  This paper presents an arbitrary order locking-free numerical scheme for
linear elasticity on general polygonal/polyhedral partitions by using weak
Galerkin (WG) finite element methods. Like other WG methods, the key idea for
the linear elasticity is to introduce discrete weak strain and stress tensors
which are defined and computed by solving inexpensive local problems on each
element. Such local problems are derived from weak formulations of the
corresponding differential operators through integration by parts. Locking-free
error estimates of optimal order are derived in a discrete $H^1$-norm and the
usual $L^2$-norm for the approximate displacement when the exact solution is
smooth. Numerical results are presented to demonstrate the efficiency,
accuracy, and the locking-free property of the weak Galerkin finite element
method.
