Design of Auxetic Structures via Mathematical Optimization
ABSTRACT The optimization and manufacturing of an auxetic structure is presented. An inverse homogenization method is used to obtain the optimized geometry shown in the figure. The resulting structure is then produced using selective electron beam melting. The numerically predicted properties are experimentally verified.
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ABSTRACT: Purpose – The purpose of this paper is to fabricate cellular Ti6Al4V with carbon nanotube (CNT)-like structures by selective electron beam melting and study the resultant mechanical properties based on each respective geometry to provide fundamental information for optimizing molecular architectures and predicting the mechanical properties of cellular solids. Design/methodology/approach – Cellular Ti6Al4V with CNT-like zigzag and armchair structures are fabricated by selected electron beam melting. The microstructures and mechanical properties of these samples are evaluated utilizing scanning electron microscopy, synchrotron radiation X-ray and compressive tests. Findings – The mechanical properties of the cellular solids depend on the geometry of strut architectures. The armchair-structured Ti6Al4V samples exhibit Young’s modulus from 501.10 to 707.60 MPa and compressive strength from 8.73 to 13.45 MPa. The zigzag structured samples demonstrate Young’s modulus from 548.19 to 829.58 MPa and compressive strength from 9.32 to 16.21 MPa. The results suggest that the zigzag structure of the Ti6Al4V cellular solids can achieve improved mechanical properties and the mechanism for the enhanced mechanical properties in the zigzag structures was revealed. Originality/value – The results provide an innovative example for modulating the mechanical properties of cellular titanium by adjusting the unit cell geometry. The Ti6Al4V cellular solids with single-walled CNT-like structures could be used as light-weight construction components or filters in industries. The Ti6Al4V with multiwalled CNT-like structures could be used as new scaffolds for biomedical applications.Rapid Prototyping Journal 11/2014; 20(6):541. DOI:10.1108/RPJ-05-2013-0050 · 1.16 Impact Factor
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ABSTRACT: A new method for the optimal design of inhomogeneous meso-structured components is presented. The method is based on a variant of the free material optimization (FMO) method. Instead of coupling a macroscopic model directly with the meso-scale in the framework of a two-scale approach, information from the meso-scale is incorporated into the FMO model by additional constraints. The FMO result, given in terms of optimized tensors, is interpreted by the inverse homogenization approach. Rather than only computing the meso-structure for each “FMO cell” independently, approximate continuity of the meso-structure is enforced. Thus, the final result is a manufacturable structurally graded material. The feasibility of the whole method is demonstrated by means of an academic example.SIAM Journal on Scientific Computing 01/2012; 34(6):711-733. DOI:10.1137/110850335 · 1.94 Impact Factor
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ABSTRACT: We systematically analyse the mechanical deformation behaviour, in particular Poisson's ratio, of floppy bar-and-joint framework based on periodic tessellations of the plane. For frameworks with more than one deformation mode, crystallographic symmetr constraints or minimization of an angular vertex energy functional are used to lift this ambiguity. Our analysis allows fo systematic searches for auxetic mechanisms in archives of tessellations; applied to the class of one- or two-uniform tessellation by regular or star polygons, we find two auxetic structures of hexagonal symmetry and demonstrate that several other tessellation become auxetic when retaining symmetries during the deformation, in some cases with large negative Poisson ratios ν<−1 for a specific lattice direction. We often find a transition to negative Poisson ratios at finite deformations for severa tessellations, even if the undeformed tessellation is infinitesimally non-auxetic. Our numerical scheme is based on a solutio of the quadratic equations enforcing constant edge lengths by a Newton method, with periodicity enforced by boundary conditions.Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 01/2013; 469(2149). DOI:10.1098/rspa.2012.0465 · 2.00 Impact Factor