A constitutive model for materials with directionally strain locking microstructures

Abstract

Strain locking materials have a limit to the extent to which they can be stretched along one or more axes. The strain limit can be due to the reorientation of stiffening phases at microstructural or molecular scales along the direction of the applied load. Both natural and manmade composites can exhibit such a response when initially wavy fibers or other corrugated structures gradually straighten and limit the extensibility of the material. A new constitutive model is developed for materials that exhibit strain locking along a preferred axis. The model assumes the microstructure is composed of linear elastic material with embedded zig-zag shaped fiber phase that is oriented along the preferred locking axis. The response is governed by a complementary energy density function which is partitioned into separate portions that represent the complementary energies within the fibers and the matrix respectively. A new, nonlinear form for the complementary energy density function of strain locking fibers is derived based on a relationship between the applied stress and the strain of the fiber. An example material that exhibits strain locking longitudinally but is transversely linear-elastic is considered. The behaviors of the example material under tension and compression along the longitudinal and transverse axis are illustrated. A comparison is made with FEM modeling of a strain locking microstructure explicitly fitting the constitutive model parameters with both FEM simulated and experimental data for real material.