Publications

2022

• Investigation of drying shrinkage of cement-based materials assisted by digital image correlation
  
  • Kinda Justin
  • Bourdot Alexandra
  • Charpin Laurent
  • Michel-Ponnelle Sylvie
  • Benboudjema Farid
  Journal of Materials in Civil Engineering, American Society of Civil Engineers, 2022, 34 (3), pp.04021477. This paper presents a validation of a new protocol for the characterization of drying shrinkage of cement paste. The method consists of using environmental scanning electronic microscope (ESEM) or climatic chamber (CC) assisted by digital image correlation (DIC) to study the drying shrinkage of cement-based materials. The final motivation is to study the influence of the drying rate on cement-based materials’ delayed strain at the microscopic scale. Hence, the impact of specimen shape, size, and the imposed relative humidity history on the drying shrinkage is studied. Results show that for a given material, the amplitude of drying shrinkage is independent of the rate of drying and the specimen shape. Advantage was taken of the two techniques proposed in this paper to perform drying length change measurement both in ESEM and CC. (10.1061/(ASCE)MT.1943-5533.0004065)
  DOI : 10.1061/(ASCE)MT.1943-5533.0004065
• A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method
  
  • Di Pietro Daniele Antonio
  • Fontana Ilaria
  • Kazymyrenko Kyrylo
  Computers & Mathematics with Applications, Elsevier, 2022, 111, pp.61-80. We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed upper bound for the dual norm of the residual. This norm is shown to control the natural energy norm up to a boundary term, which can be removed under a saturation assumption. The basic estimate is then refined to distinguish the different components of the error, and is used as a starting point to design an algorithm including adaptive stopping criteria for the nonlinear solver and automatic tuning of a regularization parameter. We then discuss an actual way of computing the stress reconstruction based on the Arnold-Falk-Winther finite elements. Finally, after briefly discussing the efficiency of our estimators, we showcase their performance on a panel of numerical tests. (10.1016/j.camwa.2022.02.008)
  DOI : 10.1016/j.camwa.2022.02.008
• Energy harvesting efficiency of unimorph piezoelectric acoustic black hole cantilever shunted by resistive and inductive circuits
  
  • Li Haiqin
  • Doaré Olivier
  • Touzé Cyril
  • Pelat Adrien
  • Gautier François
  International Journal of Solids and Structures, Elsevier, 2022. A unimorph piezoelectric cantilever equipped with an Acoustic Black Hole (ABH) termination is designed for broadband energy harvesting. The ABH termination, with its tapered region, induces a focusing of the flexural vibrations which can be used to increase the efficiency of an energy harvesting device. A modal-based analytical model is presented, providing an explicit form of the electro-mechanical coupling for each beam eigenmode. Closed-form expressions for the coupled mechanical response and electrical outputs are obtained, allowing one to draw out a complete parametric study to optimize the device. The optimization procedure is conducted following two steps: first, optimal location and dimensions of a single piezoelectric patch are achieved by maximizing the modal electro-mechanical coupling factor (MEMCF) for each structural mode. Thanks to the proposed analytical approach, it is clearly shown that by putting the piezoelectric patch at the maximum of the strain field in the tapered termination, and by adjusting its length in accordance with the focalization created by the ABH effect, the ABH cantilever produces much higher MEMCFs over a wide frequency range and thus outperforms those of a uniform beam. Second, optimization of the shunted circuit is comprehensively performed for a circuit with only resistance, or both resistance and inductance, in series or in parallel. Analytical results show that the key design rule resides in matching the time scale of the circuit with that of the forcing frequency. Addition of the inductance allows enhancing the performance, but on a narrow frequency band. Finally, broadband advantages can be further obtained by considering multiple piezoelectric patches, in which the optimum is obtained when the shunted circuit in each patch is tuned targeting an eigenmode of the ABH beam. (10.1016/j.ijsolstr.2021.111409)
  DOI : 10.1016/j.ijsolstr.2021.111409
• Efficient evaluation of three-dimensional Helmholtz Green's functions tailored to arbitrary rigid geometries for flow noise simulations
  
  • Chaillat Stéphanie
  • Cotté Benjamin
  • Mercier Jean-François
  • Serre Gilles
  • Trafny Nicolas
  Journal of Computational Physics, Elsevier, 2022, 452. The Lighthill's wave equation provides an accurate characterization of the hydrodynamic noise due to the interaction between a turbulent flow and an obstacle, that is needed to get in many industrial applications. In the present study, to solve the Lighthill's equation expressed as a boundary integral equation, we develop an efficient numerical method to determine the three-dimensional Green's function of the Helmholtz equation in presence of an obstacle of arbitrary shape, satisfying a Neumann boundary condition. This so-called tailored Green's function is useful to reduce the computational costs to solve the Lighthill's equation. The first step consists in deriving an integral equation to express the tailored Green's function thanks to the free space Green's function. Then a Boundary Element Method (BEM) is used to compute tailored Green's functions. Furthermore, an efficient method is performed to compute the second derivatives needed for accurate flow noise determinations. The proposed approach is first tested on simple geometries for which analytical solutions can be determined (sphere, cylinder, half plane). In order to consider realistic geometries in a reasonable amount of time, fast BEMs are used: fast multipole accelerated BEM and hierarchical matrix based BEM. A discussion on the numerical efficiency and accuracy of these approaches in an industrial context is finally proposed. (10.1016/j.jcp.2021.110915)
  DOI : 10.1016/j.jcp.2021.110915
• Graded damage in quasi‐brittle solids
  
  • Valoroso Nunziante
  • Stolz Claude
  Int. J. Numer. Meth. Eng., SSA, 2022, 123 (11), pp.2467-2498. A novel approach to damage modeling for quasi-brittle solids is presented relying upon a differential inclusion that is closely related to the one of implicit gradient models. The proposed formulation naturally fits in the socalled non-local standard approach, whereby the framework of Generalized Standard Materials is extended to include gradients of internal variables to account for the physics of the fracture phenomenon in a regularized sense, i.e. via extended constitutive equations in which a length scale parameter brings to the macro level information about material microstructure. This concept is fully embodied into the present approach to quasi-brittle fracture, whereby progressive damage occurs in layers of finite thickness where the gradient of damage is bounded and a fully damaged region is understood as a fracture with no ambiguity. Key to the effective implementation of the model are the choice of two constitutive functions and the implicit tracking of regions in a state of progressive damage via Lagrange multipliers acting on internal constraints. The ideas are developed for a general Cauchy continuum and representative numerical simulations are included that demonstrate the model capabilities. (10.1002/nme.6947)
  DOI : 10.1002/nme.6947
• Physically-based sound synthesis software for Computer-Aided-Design of piano soundboards
  
  • Elie Benjamin
  • Cotté Benjamin
  • Boutillon Xavier
  Acta Acustica, EDP Sciences, 2022, 6, pp.30. The design of pianos is mainly based on empirical knowledge due to the lack of a simple tool that could predict sound changes induced by modifications of the geometry and/or the mechanical properties of the soundboard. We introduce the concept of Sound Computer-Aided Design through the framework of a program that is intended to simulate the acoustic results of virtual pianos. The calculation of the sound is split into four modules that compute respectively the modal basis of the stiffened soundboard, the string dynamics excited by the hammer, the soundboard dynamics excited by the string vibration, and the sound radiation. The exact resemblance between synthesis and natural sounds is not the primary purpose of the software. However, sound synthesis of real and modified pianos are used as reference tests to assess our main objective, namely to reflect faithfully structural modifications in the produced sound, and thus to make this tool helpful for both instrument makers and researchers of the musical acoustics community. (10.1051/aacus/2022024)
  DOI : 10.1051/aacus/2022024
• A multi-physics, multi-scale and finite strain crystal plasticity-based model for pseudoelastic NiTi shape memory alloy
  
  • Ju Xiaofei
  • Moumni Ziad
  • Zhang Yahui
  • Zhang Fengguo
  • Zhu Jihong
  • Chen Zhe
  • Zhang Weihong
  International Journal of Plasticity, Elsevier, 2022, 148, pp.103146. (10.1016/j.ijplas.2021.103146)
  DOI : 10.1016/j.ijplas.2021.103146
• On the key role of crack surface area on the lifetime of arbitrarily shaped flat cracks
  
  • David L.
  • Lazarus V.
  International Journal of Fatigue, Elsevier, 2022, 154, pp.106512. (10.1016/j.ijfatigue.2021.106512)
  DOI : 10.1016/j.ijfatigue.2021.106512
• Assessment of a non-conservative Residual Distribution scheme for solving a four-equation two-phase system with phase transition
  
  • Bacigaluppi Paola
  • Carlier Julien
  • Pelanti Marica
  • Congedo Pietro Marco
  • Abgrall Rémi
  Journal of Scientific Computing, Springer Verlag, 2022, 90 (1). This work focuses on a four-equation model for simulating two-phase mixtures with phase transition. The main assumption consists in a homogeneous temperature, pressure and velocity fields between the two phases. In particular, we tackle the study of time dependent problems with strong discontinuities and phase transition. This work presents the extension of a non-conservative residual distribution scheme to solve a four-equation two-phase system with phase transition. This non-conservative formulation allows avoiding the classical oscillations obtained by many approaches, that might appear for the pressure profile across contact discontinuities. The proposed method relies on a Finite Volume based Residual Distribution scheme which is designed for an explicit second-order time stepping. We test the non-conservative Residual Distribution scheme on several benchmark problems and assess the results via a cross-validation with the approximated solution obtained via a conservative approach, based on an HLLC solver. Furthermore, we check both methods for mesh convergence and show the effective robustness on very severe test cases, that involve both problems with and without phase transition. (10.1007/s10915-021-01706-6)
  DOI : 10.1007/s10915-021-01706-6
• Simulation of ductile tearing during a full size test using a non local Gurson-Tvergaard-Needleman (GTN) model
  
  • Chen Youbin
  • Lorentz Eric
  • Dahl Anna
  • Besson Jacques
  Engineering Fracture Mechanics, Elsevier, 2022, 261, pp.108226. Ductile tearing of a full size precracked pipe is experimentally investigated. In order to model and interpret the test, the pipe material is characterized using smooth and notched tensile bars and precracked C(T) specimens. This experimental database is used to fit the parameters of the non local Gurson-Tvergaard-Needleman (GTN) proposed in [? ? ]. The model is used in finite element simulations using specific elements allowing for the control of strain/damage localization as well as volumetric locking. Mesh size independence is checked on notched tensile bars. The model is then able to represent the early stages of crack propagation in the pipe. In particular, experimentally observed crack branching is reproduced, whereas this appeared much more difficult to obtain using a local GTN model. (10.1016/j.engfracmech.2021.108226)
  DOI : 10.1016/j.engfracmech.2021.108226
• High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point
  
  • Vizzaccaro Alessandra
  • Opreni Andrea
  • Salles Loïc
  • Frangi Attilio
  • Touzé Cyril
  Nonlinear Dynamics, Springer Verlag, 2022, 110 (1), pp.525-571. Abstract This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems in oscillatory form expressed in the physical basis, so that the technique is directly applicable to mechanical problems discretised by the finite element method. Two nonlinear mappings, respectively related to displacement and velocity, are introduced, and the link between the two is made explicit at arbitrary order of expansion, under the assumption that the damping matrix is diagonalised by the conservative linear eigenvectors. The same development is performed on the reduced-order dynamics which is computed at generic order following different styles of parametrisation. More specifically, three different styles are introduced and commented: the graph style, the complex normal form style and the real normal form style. These developments allow making better connections with earlier works using these parametrisation methods. The technique is then applied to three different examples. A clamped-clamped arch with increasing curvature is first used to show an example of a system with a softening behaviour turning to hardening at larger amplitudes, which can be replicated with a single mode reduction. Secondly, the case of a cantilever beam is investigated. It is shown that invariant manifold of the first mode shows a folding point at large amplitudes. This exemplifies the failure of the graph style due to the folding point on a real structure, whereas the normal form style is able to pass over the folding. Finally, a MEMS (Micro Electro Mechanical System) micromirror undergoing large rotations is used to show the importance of using high-order expansions on an industrial example. (10.1007/s11071-022-07651-9)
  DOI : 10.1007/s11071-022-07651-9
• Effect of Active Plastic Fine Fraction on Undrained Behavior of Binary Granular Mixtures
  
  • Gobbi Stefania
  • Santisi D’avila Maria Paola
  • Lenti Luca
  • Semblat Jean-François
  • Reiffsteck Philippe
  International Journal of Geomechanics, American Society of Civil Engineers, 2022, 22 (1), pp.06021035. The mechanical behavior of binary granular mixtures strongly depends on their initial packing density, stress level, fine content, particle size distribution, mineralogy, and shape. This research aims to investigate the effect on the mechanical behavior of fine-sand mixtures of fine particle fraction through various features: grain size distribution, fine particle size, and plasticity. The concept of equivalent intergranular void ratio is proposed for this analysis. It is correlated to the micromechanical activation of fines within the sand matrix.Monotonic consolidated undrained triaxial tests are carried out for mixtures of coarse particles (sand) and fine particles (silt or clay), in the sand dominant behavior, having various shapes and grain-size distributions. Loose, medium, and dense mixtures are tested using different fine contents and confining pressures. The undrained response is strongly affected by particle interactions, depending on the packing density, particle size, and plasticity. The active fine fraction captures the active contribution of fine particles in the sand skeleton structure. It influences the equivalent intergranular void ratio estimated in these experiments and associated to the steady state of mixtures. The reliability of equivalent state theory and an original formula proposed to estimate the active fine fraction is demonstrated in the case of fine-sand mixtures having plastic fine particles and confirmed for non-plastic fines. (10.1061/(ASCE)GM.1943-5622.0002242)
  DOI : 10.1061/(ASCE)GM.1943-5622.0002242