https://www.seas.upenn.edu/%7Edischer/pdfs/Nucleus_PowerLawRheology_BJ.pdf

Power-Law Rheology of Isolated Nuclei with Deformation Mapping of Nuclear Substructures

A mechanical model is presented, in which viscoelastic response is described by the action of time-dependent latch elements. The model represents viscoelastic changes occurring through incremental jumps as opposed to continuous motion. This is supported by the observation that polymeric creep, recovery and stress relaxation can be correlated with stretched exponential functions, i.e. Weibull and Kohlrausch-Williams-Watts, since (i) the former is also used in reliability engineering to represent the failure of discrete elements and (ii) there is evidence of the latter being an approximation to the Eyring potential energy barrier relationship, which describes motion in terms of molecular jumps.

A mechanical model for creep, recovery and stress relaxation in polymeric materials

http://eavr.u-strasbg.fr/~olivier/uploads/biblio/PBMM09.pdf

Kinematic modeling of a 5-DOF parallel mechanism for semi-spherical workspace

Reduced nucleus pulposus glycosaminoglycan content alters intervertebral disc dynamic viscoelastic mechanics.

The theory for the deformations of a spheroidal particle is of great scientific interest in numerous physical and biological problems ranging from fracture analysis of plain solids to the compression of biological cells in an atomic force microscope or during micropipette aspiration Using a formulation in terms of Papkovich–Neuber potentials, we derive the deformations of a prolate, elastic spheroid under known axisymmetric loading The internal stresses to which the object is subjected are deduced from Hooke’s law of elasticity in prolate spheroidal coordinates The generalisation to layered spheroids with viscoelastic properties is also discussed Since for isotropic objects the surface displacements and stresses are directly related by the elastic modulus and Poisson’s ratio alone, the presented, closed-form, analytical solutions may be applied to deduce these important elastic constants from standard stress-deformation experiments We illustrate the versatility of the findings by analysing the surface displacements and stress states of spheroids with small and large aspect ratios in the presence of both normal and shear surface tractions Of particular interest in this study is the influence of Poisson’s ratio on the deformation of a near-spherical particle, for instance a soft cancer cell, which is subjected to surface stresses of the kind that can be found in optical traps, like the optical stretcher

Autar K. Kaw

Papers

Crc mechanical engineering series

Mechanical Engineering Series