Modeling Frequency-Dependent Longitudinal Dynamic Behavior of Linear Viscoelastic Long Fiber Composites

An approach to modeling the longitudinal dynamic behavior of unidirectional long fiber composites made from constituents having frequency-dependent material properties is described. In this approach, the total displacement field is considered to be comprised of two parts: an elastic part, and an anelastic part. Material dynamic behavior is described by constitutive equations and governing differential equations. These equations involve the coupled behavior of the total displacement field and the anelastic displacement fields. An “equation of motion” describes the time evolution of the total displacement field, while “relaxation equations” describe the time evolution of the anelastic displacement fields. Distinct anelastic displacement fields are initially associated with the constituent fiber and matrix materials. Effective composite anelastic displacement fields and material properties are then developed in terms of the corresponding constituent properties and their respective volume fractions. The determination of frequency-dependent composite modulus and damping properties from corresponding constituent properties is illustrated, using data from prior experiments. This approach to modeling composite longitudinal behavior suggests direction for the development of an approach to modeling more general behavior, as well as an approach to the analysis of thermorheologically complex materials.