Relative planar strain control and minimizing deformation work in elastomeric sheets via reinforcing fiber arrays

The strain dynamics in the composite sheet are modeled geometrically from fiber orientations, assuming that the fibers are inextensible. After the strain dynamics have been determined, the stress/strain relationship is modeled by considering the matrix and reinforcing fibers to be two separate homogeneous systems interacting through local stresses. Both steps of this modeling technique are validated experimentally showing planar strains in a preferred direction to be as high as 16 times the resulting planar strain of an equivalent unreinforced sheet by forcing negative strains in the orthogonal planar directions. The work required for deformation is derived from the stress/strain relationship by calculating the strain energy stored in the material, and an optimal balance between increased planar strain output and increased material stiffness is analyzed. It is shown that for the specific materials used to create the soft composite sheets (thermoplastic elastomer with cotton fibers) optimal fiber angles lie between 15° and 25° to minimize work required for deformation, but this optimal range will increase with increasing ratio of fiber to matrix modulus.