Research
Here you can find an overview of the research projects I am currently working on. These projects have multiple targeted applications, like head protection to soft shocks, biomedical implants, light and resilient civil engineering structures.
Head protection to soft shocks
Biomedical implant made with architectured material
Resilient seismic design of Civil Engineering structure
Light and robust Civil Engineering structure ©Marc François
Non-linear homogenization of heterogeneous materials
This research project aims at determining the equivalent behavior at the macroscopic scale of heterogeneous materials. It concerns various types of heterogeneous materials from reinforced concrete [CDV13, CDV15] to lattice materials, all of them being seen as materials where the geometrical arrangement takes place at various scales. The non-linear behavior of these materials are of interest, whether it concerns plasticity, damage, cracking or internal buckling.
Homogenization techniques are used to travel the scales, based on the Hill-Mandel principle. The objective is to provide a priori of the numerical computation some equivalent homogeneous continuum models that will display the same behavior at the macroscopic scale as the heterogeneous material of interest. These models might use generalized continuum media such as strain-gradient or micromorphic models as we have shown that classical Cauchy elasticity is sometimes not sufficient to capture the equivalent macroscopic behavior [Com23, RAC20].
My work has its originality in the fact that it accounts for the symmetries at the mesoscopic scale to predict the generic shape of the various tensors appearing in the macroscopic constitutive model either in the behavior law itself or in the definition of the linearity limit domain [JCF23]. It also accounts for non-linear effects such as damage [PYC20, PYC21], plasticity [CDV13, CDV15] or buckling [Com23]. The various models developped are justified by multiscale approaches. They are applied to civil engineering materials such as reinforced concrete but also to 3D printed materials or lattice architectured materials. It concerns static as well as dynamic vibrational behavior of the considered material.
[JCF23] V. Jeanneau, C. Combescure, M.L.M. François. Homogenized elasticity and domain of linear elasticity of 2D architectured materials, International Journal of Solids and Structures, 269 (2023) 112185
[Com23] C.Combescure, “Selecting Generalized Continuum Theories for Nonlinear Periodic Solids Based on the Instabilities of the Underlying Microstructure”, J. of Elasticity, 154 (2023) 421–441
[PYC21] P. Li, J. Yvonnet, C. Combescure, H. Makich, M. Nouari. Anisotropic elastoplastic phase field fracture modeling of 3D printed materials, Comp. Methods in Applied Mech. and Eng.386 (2021) 114086
[RAC20] G. Rosi, N. Auffray, C. Combescure. On the failure of classic elasticity in predicting elastic wave propagation in gyroid lattices for very long wavelengths”, Symmetry, 12(8) (2020) 1243
[PYC20] P. Li, J. Yvonnet, C. Combescure. An extension of the phase field method to model interactions between interfacial damage and brittle fracture in elastoplastic composites, International Journal of Mechanical Sciences 179 (2020) 105633
[CDV15] C. Combescure, H. Dumontet, F. Voldoire, Dissipative Homogenised Reinforced Concrete (DHRC) constitutive model dedicated to reinforced concrete plates under seismic loading,International Journal of Solids and Structures, 73–74 (2015) 78-98.
[CDV13] C. Combescure, H. Dumontet, F. Voldoire, Homogenised constitutive model coupling damage and debonding for reinforced concrete structures under cyclic solicitations, International Journal of Solids and Structures, 50(24) (2013) 3861-3874.
Instabilities in architected materials
This research project aims at studying the various instabilities appearing in architected materials. Indeed, architected materials are structured around three distinctive scales at which different types of instabilities can be identified [JCF23][ACD23][Com23]:
the microscopic scale is the smallest considered scale in the model which fixes the limit from which the constitutive material is considered as continuous. At this scale, an instability would correspond to Lüders bands propagating in the constitutive material for instance.
the macroscopic scale is the largest scale in the system. It corresponds to the smallest of the following two scales: that of the external shape of the object or component and the characteristic wavelength of the applied load. Instabilities at this scale correspond to global buckling or to localization phenomena such as localized buckling bands.
one or several intermediate mesoscopic scales where the matter is organized in a controlled manner to give the component the desired properties. Mesoscopic instabilities correspond to periodic buckling modes.
Thanks to Bloch-wave boundary conditions, the mesoscopic and macroscopic instabilities can be predicted separately [CHE16][CE17][CET20]. For separating microscopic material instabilities with macroscopic ones, the proper definition of instability comes into play [AC+19].
Using group theoretic tools, it is possible to predict the various patterns that a periodic architected material can display when subjected to mesoscopic instabilities.
The goal of this research project is to built predictive models to capture all three types of instabilities.
[JCF23] V. Jeanneau, C. Combescure, M.L.M. François. Homogenized elasticity and domain of linear elasticity of 2D architectured materials, International Journal of Solids and Structures, 269 (2023) 112185
[ACD23] R. Azulay, C. Combescure, J. Dirrenberger. Instability-induced pattern generation in architectured materials - a review of methods, International Journal of Solids and Structures, 274 (2023) 112240
[Com23] C.Combescure, “Selecting Generalized Continuum Theories for Nonlinear Periodic Solids Based on the Instabilities of the Underlying Microstructure”, J. of Elasticity, 154 (2023) 421–441
[CHE16] C. Combescure, P. Henry, R. S. Elliott, Post-bifurcation and stability of a finitely strained hexagonal honeycomb subjected to equi-biaxial in-plane loading, International Journal of Solids and Structures, 88–89 (2016) 296-318.
[CE17] C. Combescure, R. S. Elliott, Hierarchical honeycomb material design and optimization: Beyond linearized behavior, International Journal of Solids and Structures, 115–116 (2017) 161-169.
[CET20] C. Combescure, R.S. Elliott, N. Triantafyllidis. Deformation patterns and their stability in finitely strained circular cell honeycombs, Journal of the Mechanics and Physics of Solids, 142 (2020) 103976
[AC+19] M. Al Kotob, C. Combescure, M. Mazière, T. Rose, S. Forest. A general and efficient numerical method for the detection of loss of ellipticity in elastoplastic structures, International Journal of Numerical Methods in Engineering, 121(5) (2019);1–25.
Group theory
This research project aims at exploring the use of symmetry group theory to predict the various mechanical properties (elastic, dynamic, instabilities) of materials and structures [ACD23].
At the structural scale, the use of group theory can help numerical codes to overcome their limitations for detecting instabilities when the structure and its loading have a high degree of symmetry and thus create multiple bifurcation points [CHT23]. This research project requires structural element models that are exact in large rotations. This has been done for beams using a quaternionic formulation. The action of symmetry group elements on quaternions has been studied.
When working with architected materials, the use of group theoretic tools can help predict the elastic properties of an equivalent homogeneous material along with the various possible periodic patterns that can appear at the mesoscopic scale [CHE16][CE17][CET20]. These studies rely on a proper definition of space groups and their associated group theoretic representations.
Finally, group theoretic ideas can be used to help detect the onset of instabilities in experiments. Indeed, instabilities break symmetries and, in periodic materials, this loss of symmetry can be detected by Fourrier based algorithms [PCA23].
[ACD23] R. Azulay, C. Combescure, J. Dirrenberger. Instability-induced pattern generation in architectured materials - a review of methods, International Journal of Solids and Structures, 274 (2023) 112240
[CHT23] C. Combescure, T.J. Healey, J. Treacy. A Group-Theoretic approach to the bifurcation analysis of spatial Cosserat-rod frameworks with symmetry, Journal of Nonlinear Science, 33 (2023) 32
[CHE16] C. Combescure, P. Henry, R. S. Elliott, Post-bifurcation and stability of a finitely strained hexagonal honeycomb subjected to equi-biaxial in-plane loading, International Journal of Solids and Structures, 88–89 (2016) 296-318.
[CE17] C. Combescure, R. S. Elliott, Hierarchical honeycomb material design and optimization: Beyond linearized behavior, International Journal of Solids and Structures, 115–116 (2017) 161-169.
[CET20] C. Combescure, R.S. Elliott, N. Triantafyllidis. Deformation patterns and their stability in finitely strained circular cell honeycombs, Journal of the Mechanics and Physics of Solids, 142 (2020) 103976
[PCA23] M. Poncelet, C. Combescure, F. Amiot. Detecting bifurcations in 2D periodic metamaterials from images. Material Letters, 353 (2023) 135307.