  We devise and evaluate numerically a Hybrid High-Order (HHO) method for
finite plasticity within a logarithmic strain framework. The HHO method uses as
discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,
together with cell-based polynomials that can be eliminated locally by static
condensation. The HHO method leads to a primal formulation, supports polyhedral
meshes with non-matching interfaces, is free of volumetric locking, the
integration of the behavior law is performed only at cell-based quadrature
nodes, and the tangent matrix in Newton's method is symmetric. Moreover, the
principle of virtual work is satisfied locally with equilibrated tractions.
Various two- and three-dimensional benchmarks are presented, as well as
comparison against known solutions with an industrial software using conforming
and mixed finite elements.
