Using thermo-mechanical models to bridge scales between experimental rheology and large-scale observational constraints on mantle and plate dynamics

<p>Mantle convection and plate dynamics transfer and deform solid material on scales of hundreds to thousands of km. However, viscoplastic deformation of rocks arises from motions of defects at sub-crystal scale, such as vacancies or dislocations. In this study, results from numerical experiments of dislocation dynamics in olivine for temperatures and stresses relevant for both lithospheric and asthenospheric mantle (800–1700 K and 50–500 MPa; ) are used to derive three sigmoid parameterizations (<em>erf, tanh, algebraic</em>), which express stress evolution as a function of temperature and strain rate. The three parameterizations fit well the results of dislocation dynamics models and may be easily incorporated into geodynamical models. Here, they are used in an upper mantle thermo-mechanical model of subduction, in association with diffusion creep and pseudo-brittle flow laws. Simulations using different dislocation creep parameterizations exhibit distinct dynamics, from unrealistically fast-sinking slabs in the <em>erf</em> case to very slowly-sinking slabs in the <em>algebraic</em> case. These differences could not have been predicted a priori from comparison with experimentally determined mechanical data, since they principally arise from feedbacks between slab sinking velocity, temperature, drag, and buoyancy, which are controlled by the strain rate dependence of the effective asthenosphere viscosity. Comparison of model predictions to geophysical observations and to upper-mantle viscosity inferred from glacial isostatic adjustment shows that the <em>tanh</em> parameterization best fits both crystal-scale and Earth-scale constraints. However, the parameterization of diffusion creep is also important for subduction bulk dynamics since it sets the viscosity of slowly deforming domains in the convecting mantle. Within the range of uncertainties of experimental data and, most importantly, of the actual rheological parameters prevailing in the upper mantle (e.g. grain size, chemistry), viscosity enabling realistic mantle properties and plate dynamics may be reproduced by several combinations of parameterizations for different deformation mechanisms. Deriving mantle rheology cannot therefore rely solely on the extrapolation of semi-empirical flow laws. The present study shows that thermo-mechanical models of plate and mantle dynamics can be used to constrain the effective rheology of Earth's mantle in the presence of multiple deformation mechanisms.</p>

Characterisation of growth plate dynamics in murine models of osteoarthritis

BackgroundThe purpose of this study was to investigate growth plate dynamics in surgical and loading murine models of osteoarthritis, to understand whether abnormalities in these dynamics predict those at risk of osteoarthritis.Methods8-week-old C57BL/6 male mice underwent destabilisation of medial meniscus (DMM) (n = 8) surgery in right knee joints. Contralateral left knee joints had no intervention (controls). In 16-week-old C57BL/6 male mice (n = 6), osteoarthritis was induced using non-invasive mechanical loading of right knee joints with peak force of 11N. Non-loaded left knee joints were internal controls. Chondrocyte transiency in tibial articular cartilage and growth plate was examined by histology and immunohistochemistry. Tibial subchondral bone parameters were measured using microCT and correlated to GP bridging.ResultsHigher expression of chondrocyte hypertrophy markers; Col10a1 and MMP13 were observed in tibial articular cartilage chondrocytes of DMM and loaded mice. In tibial growth plate, Col10a1 and MMP13 expressions were widely dispersed in a significantly enlarged zone of proliferative and hypertrophic chondrocytes. 3-dimensional quantification revealed enriched growth plate bridging and higher bridge densities in medial compared to lateral tibiae of DMM and loaded knee joints of the mice. Growth plate dynamics were associated with increased subchondral bone volume fraction (BV/TV; %) in medial tibiae of DMM and loaded knee joints and epiphyseal trabecular bone volume fraction in medial tibiae of loaded knee joints.ConclusionsThe results confirm associations between aberrant chondrocyte hypertrophy marker expression and osteoarthritis pathology in a surgical and loaded murine model of osteoarthritis. Spatial variations in growth plate bridging formation revealed accelerated cartilage-bone transitions which may contribute to anatomical variation in vulnerability to osteoarthritis development in these models.

Mathematical and numerical modeling of plate dynamics with rotational inertia

We give a presentation of the mathematical and numerical treatment of plate dynamics problems including rotational inertia. The presence of rotational inertia in the equation of motion makes the study of such problems interesting. We employ HCT finite elements for space discretization and the Newmark method for time discretization in FreeFEM++, and test such methods in some significant cases: a circular plate clamped all over its lateral surface, a rectangular plate simply supported all over its lateral surface, and anL-shaped clamped plate.