A Constitutive Model for Materials with Transversely Isotropic Strain Locking Microstructures

Abstract

Strain locking materials have a limit to the degree to which they can be stretched along one or more axes. The limiting strain behavior is due to stiff microstructure components that reorient along the direction of the applied load as stretch increases. Both natural and manmade materials can exhibit such a response when initially wavy fibers or other corrugated structures gradually straighten and limit the extensibility of the material. Two new constitutive models are developed which describe materials with strain locking structures that are oriented along a particular axis. The models assume the microstructure is composed of linear elastic material with embedded zigzag shaped, series of structures oriented along a preferential axis which produce the locking behavior. The response is governed by a strain energy density function which is partitioned into separate portions that represent the stored energy within the fibers and the matrix respectively. A new, nonlinear form for the strain energy density function of strain locking fibers is derived based on the change in angle of the fiber’s vertices. Examples of the mechanical response are demonstrated for a matrix material defined by a linear elastic model. The model parameters are fit to tensile stress versus strain data generated from Finite Element Analysis of a strain locking composite RVE as well as experimental data from a strain locking composite thin-film material. Correlation with the experimental data shows that the proposed constitutive model accurately fits the initial tangent modulus and ultimate strain locking limit well.