Our research focuses on designing innovative computational methods tailored for structural calculations in civil engineering, with a particular emphasis on failure analysis. These developments include advanced techniques in numerical limit analysis, damage mechanics, and the modeling of complex materials and structural systems.

Numerical Limit Analysis

Jérémy Bleyer, Ghazi Hassen (ME)
Coll.: Vincent Leclère (Cermics)

Limit analysis and yield design theories enable direct estimation of the ultimate load that a structure can withstand, based on the material’s strength properties. These methods provide lower and upper bounds for the load capacity, derived from variational principles applied to stress and displacement. However, their numerical implementation is challenging due to the complex, non-smooth, large-scale convex optimization problems they generate. These problems are categorized under conic programming, for which specialized solvers, such as those using interior-point algorithms, have been developed.

We are advancing finite-element models for various structural types, including continua, beams, plates, and shells. These models are implemented using the FEniCS finite element library, combined with the Mosek conic programming solver. The automation of these processes is integrated into the open-source package, dolfinx_optim. More recently, we work towards extending such theories to the uncertain/stochastic cases using robust and stochastic optimization theories.

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Applications in Civil Engineering Structures

Jérémy Bleyer, Patrick de Buhan (ME), Karam Sab, Hugues Vincent (PhD), Chadi El Boustani (PhD), Sabine Boulvard (PhD)
Coll.: Mathieu Arquier (Strains), Duc Toan Pham (CSTB)

This innovative design approach allows for precise estimation of structural safety margins and associated collapse mechanisms, even in complex scenarios such as:

  • Composite beams, columns, plates, or shells
  • Materials reinforced with linear inclusions (e.g., reinforced concrete, reinforced soils)
  • Masonry structures
  • Complex steel assemblies
  • Massive reinforced concrete structures

Recent applications include the analysis of 3D steel and reinforced concrete structures, carried out in collaboration with the engineering firm STRAINS. PhD research, in partnership with CSTB, has explored simplified analytical methods and more sophisticated numerical limit analysis approaches to evaluate the load-bearing capacity of reinforced concrete structures under fire conditions, for which current engineering practices lack precise design formulas.

Collapse mechanisms obtained with computation limit analysis : circular reinforced concrete footing (left); bolted steel assembly (middle); stone abbey model (right)

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Fracture and damage mechanics in heterogeneous structures

Jérémy Bleyer, Arthur Lebée, Karam Sab, Jean-Michel Scherer (PostDoc), Paul Bouteiller (PhD), Zakaria Chafia (PhD), Gaspard Blondet (PhD), Giulia d’Orio (PhD)
Coll.: Fabrice Congourdeau (Dassault Aviation), Julien Yvonnet (UGE), François Voldoire (EDF)

Our team has also developed significant expertise in simulating material and structural damage, particularly in heterogeneous structures. For fiber-reinforced materials or multi-layered composite plates, for example, we employ generalized models that describe the kinematics of each phase or layer independently. By using well-designed homogenization procedures, we can develop models that couple different failure mechanisms, such as matrix cracking and delamination.

Modeling brittle failure in continuous media is particularly challenging due to the problem’s ill-posed nature. To address this, phase-field or damage-gradient models are among the most effective regularization methods. We apply these models to anisotropic materials, utilizing multiple phase fields to differentiate between failure modes (e.g., transverse or matrix cracking).

One notable application of this approach is our partnership with Dassault Aviation, where these models have been applied to composite laminates to account for inter-layer debonding and intra-ply damage. We are currently extending this methodology to simulate failure in wooden multi-layered plates, such as Cross-Laminated Timber (CLT), which is gaining popularity in high-rise wooden buildings. At present, no model adequately captures the interaction between the various failure mechanisms in CLT, including rolling shear failure, tensile splitting, and ply debonding. Our ongoing developments will result in advanced numerical models, essential for optimizing CLT structures and potentially reducing wood consumption.

We are also currently investigating multiscale strategies for upscaling damage evolutions in heterogeneous structures in collaboration with Julien Yvonnet (UGE) and with EDF regarding damage in reinforced concrete structures under cyclic loads.

3D Phase field fracture in dynamics (left); Matrix multi-cracking (red) and fiber/matrix interfacial debonding (blue) in fiber reinforced material (right)

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