Modeling and control of soft robots is an up-to-date and exciting area of research which has been tackled with complementary approaches so far. In this paper, we modify the existing continuum Cosserat approach optimizing it for soft robot arms which can be discretized in a finite number of sections and degrees of freedom. The resulting new piece-wise constant strain model extends the existing piece-wise constant curvature model by allowing torsion and shears strains which are fundamental to cope with out-of-the-plane external forces as appearing for example during ground locomotion. A first experimental comparison has been also conducted using one fluidic actuated leg of the soft crawler FASTT.