Many musculoskeletal soft tissues, such as tendons, ligaments, meniscus and cartilage are inhomogeneous. Hence, during mechanical loading it is likely that a nonuniform strain pattern occurs within the tissue. These nonuniform strain patterns may assist in successful load transmission and minimize rupture of the tissue during physiological loading. Determination of local material properties will likely be important for successful function and design of tissue engineered replacements. In the late 1980’s uniaxial tensile tests were conducted using a video camera in conjunction with surface markers to document local strain distributions on the surface of ligaments. Photoelasticity has also been used to document local strain patterns.

In between stress and strain, which one is the more fundamental physical quantity? Or is it the case that each is defined independent of the other and so nothing can be said about their order? Is this the case?

To begin with these questions, consider the fact that first we have to apply a force to an object and it is only then that the object is observed to have been deformed or strained. Accordingly, one may say that forces produce strains, and therefore, it seems that stress has to be more fundamental. If so, how come stress cannot be measured directly? This is the paradox I would like to address here.

Of course, to begin with, my position is that you can never directly measure stress.

We published this paper in APL on a study of the deformation near interfaces. It provides insight in the strain localization at the interface and its influence on the deformation in bulk metals. 

Abstract An optical full-field strain mapping technique has been used to provide direct evidence for the existence of a highly localized strain at the interface of stacked Nb/Nb bilayers during the compression tests loaded normal to the interface. No such strain localization is found in the bulk Nb away from the interface. The strain localization at the interfaces is due to a high void fraction resulting from the rough surfaces of Nb in contact, which prevents the extension of deformation bands in bulk Nb crossing the interface, while no distinguished feature from the stress-strain curve is detected.

A (001) surface of silicon consists of terraces of two variants, which have an identical atomic structure, except for a 90° rotation. We formulate a model to evolve the terraces under the combined action of electric current and applied strain. The electric current motivates adatoms to diffuse by a wind force, while the applied strain motivates adatoms to diffuse by changing the concentration of adatoms in equilibrium with each step. To promote one variant of terraces over the other, the wind force acts on the anisotropy in diffusivity, and the applied strain acts on the anisotropy in surface stress. Our model reproduces experimental observations of stationary states, in which the relative width of the two variants becomes independent of time. Our model also predicts a new instability, in which a small change in experimental variables (e.g., the applied strain and the electric current) may cause a large change in the relative width of the two variants.

We propose a model of persistent step flow, emphasizing dominant kinetic processes and strain effects. Within this model, we construct a morphological phase diagram, delineating a regime of step flow from regimes of step bunching and island formation. In particular, we predict the existence of concurrent step bunching and island formation, a new growth mode that competes with step flow for phase space, and show that the deposition flux and temperature must be chosen within a window in order to achieve persistent step flow. The model rationalizes the diverse growth modes observed in pulsed laser deposition of SrRuO3 on SrTiO3

 Physical Review Letters 95, 095501 (2005)

Augustin Louis Cauchy ( 21 August 1789 - 23 May 1857) was a French mathematician and mechanician. In mechanics, he in 1822 formalized the stress concept in the context of three-dimensional thoery, showed its properties as consisting of a 3 by 3 symmetric arrays of numbers that transform as a tensor, derived the equations of motion for a continuum in terms of the components of stress, and gave the specific development of the theory of linear elasticity for isotropic solids. As part of his work, Cauchy also introduced the equations which express the six components of strain, three extensinal and three shear, in terms of derivatives of displacements for the case when all those derivatives are much smaller than unity; similar expressions had been given earlier by Euler in expressing rates of straining in terms of the derivatives of the velocity field in a fluid. (cited from Mechanics of Solids by J.R. Rice) Read more...