Fiber bundle models for stress release and energy bursts during granular shearing

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

Snow is a heterogeneous material with strain- and/or load-rate-dependent strength. In particular, a transition from ductile-to-brittle failure behavior with increasing load rate is observed. The rate-dependent behavior can partly be explained with the existence of a unique healing mechanism in snow that stems from its high homologous temperature (temperature close to melting point). As soon as broken elements in the ice matrix get in contact, they start sintering and the structure may regain strength. Moreover, the ice matrix is subjected to viscous deformation, inducing a relaxation of local load concentrations and, therefore, further counteracting the damage process. Ideal tools for studying the failure process of heterogeneous materials are the fiber-bundle models (FBMs), which allow investigating the effects of basic microstructural characteristics on the general macroscopic failure behavior. We present an FBM with two concurrent time-dependent healing mechanisms: sintering of broken fibers and relaxation of load inhomogeneities. Sintering compensates damage by creating additional intact, load-supporting fibers which lead to an increase of the bundle strength. However, the character of the failure is not changed by sintering alone. With combined sintering and load relaxation, load is distributed from old stronger fibers to new fibers that carry fewer load. So as we additionally incorporated load redistribution to the FBM, the failure occurred suddenly without decrease of the order parameter-describing the amount of damage in the bundle-and without divergence of the fiber failure rate. Moreover, the b value, i.e., the power-law exponent of frequency-magnitude statistics of fibers breaking in load redistribution steps, at failure converged to b≈2, a value higher than that of a classical FBM without healing (b=3/2). These results indicate that healing, as the combined effect of sintering and load relaxation, changes the type of the phase transition at failure. This change of the phase transition is important for quantifying or predicting the failure (e.g., by monitoring acoustic emissions) of snow or other materials for which healing plays an important role.

Biomechanics of plant anchorage at early development stage

We propose a minimal model for the response of seedlings to pullout constraints. Central to our approach is the idea of capturing not only average mechanical properties but also the stochastic component of the uprooting process. Our model accounts on one hand for the tensile elastic response of root fibres and on the other hand for the friction between root fibres and the soil matrix. We present for validation a dataset of 98 uprooting experiments using Avena sativa L. seedlings (common oat), growing in non-cohesive sediment under controlled conditions. We show that even if the architecture of the roots used in the experiments and, as a consequence, the components of our model are very basic, the uprooting curve (stress vs. strain) presents a complex response, with sudden jumps followed by partial elastic recovery. Depending on the maturity of the root system, we identify a crossover in the response of the seedling to the constraint. While for younger seedlings the anchorage rapidly fails after the peak force has been reached, more mature root systems recover from partial failures. Finally, we discuss the importance of the characteristics of the uprooting curve (maximal uprooting force and total uprooting work) regarding the ability of seedlings to withstand environmental constraints in terms of duration or intensity.