The Stefan problem in a thermomechanical context with fracture and fluid flow

The classical Stefan problem, concerning mere heat-transfer during solid-liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba-Jaumann corotational time derivatives, linearized by exploiting the additive Green-Naghdi’s decomposition in (objective) rates. In particular, the liquid phase is a viscoelastic fluid while creep and rupture of the solid phase is considered in the Jeffreys viscoelastic rheology exploiting the phase-field model, exploiting a concept of slightly (so-called “semi”) compressible materials. The $L^1$-theory for the heat equation is adopted for the Stefan problem relaxed by allowing for kinetic superheating/supercooling effects during the solid-liquid phase transition. A rigorous proof of existence of week solutions is provided for an incomplete melting, exploiting a time-discretisation approximation.

Junctional and cytoplasmic contributions in wound healing

Wound healing is characterized by the re-epitheliation of a tissue through the activation of contractile forces concentrated mainly at the wound edge. While the formation of an actin purse string has been identified as one of the main mechanisms, far less is known about the effects of the viscoelastic properties of the surrounding cells, and the different contribution of the junctional and cytoplasmic contractilities. In this paper, we simulate the wound healing process, resorting to a hybrid vertex model that includes cell boundary and cytoplasmic contractilities explicitly, together with a differentiated viscoelastic rheology based on an adaptive rest-length. From experimental measurements of the recoil and closure phases of wounds in the Drosophila wing disc epithelium, we fit tissue viscoelastic properties. We then analyse in terms of closure rate and energy requirements the contributions of junctional and cytoplasmic contractilities. Our results suggest that reduction of junctional stiffness rather than cytoplasmic stiffness has a more pronounced effect on shortening closure times, and that intercalation rate has a minor effect on the stored energy, but contributes significantly to shortening the healing duration, mostly in the later stages.

Going from stable creep to aseismic slow slip events in the ductile realm

<p>The accommodation of motion on faults spans a large spectrum of slip modes, ranging from stable creep to earthquakes. While seismic slip modes certainly have the largest impact on the surface due to the induced ground shaking, it has been recognized that slow aseismic slip modes relax most of the accumulated stresses on a fault. It has also been suggested that aseismic slip controls seismic events, thus making this kind of slip mode key for earthquake prediction.</p><p>Despite the importance of aseismic slow slip, its underlying physical mechanisms are still unclear. Commonly, slow slip events are modeled in terms of frictional failure, employing a rate-and-state model of fault friction, often also invoking fluids that alter frictional properties on the fault. However, at larger depths, frictional processes become increasingly difficult to activate due to the increase in ambient pressure and ductile processes are more likely to dominate deformation.</p><p>Here we therefore investigate deep aseismic slip processes governed by ductile deformation mechanisms using 2D numerical models, where we employ a composite viscoelastic rheology combined with grain size reduction and shear heating as weakening processes. We show that the collaborative action of these two weakening mechanisms is sufficient to create the entire spectrum of aseismic slip, ranging from stable creep to long-term slow slip events. The results show that ductile deformation does not necessarily result in stable slip and induces slip modes with considerably larger velocities than the far-field plate velocities. Moreover, the propagation of ductile ruptures induces large stresses in front of the rupture tip which may also trigger short-term seismic events.</p>

Tidal heating and the habitability of the TRAPPIST-1 exoplanets

Context. New estimates of the masses and radii of the seven planets orbiting the ultracool M-dwarf TRAPPIST-1 star permit improved modelling of their compositions, heating by tidal dissipation, and removal of tidal heat by solid-state convection. Aims. Here we compute the heat flux due to insolation and tidal heating for the inner four planets. Methods. We apply a Maxwell viscoelastic rheology to compute the tidal response of the planets using the volume-weighted average of the viscosities and rigidities of the metal, rock, high-pressure ice, and liquid water/ice I layers. Results. We show that TRAPPIST-1d and e can avoid entering a runaway greenhouse state. Planet e is the most likely to support a habitable environment, with Earth-like surface temperatures and possibly liquid water oceans. Planet d also avoids a runaway greenhouse, if its surface reflectance is at least as high as that of the Earth. Planets b and c, closer to the star, have heat fluxes high enough to trigger a runaway greenhouse and to support volcanism on the surfaces of their rock layers, rendering them too warm for life. Planets f, g, and h are too far from the star to experience significant tidal heating, and likely have solid ice surfaces with possible subsurface liquid water oceans.