Indentation of a spherical cavity in an elastic body by a rigid spherical inclusion: influence of non-classical interface conditions

Selvadurai, A. P. S.

doi:10.1007/s00161-015-0481-y

Cited by 14 publications

(16 citation statements)

References 102 publications

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“…Moreover, higher values of Va yield larger stresses at the same strain, consistent with the behavior of poroelastic materials. In addition, according to the analytical solution of the inclusion problem of a spherical rigid inclusion within an elastic medium (27), the Young's modulus of the medium E can be obtained as E…”

Section: Resultsmentioning

confidence: 99%

Size- and speed-dependent mechanical behavior in living mammalian cytoplasm

Jafari

Han

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

104

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Active transport in the cytoplasm plays critical roles in living cell physiology. However, the mechanical resistance that intracellular compartments experience, which is governed by the cytoplasmic material property, remains elusive, especially its dependence on size and speed. Here we use optical tweezers to drag a bead in the cytoplasm and directly probe the mechanical resistance with varying size and speed We introduce a method, combining the direct measurement and a simple scaling analysis, to reveal different origins of the size- and speed-dependent resistance in living mammalian cytoplasm. We show that the cytoplasm exhibits size-independent viscoelasticity as long as the effective strain rate / is maintained in a relatively low range (0.1 s < / < 2 s) and exhibits size-dependent poroelasticity at a high effective strain rate regime (5 s < / < 80 s). Moreover, the cytoplasmic modulus is found to be positively correlated with only / in the viscoelastic regime but also increases with the bead size at a constant / in the poroelastic regime. Based on our measurements, we obtain a full-scale state diagram of the living mammalian cytoplasm, which shows that the cytoplasm changes from a viscous fluid to an elastic solid, as well as from compressible material to incompressible material, with increases in the values of two dimensionless parameters, respectively. This state diagram is useful to understand the underlying mechanical nature of the cytoplasm in a variety of cellular processes over a broad range of speed and size scales.

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Section: Resultsmentioning

confidence: 99%

Size- and speed-dependent mechanical behavior in living mammalian cytoplasm

Jafari

Han

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

104

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“…Note that for techniques based on spherical harmonics, the shear modulus G is typically more convenient to use than Young's modulus E = 2G(1 + ν), where ν is Poisson's ratio. This has been the case in nearly all previous theoretical literature on related problems [3,12,14,16], and in this paper, we also use shear modulus to describe the problem and express the solution.…”

Section: Background and Problem Statementmentioning

confidence: 97%

“…Subsequently, the problem for some specific cases was solved. For example, Selvadurai developed the solution for a rigid sphere in an incompressible matrix [12], Zureick presented an analogous solution for the case of a transversely isotropic matrix [13], and Selvadurai considered the case of a frictionless "bilateral" interface between the inclusion and the matrix [14]. Following Kupradze [2] and Lurie and Belyaev [3], the rigid inclusion translation problem considered in the present study is referred to as Robin's problem.…”

Section: Background and Problem Statementmentioning

confidence: 99%

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Translation of a Coated Rigid Spherical Inclusion in an Elastic Matrix: Exact Solution, and Implications for Mechanobiology

Chen

Liu

et al. 2019

Journal of Applied Mechanics

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The displacement of relatively rigid beads within a relatively compliant, elastic matrix can be used to measure the mechanical properties of the matrix. For example, in mechanobiological studies, magnetic or reflective beads can be displaced with a known external force to estimate the matrix modulus. Although such beads are generally rigid compared to the matrix, the material surrounding the beads typically differs from the matrix in one or two ways. The first case, as is common in mechanobiological experimentation, is the situation in which the bead must be coated with materials such as protein ligands that enable adhesion to the matrix. These layers typically differ in stiffness relative to the matrix material. The second case, common for uncoated beads, is the situation in which the beads disrupt the structure of the hydrogel or polymer, leading to a region of enhanced or reduced stiffness in the neighborhood of the bead. To address both cases, we developed the first analytical solution of the problem of translation of a coated, rigid spherical inclusion displaced within an isotropic elastic matrix by a remotely applied force. The solution is applicable to cases of arbitrary coating stiffness and size of the coating. We conclude by discussing applications of the solution to mechanobiology.

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“…Although the preceding references also contain citations of frictional contact problems, the articles by Spence 31 , 32 , Paggi et al . 22 and Selvadurai 33 can be consulted to determine the various approaches to the formulation and solution of frictional contact problems.…”

Section: Introductionmentioning

confidence: 99%

Indentation of a surface-stiffened elastic substrate

Selvadurai

2018

Sci Rep

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The paper deals with the problem of the indentation of a substrate in the form of an isotropic elastic halfspace that is reinforced at the surface by a bonded layer, which has flexibility characteristic of a Poisson-Kirchhoff-Germain thin plate. The presence of the reinforcing layer changes the characteristics of the indentation problem, in that the techniques that are applicable for the solution of the direct indentation of the halfspace cannot be applied to develop a load-displacement relationship for the indenter. The integro-differential equation governing the indentation of the surface reinforced halfspace is solved using a discretization approach and numerical results are presented to demonstrate the influence of the stiffness of the reinforcing layer on the Boussinesq indention problem.

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Indentation of a spherical cavity in an elastic body by a rigid spherical inclusion: influence of non-classical interface conditions

Cited by 14 publications

References 102 publications

Size- and speed-dependent mechanical behavior in living mammalian cytoplasm

Size- and speed-dependent mechanical behavior in living mammalian cytoplasm

Translation of a Coated Rigid Spherical Inclusion in an Elastic Matrix: Exact Solution, and Implications for Mechanobiology

Indentation of a surface-stiffened elastic substrate

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