Some models of crack growth in brittle materials

This work is devoted to the study of models of fractures growth in brittle elastic materials; it collects the results obtained during my Ph.D., that are contained in [77, 76, 78]. We consider quasi-static rate-independent models, as well as rate-dependent ones and the case in which the first ones are limits of the second ones when certain physical parameters vanish. The term quasistatic means that, at each instant, the system is assumed to be in equilibrium with respect to its time-dependent data; this setting is typical of systems whose internal time scale is much smaller than that of the loadings. By rate-independent system we mean that, if the time-dependent data are rescaled by a strictly monotone increasing function, then the system reacts by rescaling the solutions in the same manner

Discrete Geometry (hybrid meeting)

A number of important recent developments in various branches of discrete geometry were presented at the workshop, which took place in hybrid format due to a pandemic situation. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as topology, combinatorics, algebraic geometry or functional analysis. The open questions abound and many of the results presented were obtained by young researchers, confirming the great vitality of discrete geometry

Biocomposites including nano-scale dispersed phase and polymers from renewable resources

Poly(lactic acid) (PLA) was physically modified by filling with an inorganic additive, natural fibres as well as with a tributyl citrate (TBC). PLA composites were prepared with a film stacking method and analysed by scanning electron microscopy (SEM), thermogravimetry (TGA), thermomechanometry and differential scanning calorimetry (DSC) to investigate the physical and mechanical properties of the hybrid composites. PLA composites reinforced with hemp fibres in combination with nanosilica are thermally stable as the maximum rate of weight loss of the composites shifted to the highest temperature observed in TGA results. Dynamic mechanical properties of PLA composites showed that the reinforcement of hemp fibre and nanosilica strongly affected the mechanical properties of the composites. The highest storage modulus improvements were reached by addition of hemp fibre and nanosilica without plasticiser. An increase in storage modulus monitored in the temperature region from 70 to 100 °C reflected an increase in structural stiffness due to recrystallisation activity in the composites. The addition of TBC reduced the modulus though initiated the crystallisation on cooling, enhanced the nucleating ability of the fillers and chain mobility in PLA composites. The melting and crystallisation behaviour of PLA composites was explored with non isothermal DSC at various scanning rates. The characteristics of the crystallisation and melting behaviour of PLA composites were explained by the slow rate of crystallisation and recrystallisation, which is in agreement with DMA results. Non-isothermal crystallization kinetics shows that the crystallization rate of PLA composites was higher than of neat PLA and further increased with presence of TBC, indicating that the addition of plasticiser and nucleating agents enhanced the transportation ability of polymer chains. SEM revealed a good distribution of nanosilica for composites with and without TBC. A great transfer of stress between hemp fibres and PLA nanosilica matrix resulted in improved of physical and mechanical properties as evidenced by DMA and DSC results

Articles publicats per investigadors de l'ETSEIB. Producció científica a Futur 2015

Postprint (author's final draft

Articles publicats per investigadors de l'ETSEIB. Producció científica a Futur 2015

Postprint (author's final draft

Continuous precipitation of yttrium hydroxycarbonate spheres of narrow size distribution

Submicron spherical particles of the yttria precursor Y(OH)CO[subscript]3·H[subscript]2O were continuously precipitated in three types of reactors: (1) mixed-suspension mixed-product removal (MSMPR), (2) semi-batch, and (3) packed bed. The homogeneous precipitation occurred as a result of the thermal decomposition of urea in an aqueous yttrium nitrate solution;A wide variety of particle size distributions were produced from these reactors. Mathematical models, which assumed that particle growth was by a diffusion mechanism, successfully allowed the size and shape of the particle size distributions to be predicted and controlled. It was shown that the concentration of the rate-limiting diffusing species could be calculated from a simple analysis of the particle size distribution from the MSMPR reactor. From such an analysis, it appeared that carbonate was the rate-limiting diffusant

LINEAR AND NONLINEAR MODELING OF ASPERITY SCALE FRICTIONAL MELTING IN BRITTLE FAULT ZONES

Study of pseudotachylytes (PT) (frictional melts) can provide information on the physical and chemical conditions at the earthquake source. This study examines the influence of asperityscale fault dynamics on asperity temperature distribution, and therefore, the potential for frictional melting to occur. Frictional melting occurs adiabatically, and is initiated between opposing asperity tips during fault slip. Our model considers 2-D heat conduction in elastic, isotropic, hemispherical asperities, with temperature dependent thermal properties. The only heat source is a point heat flux pulse at the asperity tip. The non-linear problem was solved using the -form of Newton-Kantorovich procedure coupled with the -form of Douglas-Gunn two level finite difference scheme, while the linear problem required only the latter method. Results for quartz and feldspar indicate that peak temperatures can reach melting point values for typical asperity sizes (1-100 mm), provided that contact (frictional) shear stress is sufficiently high. For any asperity size, the temperature distribution peak becomes insignificant by the time it reaches the asperity center. These results imply that much of asperity scale melting is highly localized, which may explain why most PT veins in the field are usually very thin. However, in some cases, successive asperity encounters may generate temperature increases large enough to trigger the massive melting inferred from typical PT exposures. Significant differences were observed between the results of the linear and nonlinear models