Solid Mechanics

Abstract

This chapter provides an overview of solid mechanics with applications in biomechanics. It begins wih a coverage of tensors, including the tensor transformation law and tensor invariants, before proceeding to the basic mechanical concepts of stress and strain. Stress and strain are then related via material constitutive laws, the most basic being that of linear elasticity. The concepts of hydrostatic stresses and strains are also introduced, along with the notion of von Mises stress as a representative scalar stress indicator. Other material laws relevant to biological tissues are presented, including linear viscoelasticity and hyperelasticity, as well as anisotropic hyperelastic material laws. Detailed examples of models solved in COMSOL include a strap tension testing device for a respirator mask, as well simulations of simple shear experiments in myocardial tissue. The chapter ends with a set of theoretical and computational COMSOL problems, with fully-worked answers provided in the solution section of the text.