  A homogeneous elastic solid, bounded by a flat surface in its unstressed
configuration, undergoes a finite strain when in frictionless contact against a
rigid and rectilinear constraint, ending with a rounded or sharp corner, in a
two-dimensional formulation. With a strong analogy to fracture mechanics, it is
shown that (i.) a path-independent $J$--integral can be defined for
frictionless contact problems, (ii.) which is equal to the energy release rate
$G$ associated with an infinitesimal growth in the size of the frictionless
constraint, and thus gives the value of the configurational force component
along the sliding direction. Furthermore, it is found that (iii.) such a
configurational sliding force is the Newtonian force component exerted by the
elastic solid on the constraint at the frictionless contact. Assuming the
kinematics of an Euler-Bernoulli rod for an elastic body of rectangular shape,
the results (i.)--(iii.) lead to a new interpretation from a nonlinear solid
mechanics perspective of the configurational forces recently disclosed for
one-dimensional structures of variable length. Finally, approximate but
closed-form solutions (validated with finite element simulations) are exploited
to provide further insight into the effect of configurational forces. In
particular, two applications are presented which show that a transverse
compression can lead to Eulerian buckling or to longitudinal dynamic motion,
both realizing novel examples of soft actuation mechanisms. As an application
to biology, our results may provide a mechanical explanation for the observed
phenomenon of negative durotaxis, where cells migrate from stiffer to softer
environments.
