**Technical**** University**** of Łdź**

**Department of Technical Mechanics and Informatics**

**ul. Żeromskiego 116, 90-924 Łdź,
Poland**

**Phone: (48) (42) 636 14 29**

**E-mail: piotr.szablewski@p.lodz.pl**

**Abstract**

*This paper describes a simple sinusoidal geometrical
model of textile composite. On the basis of this model it will be presented how
to obtain certain geometrical parameters which fully characterize the geometry
of composite structure. Using geometrical considerations it is possible to
obtain from this model basic mechanical parameters very useful for further
strength analysis. Such mechanical considerations and method for calculating
mechanical parameters will be presented in future article.*

*On the basis of above‑mentioned theoretical
considerations a special computer program was developed. The method of
calculation presented in this paper can be applied to more complicated models
of textile composites.*

**Key words**: textile composites, textile mechanics, numerical
methods, woven fabric, unit cell model.

**1.
Introduction**

Textile composites represent a class of advanced
materials which are reinforced with textile preforms for structural or load
bearing applications. In general, composites can be defined as a select combination
of dissimilar materials with a specific internal structure and external shape.
The unique combination of two material components leads to singular mechanical
properties and superior performance characteristics not possible with any of
the components alone (see ref. [1], [2], [3]). The range of
applications for composite materials appears to be limitless. Textile
composites can be defined as the combination of a resin system with a textile
fiber, yarn or fabric system. They may be either flexible or quite rigid. In
this paper will be presented how to build a simple geometrical model of textile
composite and how to get from this model certain geometrical and mechanical
parameters, very useful for further strength analysis.

**2. The
geometrical model of textile composite**

Let us consider a balanced plain weave textile
composite in which the warp and fill yarns contain the same number of fibers *n*
with all filaments having the same diameter _{}, and with the warp and fill yarns
having the same yarn packing density _{}. The cross-sectional area of the yarns is
given by _{}.

The representative unit cell (RUC) is a rectangular
consisting of two warp yarns interlaced with two fill yarns with resin matrix
filling the remaining portion of the volume.

Its dimensions are _{}and its thickness is denoted by *H*.
The other parameters are denoted and shown in Figure 1. The thickness of
the yarn along the centerline of the yarn path is denoted by *t*. If the
fiber volume fraction specified for the unit cell is too small, it is necessary
to add an additional resin layer of thickness _{}to the unit cell. The geometry of
the path of the warp or fill yarn is modelled using two assumptions:
1 - the centerline of the yarn path consists of undulation portions
and straight portions, with the centerline of the undulating portions described
by the sine function, 2 - the cross‑sectional area and the
thickness of the yarn normal to its centerline are uniform along the arc-length
of the centerline. The centerline of the warp yarn path in an undulating region
is specified by

_{}, _{}. (1)

The trigonometric
functions of the angle _{}in terms of function _{}are

_{}, _{}, _{}. (2)