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A relief cutting method, or kerfing, is considered to create flexible freeform surfaces from relatively stiff and thick panels. The flexibility and moldability are achieved by introducing slender components within the panel, forming kerf patterns, and hence reducing the second moment and polar moment of an area of the solid panel. This paper presents a systematic study on the deformations of kerf unit-cells and of kerf panels. Two different kerf patterns, i.e., square and hexagon, with various cut densities are studied. The effects of different cutting density and kerf patterns on the stretching, bending, and twisting deformations are examined. Understanding the influence of kerf patterns and cut densities on various deformation mechanisms will guide the design of freeform complex shapes out of kerf panels. Experimental tests were performed on unit-cells under different boundary conditions, e.g., uniaxial and biaxial stretching and bending. The tests were also performed on kerf panels with different kerf patterns and varying cut densities. We used a nonlinear beam element in order to describe the deformations of the slender components within the kerf patterns. We compared the overall deformations in the kerf unit-cells and panels from the beam element model and experimental tests. Using the kerfing technique allows for generating flexible structures with complex geometries from mass-produced panels of standard shape and size. When using the kerfing method to achieve the desired surface topology, the stresses, strains, and displacements in the surface will depend on the kerf pattern, cut density, and constituent behavior.

We present a relief cutting method to turn rigid planar surfaces into flexible ones using meander patterns that consist of interlocked Archimedean spirals. We have developed an approach to obtain all possible such 2D meander patterns with a set of simple remeshing processes. Our algorithm can be applied to any polygonal mesh to produce 2D meander patterns. Since these meander patterns are obtained by remeshing processes, we can control the local properties of the pattern with intensity of images to obtain different stiffness values in different regions. This approach provides a simple interface to construct desired patterns.

In this work, we demonstrate that quad-edge mesh data structure can efficiently be used to construct large shapes. We have developed a system to unfold any polygonal mesh based on quad-edge structure. Using our system, any shape can be constructed by using laser-cut developable panels. This approach is particularly suitable to construct complicated sculptural and architectural shapes from anisotropic materials that can only be bent in one direction. Graphical abstractDisplay Omitted HighlightsWe have classified multi-panel unfolding and construction methods.For classification, we employed widely used polygonal mesh data structures.We have implemented each one of these multi-panel unfolding methods for comparison.We have identified quad-edge based construction is best for our purposes.We have constructed physical shapes to demonstrate the feasibility of the approach.Our software is used in a Freshman Architecture studio.