Sample-based Design of Functionally Graded Material Structures

Spatial variation of material structures is a principal mechanism for creating and controlling spatially varying material properties in nature and engineering. While the spatially varying homogenized properties can be represented by scalar and vector fields on the macroscopic scale, explicit microscopic structures of constituent phases are required to facilitate the visualization, analysis and manufacturing of functionally graded material (FGM). The challenge of FGM structure modeling lies in the integration of these two scales. We propose to represent and control material properties of FGM at macroscale using the notion of material descriptors which include common geometric, statistical, and topological measures, such as volume fraction, correlation functions and Minkowski functionals. At microscale, the material structures are modeled as Markov random fields: we formulate the problem of design and (re)construction of FGM structure as a process of selecting neighborhoods from a reference FGM, based on target material descriptors fields. The effectiveness of the proposed method in generating a spatially varying structure of FGM with target properties is demonstrated by two examples: design of a graded bone structure and generating functionally graded lattice structures with target volume fraction fields. 1 Modeling of functionally graded material structures 1.1 Functionally graded materials Functionally graded materials (FGMs) are heterogeneous materials made of two or more constituent phases with properties changing gradually with position [1]. The spatial variation (gradation) of properties is determined by changes in the geometric configuration of the constituent phases (a.k.a. material structure) that serve particular mechanical (or more generally, physical) function. FGMs are ubiquitous in nature due to their abilities to satisfy multifold functional constraints and adapt to conflicting requirements; this also explains why FGMs are a popular candidate as engineering materials. FGMs may be found in a broad spectrum of applications, including filters [2], wear resistant coatings [3], bone and dental implants [4,5,6], and cutting tools [7, 8]. Teeth [4], bones [5] and bamboos [9, 10] are a few examples of FGM in nature. Traditionally, the modeling of FGM focuses on the level of macroscopic properties [11, 12, 7]. However, it is the underlying spatial variation of material structures that create and control the spatially varying properties. Recent advances in additive manufacturing [1, 13, 14, 15] and exponentially growing computing power enables the shift of engineering design from the classical material selection paradigm into a simultaneous design of material composition and structure [16, 17]. Systematic modeling and design of graded structures with desired mechanical properties is a key ingredient of this paradigm shift. In this paper, we study the synthesis of two-phase structures, such as porous structures, from a reference material sample. The material structures are discretized into sets of voxels, which is consistent with the popular image acquiring techniques such as micro – computed tomography (μCT) and Magnetic resonance imaging (MRI). 1 Copyright © 2016 by ASME Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2016 August 21-24, 2016, Charlotte, North Carolina