Linear Algebra Provides a Basis for Elasticity without Stress or Strain

Linear algebra provides insights into the description of elasticity without stress or strain. Classical descriptions of elasticity usually begin with defining stress and strain and the constitutive equations of the material that relate these to each other. Elasticity without stress or strain begins with the positions of the points and the energy of deformation. The energy of deformation as a function of the positions of the points within the material provides the material properties for the model. A discrete or continuous model of the deformation can be constructed by minimizing the total energy of deformation. As presented, this approach is limited to hyper-elastic materials, but is appropriate for infinitesimal and finite deformations, isotropic and anisotropic materials, as well as quasi-static and dynamic responses.