Finite element modeling of two-dimensional woven materials using mechanically equivalent continua

The aim of this thesis is to find a way to model a woven fabric as a mechanically equivalent continuum. The term "mechanically equivalent" means that a given set of applied forces produces the same displacements for both the fabric and the continuum. The fabric is first idealized in a fiber model. To analyze the fiber model, a computer code is programmed based on first principles. The equivalent continuum model is analyzed using an exist- ing finite element code. Both models are two-dimensional. The continuum model is assumed to be orthotropic with no shear resistance and no Poisson effect. For the fiber model, the interaction between yarns is ignored.

Uniaxial loading and pure shear loading are examined in Chapter 5. Symmetric biaxial loading case is examined in Chapter 6. In both chapters, the results are confirmed through closed-form analysis. In Chapter 7, asymmetric loading case is explored. The results from these three chapters show that when fibers are uniformly spaced and parallel to the sides of the element, mechanical equivalence is achieved if the number of fibers in the fiber model is sufficiently large.

In chapter 8, the restrictions on fiber locations and orientation are re- moved. For non-uniform spacing, mechanical equivalence is achieved when two fibers pass through the Gaussian quadrature points. When each fiber set has fibers making angles of 45 degrees with the element's sides, mechanical equivalence is not achieved.