Strain Mapping in Materials

When inspecting materials under stress, accurate measurements of surface strain are important for predicting the probable locations of fractures and failures. Our work provides new computational techniques for mesomechanics, which is concerned with the deformation of solids at a scale lying between the microscopic and macroscopic levels. Of particular interest is the inspection of aluminium-based alloys and composite materials used in the aerospace industry.

We have developed a computer-based optical technique (see Optical Flow, below) for calculating the surface strain of an untreated sample of material from two or more images taken during the application of force from a test rig. Here is a pair of images of an aluminium-based alloy:
Each image shows a region about 2mm across. The first step is to estimate the optical flow field for the pair of images. The flow field shows how the material deforms over an interval of time. At each point of the image sequence, a flow vector is estimated by marginalising a displacement probability over a disc-shaped region centred on the point. The displacement with the maximum likelihood is chosen as the flow vector estimate. Unlike previous methods based on differentiation or cross-correlation, our probability-based approach gives accurate results near shear boundaries.

The strain tensor is estimated by solving for six parameters (the tensor and an (x,y) origin) given the observed flow field using Gauss-Jordan elimination. The strain tensor can be used to synthesise an ideal flow model that is not affected by missing and noisy data.
Collaborators have included: Stuart Hill, Katherine Chivers, Shivani Agarwal, Joao Quinta da Fonseca and Phil Withers.

Strain Mapping in Human Tissues

I have worked with Gerard Lambe of Liverpool University to develop new methods for the quanitification of strain in certain tendons of the hand. Tendon boundaries are obtained from MRI images of the fingers under load. We have developed algorithms to construct a strain map, that is, for each point on an image of the tendon, estimate the amount of deformation at that point due to the movement of the tissue from the unloaded state to the loaded state. Most methods for estimating strain in materials measure an optical displacement field using the brightness variation of the material. However, the MRI imagery shows the tendon as an area of fairly uniform brightness, so there is no significant texture on which conventional algorithms can get reliable purchase. Instead, the deformation of the boundary can be used as a source of information about internal strain.

Collaborators in addition to Gerard Lambe were Glyn Coutts (North Western Medical Physics, Christie Hospital, Manchester) and Paul McArthur (Royal Liverpool Children's Hospital, Dept of Congenital Hand Surgery). The project was funded by a grant from the Royal College of Surgeons and the Hand Society.