a strong correlation between the cross-sectional slenderness ratio and section capacity. Design rules are proposed and discussed.

The proper sizing of Cross Laminated Timber (CLT) walls for the construction of high rise buildings requires to take into account their low shear stiffness and their viscoelastic properties and to integrate them into the framework of actual building codes which are all based upon Ayrton-Perry approach of imperfect columns. The present paper starts thus by recalling the framework of Linear Buckling Analysis of shear weak columns using the Timoshenko beam model. Then, Ayrton-Perry approach of the buckling of imperfect columns is introduced and used to develop a normal stress strength criterion for CLT walls but also an additional shear strength criterion. Both criteria are compared for three characteristic sizes of initial imperfections. Afterwards, orthotropic creep is introduced and its effect on long term stability of shear weak members is investigated and an extension of the previous criteria to long term behaviour is developed. Throughout the study, three numerical examples are used for illustration (a low strength panel, a high strength and an aerated panel) revealing the importance of proposed shear strength verification and the need of experimental characterisation.