Mechanics of hyperelastic composites reinforced with nonlinear elastic fibrous materials in finite plane elastostatics

A model for the mechanics of a hyperelastic material reinforced with unidirectional and bidirectional fibers is presented in finite plane elastostatics. This includes the refinement/development of a series of continuum-based prediction models to accommodate the nonlinear responses of both the matrix material and the reinforcing fibers. The kinematics of the embedded fibers, including the torsional kinematics between two adjoining fibers, are formulated via the first and second gradient of continuum deformations. Within the framework of variational principles and a virtual work statement, the Euler equation and the admissible boundary conditions are derived. To this end, a set of inhouse experiments are performed for the purpose of cross-examination and model implementation. The obtained models successfully predict the strain-stiffening responses of the elastomer – polyester fiber composites together with other key design considerations such as, deformation profiles, shear strain distributions, and the deformed configurations of a local unit fiber mesh. The Euler – Almansi strain integrate model is also proposed through which the strain-softening behaviors of a certain type of polyurethane fiber composites are predicted, yet further implementation of the obtained Euler – Almansi model remains to be determined due to the paucity of available data. The practical utility of the proposed models may be expected in the design and analysis of hyperelastic composites exhibiting strain-stiffening/softening responses by providing instant estimations of the resultant properties of intended composites.