Non-Linear Mechanical Behavior of Visco-Elastic Biological Structures – Measurements and Models

Mechanical properties of biological structures affect functional ability of organism. Current knowledge is prevailingly concentrated on static characteristics. The present work analyzed dynamic mechanical responses of various biological materials. Following biological structures were measured: samples of aorta walls of human origin and from model organisms, human body surface, and samples of bones of various types and origin. Linear approximation leads in case of aortas and bones to simple Voight's model. Modules of elasticity (in tensile loading) of aortas were from 102 kPa to 103 kPa. Module of elasticity of bones were from 106 Pa to 1010 Pa. Viscous coefficients of aortas were from 102 Pa.s to 103 Pa.s. Viscous coefficients of bones were from 100 Pa.s to 102 Pa.s. Nonlinearities: We found that following types of nonlinearities are significant: strain-stress relationship, time-dependent changes in elastic as well as viscose bodies. Strain and stress is well approximated by quadratic function σ = a ε2 + b ε + c with parameters a = 1833, b = 135, c = 20.0 (porcine aorta). Time-dependence in elastic coefficient: At the beginning of responses the elastic coefficient was of 42% lower then at 0.02 s of duration of the response (porcine aortas). Analogical results follow also from experiments on other structures (skin, bones)