David Amitrano

A new modeling framework for sea-ice mechanics based on elasto-brittle rheology

Abstract We present a new modeling framework for sea-ice mechanics based on elasto-brittle (EB) behavior. the EB framework considers sea ice as a continuous elastic plate encountering progressive damage, simulating the opening of cracks and leads. As a result of long-range elastic interactions, the stress relaxation following a damage event can induce an avalanche of damage. Damage propagates in narrow linear features, resulting in a very heterogeneous strain field. Idealized simulations of the Arctic sea-ice cover are analyzed in terms of ice strain rates and contrasted to observations and simulations performed with the classical viscous–plastic (VP) rheology. the statistical and scaling properties of ice strain rates are used as the evaluation metric. We show that EB simulations give a good representation of the shear faulting mechanism that accommodates most sea-ice deformation. the distributions of strain rates and the scaling laws of ice deformation are well captured by the EB framework, which is not the case for VP simulations. These results suggest that the properties of ice deformation emerge from elasto-brittle ice-mechanical behavior and motivate the implementation of the EB framework in a global sea-ice model.

From diffuse to localised damage through elastic interaction

Local damage processes that have been reported for ductile and brittle macroscopic behaviours are shown here to provide a possible link between these two contrasting behaviours. Using a local progressive damage law within a linear tensorial elastic interaction model, we reproduce experimentally observed macroscopic non-linear behaviours that continuously range from ductility with diffuse damage to brittleness with localised damage. The model exhibits power law distributions of damage events in space and size domains. The diffuse-localised and induced ductile-brittle transition appear to be controlled by the internal friction angle which influences the local interaction geometry.

Failure as a critical phenomenon in a progressive damage model

The critical point hypothesis for fracture is tested using a progressive damage model. The advantage of the present model, based on continuum mechanics, is the possibility of tracking the approach to final failure in terms either of discrete events (the avalanches) or of the resulting continuous strain field. Different but actually closely linked phenomena are reported. In terms of damage avalanches, power law distributions of avalanche sizes and energies are observed associated with a finite size scaling. The finite size scaling is also observed for the spatial correlations of damage events. A divergence of the correlation length is reported in the vicinity of final failure, from a correlation analysis of discrete events and from a scaling analysis of the continuous strain rate field. We also show that multifractal properties of the deformation emerge from the long-range elastic interactions that occur near final failure. All of these results argue for a critical point interpretation of failure. Finally, we discuss the implications of our results for the criticality of fracture and deformation of geophysical objects, and for associated precursory phenomena.

Crossover from quasi-static to dense flow regime in compressed frictional granular media

Being ubiquitous in a large variety of geomaterials, granular assemblies play a crucial role in the mechanical stability of engineering and geophysical structures. For these applications, an accurate knowledge of the processes at the origin of shear localization, i.e. faulting, in frictional granular assemblies submitted to compressive loading is needed. Here we tackle this problem by performing discrete-element numerical simulations. A thorough analysis of the evolution of multi-scale mechanical properties as approaching sample macroscopic instability is performed. Spatial correlations operating within the shear stress and strain fields are analyzed by means of a coarse-graining analysis. The divergence of correlation lengths is reported on both shear stress and strain fields as approaching the transition to sample instability. We thus show that the crossover from a quasi-static regime where the sample deforms infinitely slowly to a dense flow regime, where inertial forces play a significant role, can be interpreted as a critical phase transition. At this transition, no shear band of characteristic thickness can be defined.

Fiber bundle model under fluid pressure

Internal fluid pressure often plays an important role in the rupture of brittle materials. This is a major concern for many engineering applications and for natural hazards. More specifically, the mechanisms through which fluid pressure, applied at a microscale, can enhance the failure at a macroscale and accelerate damage dynamics leading to failure remains unclear. Here we revisit the fiber bundle model by accounting for the effect of fluid under pressure that contributes to the global load supported by the fiber bundle. Fluid pressure is applied on the broken fibers, following Biots theory. The statistical properties of damage avalanches and their evolution toward macrofailure are analyzed for a wide range of fluid pressures. The macroscopic strength of the new model appears to be strongly controlled by the action of the fluid, particularly when the fluid pressure becomes comparable with the fiber strength. The behavior remains consistent with continuous transition, i.e., second order, including for large pressure. The main change concerns the damage acceleration toward the failure that is well modeled by the concept of sweeping of an instability. When pressure is increased, the exponent β characterizing the power-law distribution avalanche sizes significantly decreases and the exponent γ characterizing the cutoff divergence when failure is approached significantly increases. This proves that fluid pressure plays a key role in failure process acting as destabilization factor. This indicates that macrofailure occurs more readily under fluid pressure, with a behavior that becomes progressively unstable as fluid pressure increases. This may have considerable consequences on our ability to forecast failure when fluid pressure is acting.