Stress and Deformation in Living Tissues

Materials respond to forces by deforming, with the relationship between stress (force per unit area) and strain (deflection per unit length) being dependent on the type of material. Linearly elastic materials have a distinctive modulus of elasticity as a measure of their resistance to axial deformation. Generalized Hooke’s Law relates stress and strain for materials acted on by axial forces in three dimensions. Stresses can also be determined for elastic materials in response to forces producing bending, torsion, and direct shear. The resulting equations can then be superposed in cases of combined loadings. Finally, buckling is a phenomenon that occurs when a compressive load acting on a long, slender member exceeds a critical value. For bones and stiff solid implants, these classical elastic relations are used to determine stresses resulting from all combinations of applied forces and can predict when and how fractures and implant failures might occur.