Missions

In many engineering domains, materials undergo deformation at high rates. This is the case when structures are subjected to explosion or impact either in military context, planetary science or e.g. when a satellite meets a constellation of space junk. High strain-rates are also involved in a variety of dynamic processing techniques; including friction-stir welding or electro-magnetic forming or pulse welding. Such extreme types of deformation usually trigger localization mechanisms and material instabilities. In metals in particular, these heterogeneous mechanisms of deformation and strong thermomechanical coupling induce significant modification of the material microstructure.

The ANR project IChar aims at investigating, with new eyes, cascade thermomechanical mechanisms operating at grain-scale during very-high strain rate loading, resulting eventually in extreme solid-state-flow, in particular during electromagnetically driven oblique impacts. From a numerical method point of view, new means to quantitatively probe local mechanical response in heterogeneous (possibly evolving) microstructures are needed. Among the variety of Image-based inverse methods for material parameter identification the finite element model updating (FEMU) [1] or the virtual field method (VFM) [2] are the most known (see [3] for global review). Nevertheless, such numerical methods are parametric per nature: they relie on the a priori choice of a constitutive model to compute mechanical fields. When the objective is to study the underlying physics and build models with a minor a priori, there is a need for alternative routes. Data-driven-identification (DDI) sounds like a promising candidate. In 2018, Leygue [4] formulated an inverse identification problem where stress tensor fields can be reconstructed from full-field kinematic (obtained by digital image correlation (DIC)) and net force measurements only. It consists in a minimization problem under constraints which search, among the infinity of statistically admissible stress fields, for the one that piecewisely minimise the spread around a mean response in a wisely defined constitutive space. In short, instead of trying to identify a small number of constitutive modeling parameters, the methods tends to identify fields of stress tensor. So far, the method has been numerically tested on homogeneous and heterogeneous hyper-elastic materials (e.g. [5]), while experimentally applied to hyper-elastic [6], history [7] and rate-dependent elasto-plastic [8] homogeneous materials all in quasi-static like regimes. To date, its application to a transient dynamic case (with inertia involved) has only been tested on noise-free FE data [9]. One current limiting point regarding its application in a true ultra-high-speed (beyond 1 Million fps) experimental context is the proper evaluation of the local acceleration (contrary to large domain average used in other acceleration-based techniques [10]). Key points are the choices of DIC and DDI discretisation schemes (space and time) allowing to address sharp waves propagation and experimental noise issues.

The objective of the postdoc is to develop a new formulation of the DDI problem, accommodating strong experimental acceleration noise and allowing possible space-time discontinuities to temper spurious high-frequency oscillations coming from Newmark's type integrator. The idea would be to propose a multi-field formulation of the DDI problem, analog to these encountered in various discontinuous-Galerkin (DG) contexts, allowing the smoothing of the acceleration via a dedicated approximation rather than through filtering operations.

[1] K. T. Kavanagh, R. W. Clough, International Journal of Solids and Structures (1971), 7, 11–23.
[2] M. Grédiac, Comptes rendus de l'Académie des sciences. Série 2 Mécanique (1989), 309, 1–5.
[3] S. Avril, M. Bonnet, A.-S. Bretelle, M. Grédiac, F. Hild, et. al, Experimental Mechanics (2008), 48, 381–402.
[4] A. Leygue, M. Coret, J. Réthoré, et al., Computer Methods in Applied Mechanics and Engineering 2018, 331, 184–196.
[5] Valdés-Alonzo, G., Binetruy, C., Eck, B., García-González, A., & Leygue, A. (2022). Phase distribution and properties identification of heterogeneous materials: A data-driven approach. Computer Methods in Applied Mechanics and Engineering, 390, 114354.
[6] Dalémat, M., Coret, M., Leygue, A., & Verron, E. (2019). Measuring stress field without constitutive equation. Mechanics of Materials, 136, 103087.
[7] Langlois, R., Coret, M., & Réthoré, J. (2022). Non‐parametric stress field estimation for history‐dependent materials: Application to ductile material exhibiting Piobert–Lüders localization bands. Strain, 58(4), e12410.
[8] Vinel, A., Seghir, R., Berthe, J., Portemont, G., & Réthoré, J. (2023). Experimental characterization of material strain-rate dependence based on full-field Data-Driven Identification. hal-04048778
[9] Leygue, A., Seghir, R., Réthoré, J., Coret, M., Verron, E., & Stainier, L. (2019). Non-parametric material state field extraction from full field measurements. Computational Mechanics, 64(2), 501-509.
[10] Pierron, F., Zhu, H., & Siviour, C. (2014). Beyond Hopkinson's bar. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 372(2023), 20130195.
[11] I. Bataev, S. Tanaka, Q. Zhou, D. Lazurenko, et al., Materials & Design 2019, 169, 107649.

Activities

Tasks coming with the position are :
• mastering of DDI and DIC concepts in quasi-static contexts,
• deriving one (or various) multi-field formulation of the DDI problem,
• performing consistency checks on digital twin (wave propagation in heterogeneous elasto-plastic media),
• validating the method on magnetically driven impact simulations,
• eventually, the experimental application of the method could be considered.

Skills

We are looking for a young PhD researcher in mechanics with strong background in continuum mechanics, and a keen knowledge in numerical methods (especially through coding in a finite element context). Experience in DIC and DIC-based inverse methods would be a plus.

Work Context

The research laboratory involved is GeM (UMR6183).
The GeM is a Joint Research Unit of Centrale Nantes, the University of Nantes and the CNRS. This laboratory was founded in 2004 and has around 240 staff spread across 3 sites in Nantes and Saint-Nazaire.
The GeM is very involved in training through research: it has around a hundred doctoral students and holds several master's degrees. The research axes of the 9 Thematic Research Units (UTR) revolve around the triptych Materials – Processes – Structure. Internal skills include experimental techniques, modeling and digital simulation.
The work is part of the ANR project Ichar.
The work will take place with GeM laboratory at l'Ecole Centrale de Nantes ender the supervision of Rian Seghir (CR CNRS), Thomas Heuzé (MCF HDR) and Xiaodong Liu (IR CNRS).

Constraints and risks

None