An energy based model for the flattening of woven fabrics

Applications such as garment manufacture and composite structure fabrication require a two dimensional (2D) woven material to assume a three dimensional (3D) shape. The specification of the process is usually initiated by defining the 3D surface. Hence, the problem arises of determining the best 2D pattern. The problem is made more complex by the anistropic nature of woven fabrics which are often used as raw material. Such materials display a variation in mechanical properties with respect to the woven structure. This paper presents a model for determining the optimum 2D pattern for a specified 3D surface where optimality is determined in terms of minimising the energy distribution required to force the 2D pattern to assume the 3D shape. The 3D surface specification is assumed to consist of a polygonal mesh. The model allows affine transformations to be applied to the weave structure which can be unique for each polygon in the mesh. Important considerations in the modelling process include the following: 1. The degree to which the specified 3D surface departs from a developable surface. 2. The energy components used to model the woven structure and their sensitivity to weave direction. Essentially, these stem from tensile strain in each direction of the weave and shear strain. 3. The prediction of weave geometry as it reacts to the energy distribution being applied. The model is demonstrated by applying it to a relatively simple pyramidal 3D shape. Energy values are optimised to produce a pattern that requires the minimum overall energy to be applied to the 2D pattern in order for it to assume the 3D shape. This 2D pattern is sensitive to the orientation of the woven structure with predictions being made of how the woven structure will behave in 3D.