Séminaire de Jean-François Molinari

Th. Ghesquière-Diericks (1) , G. Anciaux (1), V. Acary (2), J.F. Molinari (1)

1: Department of Civil Engineering, EPFL, Lausanne, Switzerland
2: TRIPOP, INRIA, Center of University Grenoble Alpes, France 

 

The increasing overcrowding of Earth’s orbits has become a major concern. Commercial space launches are growing rapidly, and collisions or breakups of space objects lead to an uncontrolled proliferation of debris, further congesting orbital environments. This self-reinforcing process, known as the Kessler syndrome, poses a serious threat to space operations. To assess collision risks, space agencies such as NASA and ESA rely on breakup models, which in turn depend on empirical parameters. Physics-based models of dynamic fragmentation can significantly improve these inputs.
We have developed a high-performance finite-element framework with dynamic insertion of cohesive elements to capture crack initiation, propagation, branching, and coalescence. These dynamic fragmentation simulations provide detailed statistics of fragment masses, shapes, and velocities. We will discuss how this class of models compares favorably with analytical energy-based approaches for benchmark tests such as expanding rings or spherical membranes that mimic exploding fuel tanks. Fragment mass distributions de-pend strongly on geometry and loading conditions. In particular, high-velocity impacts produce power-law fragment size distributions (fig. 1a), and accurate velocity statistics require a robust treatment of fragments collisions and self-contact within partially dam-aged cohesive elements. This presentation focuses on the associated numerical challeng-es.
A common approach for handling contact in explicit dynamics combines extrinsic cohe-sive elements with penalty-based contact. While effective over short time scales, we show that this method leads to exponential energy growth and artificial fragmentation at longer times. We present a systematic analysis of the sources of instability [1], identify-ing three dominant mechanisms: (i) excessively large initial cohesive stiffness, which restricts the stable time step; (ii) discontinuous stiffness jumps at the cohesive–contact interface; and (iii) discontinuities introduced by cohesive softening. Analytical error es-timates, phase-space analysis, and energy growth metrics demonstrate that repeated switching between cohesive and contact states accumulates small per-step errors into a significant long-term energy drift. Within the explored parameter space, stability can only be maintained using time steps far below conventional limits. To reduce these artifacts, we evaluate an adaptive penalty strategy that links the contact stiffness to the evolving cohesive stiffness (fig. 1b). Although this approach restores energy conservation by re-moving stiffness discontinuities, it permits larger interpenetrations and is therefore better suited as a diagnostic tool than as a definitive solution. Overall, our findings show that penalty-based contact is not suitable for long-term, energy-consistent fragmentation sim-ulations with physically meaningful fragment statistics.
To overcome these limitations, we propose an impulse-based contact formulation that explicitly accounts for the non-smooth nature of contact mechanics. The method is em-bedded implicitly within an explicit time-integration framework using the non-smooth Newmark-β scheme of Chen et al. [2]. Applied to one-dimensional dynamic fragmenta-tion problems, this approach restores energy conservation and substantially improves robustness and accuracy in long-term simulations. Although the implicit contact resolu-tion introduces additional computational cost, the enhanced stability enables larger time steps, resulting in overall performance comparable to—or even exceeding—that of penal-ty-based methods. These results demonstrate the potential of impulse-based contact as a reliable and efficient alternative for long-term dynamic fragmentation simulations.

References
[1] Th. Ghesquière-Diérickx, J.F. Molinari, G. Anciaux, Stability of extrinsic cohesive-zone model with penalty-based contact in explicit dynamic fragmentation simulations, arXiv:2511.14323 , 2025.
[2] Q.Z. Chen, V. Acary, G. Virlez, O. Brüls, A nonsmooth generalized‐α scheme for flexible multi-body systems with unilateral constraints, International Journal for Numerical Methods in Engineer-ing, 96(8), 487-511, 2013.