Boundary representations (B-reps) that are spline based, have served as the geometric representation of choice for over four decades. That said, the gap between design and modern (additive) manufacturing, due to the lack of appropriate geometric tools for supporting porosity, heterogeneity and anisotropy in designs, is expanding. Contemporary CAD systems can’t be utilized to provide solutions for volumetric modeling, as these systems, inherently, offer only B-rep modeling capabilities. Further, analysis has always required a volumetric representation of geometry, and the conversions of B-reps to analysis suitable (finite element) representations have always been a challenging task, as was the mapping back of the analysis results. It is not surprising then that a common geometric representation in the design and the analysis stages, in an attempt to tighten the bond between the geometrical design and analysis stages, has always been a worthy yet unattainable goal.
A unique volumetric modeling technology, that is patented, has been developed at the Technion for the last several years. With this volumetric representation (V-rep), it is possible to represent the interior of geometrical objects as well as their boundaries. Volumetric attributes in the design of functionally graded material (FGM) or some physical properties are considered as part of the V-rep and are carried along with the geometric model. The same representation is used, unaltered, in other stages of the design, including analysis, optimization and manufacturing, completely eliminating these tedious conversions that are required today.
- Freeform microstructures construction: Using unique spline functional composition and symbolic computation algorithms, we provide methods for smoothly tiling the interior of any freeform object with any given tile that consists of curves, or (trimmed) surfaces/trivariates. The constructed geometry is precise (machine precision), continuous, and watertight. Further and following analysis and optimization, the geometry, topology, and material content of individual tiles can be modified.
- A volumetric geometric modeling: a framework that provides a representation for volumetric objects, and supports algorithms for constructing and managing these objects, while offering:
- Compatibility with modern (iso-geometric) analysis tools, bridging the gap between design and analysis and eliminating any potential conversion needs
- A direct interface with 3D printers, including those supporting anisotropic/heterogeneous materials
- A seamless migration path from existing boundary representation (B-rep) modeling systems
Applications and Opportunities
- Companies that employ (high end) CAGD tools as part of their development process
- Additive manufacturing companies and users