Soft material robotics is a rather young research field in the robotics and material science communities. A popular design is the soft pneumatic actuator (SPA) which, if connected serially, becomes a highly compliant manipulator. This high compliance makes it possible to adapt to the environment and in the future might be very useful for manipulation tasks in narrow and wound environments. A central topic is the modelling of the manipulators. While comparatively rigid continuum robots are build of metal or other materials, that conduct a linear behaviour, the material used in soft material robotics often exhibits a nonlinear stress-strain relationship. In this paper we contribute an identification method for material parameters and data-based approach within the constitutive equations of a Cosserat rod model. We target bending and extension stiffness, consider shear and neglect torsional strains. The proposed method is applicable to any continuum robot which can be modelled by the classic theory of special Cosserat rods, including constraint models, and shows great improvement in experimental results with mean position errors of 0.59% reference length.