Decay of Local Loads in Biological Materials

Saint-Venant Principle (SVP) is widely regarded as a sine qua non in applied structural engineering. Indeed, it is nearly impossible to envisage present day stress analysis and structural engineering, over several fields, without considering (even tacitly) the validity of that principle. However, while much work is available on the validity of SVP for standard materials, only few studies have examined its validity for biological tissues. This is surprising since there are numerous situations, like presence of defects in arteries walls, onset of aneurysm, stent insertion, skin injuries, hip implant and bio-membrane perforation, which impose local loads on bio-tissues. The present research examines decay of local perturbations, applied to bio-tissues, particularly in presence of tissue/rigid interfaces, encountered with stents, and orthopaedic or orthodontic implants. We seek to determine constitutive sensitivities of axial decay rate, with emphasis on the coupled influence of material orthotropy with interface rigidity. Following the classical (1942) Fadle-Papkovich analysis of exponential decay of end loads, applied to plane elastic strips with free boundaries, we have studied the influence of a single rigid (clamped) boundary on axial decay rate of end loads applied to bio-tissues. Unlike isotropic solids, decay rates in biological materials display considerably sensitivity induced by orthotropy, compressibility and presence of rigid boundary interface. Hence, for biological tissues, high rates of decay with distance from a locally perturbed zone (as implied by the classical SVP) cannot be assumed a-priory. The research will evaluate implications of that observation to tissue engineering, stent design, medical procedures, and test protocols.

The work is towards a PhD degree under the supervision of Prof David Durban & Dr Baruch Karp, Aerospace Engineering Department, Technion