  We derive expressions for determination of the stress and the elastic
constants in systems composed of particles interacting via non-central two-body
potentials as thermal averages of products of first and second partial
derivatives of the interparticle potentials and components of the interparticle
separation vectors. These results are adapted to hard potentials, when the
stress and the elastic constants are expressed as thermal averages of the
components of normals to contact surfaces between the particles and components
of vectors separating the centers of the particles. The averages require the
knowledge of simultaneous contact probabilities of two pairs of particles. We
apply the expressions to particles for which a contact function can be defined,
and demonstrate the feasibility of the method by computing the stress and the
elastic constants of a two-dimensional system of hard ellipses using Monte
Carlo simulations.
