A study of the rheological properties of visco-elastic materials using fractional calculus

Explicit scheme for solving variable-order time-fractional initial boundary value problems

The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme's stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made.

Enhanced cluster order-disorder transition-induced dilatancy in silane-functionalized nanosilica colloids

Herein, we report a novel nanosilica-based shear-thickening fluid, whose shear-thickening performance has been largely augmented by surface functionalizing silica employing silane chains. The functionalized shear-thickening colloids were transparent; this suggested that they have promise for application. An enhancement in viscosity was observed by over an order of magnitude by the usage of functionalized particles, which could be explained on the basis of enhanced hydroclustering and an order-to-disorder transition of the particles due to physical bonding of the silane with the base polymer. It was also observed that the shear-thickening behavior was grossly modified due to the presence of the functionalized nanoparticles. Oscillatory analysis showed that the functionalized colloids exhibited an improved dynamic response, with enhanced elastic behavior under variant strain and frequency conditions. Additionally, impact resistance tests revealed that the thickening of the viscosity upon impact was augmented by over an order of magnitude; this established these functionalized colloids as excellent candidates for liquid armors. The viscoelastic behavior was modeled based on the Cox-Merz formalism. Additionally, three-element viscoelastic modeling was performed, and it was observed that while the silica-based colloids conformed to the predominantly viscous model, the functionalized system transited to a predominantly elastic model. The present article can have important implications for the design and engineering of shear-thickening fluids employing nanomaterials.

Formation of desiccation crack patterns in electric fields: a review

Desiccation crack formation is an important and interesting part of the broad area of fracture mechanics. Generation of cracks due to drying depends on ambient conditions, which may include externally applied fields. In this review, we discuss the effect of both direct and alternating electrical fields on desiccation crack formation. After a brief introduction to materials which crack on drying, e.g. colloids, clay and ceramics we discuss how they respond to an electric field. Following that, we present an account of experiments and modelling studies performed on granular pastes or clays drying while exposed to an electric field. Specific patterns formed under different geometries, strengths and frequencies of the electric field are described and explained. The review includes work on cracks formed in clay droplets, where a memory effect has been observed and analysed using a generalized calculus formalism.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

The Role of Oral Cavity Biofilm on Metallic Biomaterial Surface Destruction-Corrosion and Friction Aspects

Metallic biomaterials in the oral cavity are exposed to many factors such as saliva, bacterial microflora, food, temperature fluctuations, and mechanical forces. Extreme conditions present in the oral cavity affect biomaterial exploitation and significantly reduce its biofunctionality, limiting the time of exploitation stability. We mainly refer to friction, corrosion, and biocorrosion processes. Saliva plays an important role and is responsible for lubrication and biofilm formation as a transporter of nutrients for microorganisms. The presence of metallic elements in the oral cavity may lead to the formation of electro-galvanic cells and, as a result, may induce corrosion. Transitional microorganisms such as sulfate-reducing bacteria may also be present among the metabolic microflora in the oral cavity, which can induce biological corrosion. Microorganisms that form a biofilm locally change the conditions on the surface of biomaterials and contribute to the intensification of the biocorrosion processes. These processes may enhance allergy to metals, inflammation, or cancer development. On the other hand, the presence of saliva and biofilm may significantly reduce friction and wear on enamel as well as on biomaterials. This work summarizes data on the influence of saliva and oral biofilms on the destruction of metallic biomaterials.