Upper and lower bounds to the overall incremental stiffness of hyperelastic composites

Abstract Bounds to the overall stiffness of a composite are well-known within classical theory elasticity. They based on positive-definiteness local stiffness. A transfer prestressed state is not trivial. We may study incremental that connects nominal stress rate with velocity gradient. But when there mainly compressive stresses, then can only be secured if this replaced by pseudo-stiffness. Its existence equivalent strengthened form uniform infinitesimal polyconvexity and independent geometry. The same case crude Voigt Reuss bounds. More refined kinematic or dynamic approximations do, course, depend This demonstrated unidirectional reinforcement matrix.