Review of heterogeneous material objects modeling in additive manufacturing

Li, Bin; Fu, Jianzhong; Feng, Jiawei; Shang, Ce; Lin, Zhiwei

doi:10.1186/s42492-020-0041-6

Cited by 20 publications

(10 citation statements)

References 125 publications

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“…It is however of reduced size for the field associated to the surface forces: Only the active projection basis functions at the current face, i.e. contained in the set denoted I F in Equation (45), are involved in the system to be solved.…”

Section: Identification Of the Macro-fields To Projectmentioning

confidence: 99%

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Fast and multiscale formation of isogeometric matrices of microstructured geometric models

2021

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The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly time in the context of isogeometric linear elasticity of complex microstructured geometries modeled via spline compositions. The developed isogeometric approach involves a polynomial approximation occurring at the macro-scale and the use of lookup tables with pre-computed integrals incorporating the micro-scale information. We provide theoretical insights and numerical examples to investigate the performance of the procedure. The strategy turns out to be of great interest not only to form finite element operators but also to compute other quantities in a fast manner as for instance sensitivity analyses commonly used in design optimization.

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Section: Identification Of the Macro-fields To Projectmentioning

confidence: 99%

“…Methods based on homogenization principle seems not applicable in our context. Here, the focus is on heterogeneous structures in the context of Additive Manufacturing and 3D printing [ 45 ]. The precision of the printers constrains the achievable length scale range of the heterogeneities.…”

Section: Introductionmentioning

confidence: 99%

Fast and multiscale formation of isogeometric matrices of microstructured geometric models

2021

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“…Heterogeneous object (HE object) modeling is paramount for natural object representation [19], such as tissue modeling, physically based anisotropic simulation [20], and additive manufacturing [21]. However, a 2D region is usu-ally represented by its contours.…”

Section: In the Computer Graphics Communitymentioning

confidence: 99%

Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves

Wang

Liu

et al. 2021

IEEE Comput. Grap. Appl.

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The skeleton, or medial axis, is an important attribute of 2D shapes. The disk B-spline curve (DBSC) is a skeleton-based parametric freeform 2D region representation, which is defined in B-spline form. The DBSC describes not only a 2D region, which is suitable for describing heterogeneous materials in the region, but also the center curve (skeleton) of the region explicitly, which is suitable for animation, simulation and recognition. In addition to being useful for error estimation of the B-spline curve, the DBSC can be used in designing and animating freeform 2D regions. Despite increasing DBSC applications, its theory and fundamentals have not been thoroughly investigated. In this paper, we discuss several fundamental properties and algorithms, such as the de Boor algorithm for DBSCs. We first derive the explicit evaluation and derivatives formulas at arbitrary points of a 2D region (interior and boundary) represented by a DBSC and then provide heterogeneous object representation. We also introduce modeling and interactive heterogeneous object design methods for a DBSC, which consolidates DBSC theory and supports its further applications.

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“…For some objects, we demonstrate both synthetic results as well as 3D printouts. One has to mention that 3D printing hardware for varying density is still in an early development state [8,13,19] and the range of available densities is limited. On recent Prusa FDM printers, however, it is possible to alter the extrusion rate while printing.…”

Section: D Printing Of Varying Densitymentioning

confidence: 99%

Tetrahedra of varying density and their applications

Bukenberger

Lensch

2021

Vis Comput

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We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve $$L_{2|\infty }$$ L 2 | ∞ Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations. Graphic abstract

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Review of heterogeneous material objects modeling in additive manufacturing

Cited by 20 publications

References 125 publications

Fast and multiscale formation of isogeometric matrices of microstructured geometric models

Fast and multiscale formation of isogeometric matrices of microstructured geometric models

Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves

Tetrahedra of varying density and their applications

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