Bifurcation points in unsymmetric laminates and their influence on lay-up design for 4D printing of composites

Abstract

4D printing of composites (4DPC) is a technique that can make composite structures with curved geometry without the need to use a curved mold (only a flat mold is used). This technique has been used to make composite springs and cones, where not only the shape is obtained but the mechanical properties are equivalent to those made using conventional technique (where a curved mold is used). The principle of operation of 4DPC utilized anisotropy in unsymmetric laminates as the mechanism for the shape transformation. However it is not always straightforward that a certain unsymmetric lay-up of composite layers will provide a certain shape. Hyer [1,2] observed that laminate theory is accurate to predict the shape of the [0/90] laminate only in some cases, but not in all cases. He attributed this to the assumption of linear relation between the strains and displacements. He then used the non-linear relation between strains and displacements and assumed some functional forms for them. This approach was able to predict the shape of square thin laminates such as those made of [0/90] and [0₂/90₂] lay sequences, but not for rectangular laminates or laminates of other shapes. Finite element method was also used for this prediction. This method worked only with some twikking of the modeling procedure. As such work of previous researchers in the past more than 40 years only show success in ad-hoc situations. The reason for this is due to the lack of an explanation for why there are so many different shapes in different situations. The work in this paper provides an explanation as to why there are different shapes for different situations. This understanding provides a direction for the development of a new finite element procedure that can determine the shape of the laminates in different situations. The new understanding is used to explain the behavior of many cases. This new finite element procedure is then used to generate guidelines on the effect of different parameters such as the effect of geometric dimensions, and material properties on the final shape. These guidelines are useful for the selection of lay-up sequences to make structures in the technique of 4D printing of composites.