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Indentation into a plastic fluid layer.

ABSTRACT: We study the indentation of a rigid object into a layer of a cohesive or non-cohesive plastic material. Existing approaches to this problem using slip-line theory assume that the penetration depth is relatively small, employing perturbation theory about a flat surface. Here, we use two alternative approaches to account for large penetration depths, and for the consequent spreading and uplift of the surrounding material. For a viscoplastic fluid, which reduces to an ideal plastic under the limit of vanishing viscosity, we adopt a viscoplastic version of lubrication theory. For a Mohr-Coulomb material, we adopt an extension of slip-line theory between two parallel plates to account for arbitrary indenter shapes. We compare the theoretical predictions of penetration and spreading with experiments in which a flat plate, circular cylinder or sphere are indented into layers of Carbopol or glass spheres with successively higher loads. We find reasonable agreement between theory and experiment, though with some discrepancies that are discussed. There is a clear layer-depth dependence of the indentation and uplift for the viscoplastic material. For a cylinder indented into a Mohr-Coulomb material, there is a much weaker dependence on layer depth.

SUBMITTER: Ball TV

PROVIDER: S-EPMC6501664 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature

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Indentation into a plastic fluid layer.

Ball Thomasina V TV Balmforth Neil J NJ Hewitt Ian J IJ

Proceedings. Mathematical, physical, and engineering sciences 20190410 2224

We study the indentation of a rigid object into a layer of a cohesive or non-cohesive plastic material. Existing approaches to this problem using slip-line theory assume that the penetration depth is relatively small, employing perturbation theory about a flat surface. Here, we use two alternative approaches to account for large penetration depths, and for the consequent spreading and uplift of the surrounding material. For a viscoplastic fluid, which reduces to an ideal plastic under the limit ...[more]

PMID: 31105453

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Project description:Blood flow produces mechanical frictional forces, parallel to the blood flow exerted on the endothelial wall of the vessel, the so-called wall shear stress (WSS). WSS sensing is associated with several vascular pathologies, but it is first a physiological phenomenon. Endothelial cell sensitivity to WSS is involved in several developmental and physiological vascular processes such as angiogenesis and vascular morphogenesis, vascular remodeling, and vascular tone. Local conditions of blood flow determine the characteristics of WSS, i.e., intensity, direction, pulsatility, sensed by the endothelial cells that, through their effect of the vascular network, impact WSS. All these processes generate a local-global retroactive loop that determines the ability of the vascular system to ensure the perfusion of the tissues. In order to account for the physiological role of WSS, the so-called shear stress set point theory has been proposed, according to which WSS sensing acts locally on vessel remodeling so that WSS is maintained close to a set point value, with local and distant effects of vascular blood flow. The aim of this article is (1) to review the existing literature on WSS sensing involvement on the behavior of endothelial cells and its short-term (vasoreactivity) and long-term (vascular morphogenesis and remodeling) effects on vascular functioning in physiological condition; (2) to present the various hypotheses about WSS sensors and analyze the conceptual background of these representations, in particular the concept of tensional prestress or biotensegrity; and (3) to analyze the relevance, explanatory value, and limitations of the WSS set point theory, that should be viewed as dynamical, and not algorithmic, processes, acting in a self-organized way. We conclude that this dynamic set point theory and the biotensegrity concept provide a relevant explanatory framework to analyze the physiological mechanisms of WSS sensing and their possible shift toward pathological situations.

Project description:ObjectivesBone material properties are a major determinant of bone health in older age, both in terms of fracture risk and implant fixation, in orthopaedics and dentistry. Bone is an anisotropic and hierarchical material so its measured material properties depend upon the scale of metric used. The scale used should reflect the clinical problem, whether it is fracture risk, a whole bone problem, or implant stability, at the millimetre-scale. Indentation, an engineering technique involving pressing a hard-tipped material into another material with a known force, may be able to assess bone stiffness at the millimetre-scale (the apparent elastic modulus). We aimed to investigate whether spherical-tip indentation could reliably measure the apparent elastic modulus of human cortical bone.Materials and methodsCortical bone samples were retrieved from the femoral necks of nineteen patients undergoing total hip replacement surgery (10 females, 9 males, mean age: 69 years). The samples underwent indentation using a 1.5 mm diameter, ruby, spherical indenter tip, with sixty indentations per patient sample, across six locations on the bone surfaces, with ten repeated indentations at each of the six locations. The samples then underwent mechanical compression testing. The repeatability of indentation measurements of elastic modulus was assessed using the co-efficient of repeatability and the correlation between the bone elastic modulus measured by indentation and compression testing was analysed by least-squares regression.ResultsIn total, 1140 indentations in total were performed. Indentation was found to be repeatable for indentations performed at the same locations on the bone samples with a mean co-efficient of repeatability of 0.4 GigaPascals (GPa), confidence interval (C.I): 0.33-0.42 GPa. There was variation in the indentation modulus results between different locations on the bone samples (mean co-efficient of repeatability: 3.1 GPa, C.I: 2.2-3.90 GPa). No clear correlation was observed between indentation and compression values of bone elastic modulus (r = 0.33, p = 0.17). The mean apparent elastic modulus obtained by spherical indentation was 9.9 GPa, the standard deviation for each indent cycle was 0.11 GPa, and the standard deviation between locations on the same sample was 1.01 GPa. The mean compression apparent elastic modulus was 4.42 GPa, standard deviation 1.02 GPa.DiscussionSpherical-tip indentation was found to be a repeatable test for measuring the elastic modulus of human cortical bone, demonstrated by a low co-efficient of repeatability in this study. It could not, however, reliably predict cortical bone elastic modulus determined by platens compression testing in this study. This may be due to indentation only probing mechanical properties at the micro-scale while platens compression testing assesses millimetre length-scale properties. Improvements to the testing technique, including the use of a larger diameter spherical indenter tip, may improve the measurement of bone stiffness at the millimetre scale and should be investigated further.

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Indentation into a plastic fluid layer.

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Indentation into a plastic fluid layer.

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