Topology Optimization using the Discrete Element Method. Part 1: Methodology, Validation, and Geometric Nonlinearity

Structural Topology optimization is attracting increasing attention as a complement to additive manufacturing techniques. The optimization algorithms usually employ continuum-based Finite Element analyses, but some important materials and processes are better described by discrete models, for example granular materials, powder-based 3D printing, or structural collapse. To address these systems, we adapt the established framework of SIMP Topology optimization to address a system modelled with the Discrete Element Method. We consider a typical problem of strain energy minimization, for which we define objective function and related sensitivity for the Discrete Element framework. The method is validated for simply supported beams discretized as interacting particles, whose predicted optimum solutions match those from a classical continuum-based algorithm. A parametric study then highlights the effects of mesh dependence and filtering. An advantage of the Discrete Element Method is that geometric nonlinearity is captured without additional complexity; this is illustrated when changing the beam supports from rollers to hinges, which indeed generates different optimum structures. The proposed Discrete Element Topology Optimization method enables future incorporation of nonlinear interactions, as well discontinuous processes such as during fracture or collapse.

3D Topology Optimization and Mesh Dependency for Redesigning Locking Compression Plates Aiming to Reduce Stress Shielding

Current fixation plates for bone fracture treatments are built with biocompatible metallic materials such as stainless steel, titanium, and its alloys (e.g., Ti6Al4V). The stiffness mismatch between the metallic material of the plate and the host bone leads to stress shielding phenomena, bone loss, and healing deficiency. This paper explores the use of three dimensional topology-optimization, based on compliance (i.e., strain energy) minimization, reshaping the design domain of three locking compression plates (four-screw holes, six-screw holes, and eight-screw holes), considering different volume reductions (25, 45, and 75%) and loading conditions (bending, compression, torsion, and combined loads). A finite-element study was also conducted to measure the stiffness of each optimized plate. Thirty-six designs were obtained. Results showed that for a critical value of volume reductions, which depend on the load condition and number of screws, it is possible to obtain designs with lower stiffness, thereby reducing the risk of stress shielding.

An approach for the design of multi-material mechanical components

A computational procedure for the calculation of the material parameters involved in the structural design of multi-material components is presented. The developed scheme can be used in the design process for the full or partial replacement of a metallic part with a metal/fiber–reinforced composite bi-material, aiming at weight savings. Finite element simulations are incorporated into an algorithm that rapidly reduces the design space until a good set of design variables has been reached. The process is controlled by two objective functions (mass and strain energy minimization) and is subjected to several constraints according to the component’s design requirements. Three examples have been adopted to demonstrate the effectiveness of the approach. The results show that the upper limit for weight reduction is constrained by the yield strength of the metal component and therefore its corresponding thickness. Based on the design configuration, weight savings up to 25% could be reached.

A Molecular Dynamics Simulation Study of the Mechanical Properties of Carbon-Nanotube Reinforced Polystyrene Composite

In recent years, polymer/carbon nanotube composites have attracted increased attention because the polymer properties have significantly improved. In this paper, a single walled carbon nanotube (SWCNT) is used to reinforce polystyrene matrix. Molecular dynamics (MD) simulations are used to study two periodic systems - a long CNT-reinforced polystyrene composite and amorphous polystyrene matrix itself. The axial and transverse elastic moduli of the amorphous polystyrene matrix and nanocomposites are evaluated using constant-strain energy minimization method. The results from MD simulations are compared with corresponding rule-of-mixture predictions. The simulation results show that CNTs significantly improve the stiffness of polystyrene/CNT composite, especially in the longitudinal direction of the nanotube. Polystyrene posses a strong attractive interaction with the surface of the SWCNT and therefore play an important role in providing effective adhesion. The conventional rule-of-mixture predicts a smaller value than MD simulation where there are strong interfacial interactions. Here the authors report a study on the interfacial characteristics of a CNT-PS composite system through MD simulations and continuum mechanics.

A Molecular Dynamics Simulation Study of the Mechanical Properties of Carbon-Nanotube Reinforced Nylon 6 Composite

In recent years, polymer/carbon nanotube composites have attracted a lot of attention because the polymer properties are significantly improved. In particular, intensive efforts have been directed toward synthesizing, characterizing and understanding polymer/CNT composites. In this paper, as an effort to explore the effective use of carbon nanotubes as a reinforcing material for advanced nanocomposites with polymer matrix, a single walled carbon nanotube (SWCNT) is used to reinforce Nylon 6 matrix. Molecular dynamics (MD) simulations are used to study two periodic systems - a long CNT-reinforced Nylon 6 composite and amorphous Nylon 6 matrix itself. The axial and transverse elastic moduli of the amorphous Nylon 6 matrix and nanocomposites are evaluated using constant-strain energy minimization method. The results from molecular dynamics simulations are compared with corresponding rule-of-mixture predictions. The simulation results show that CNTs significantly improve the stiffness of Nylon 6/CNT composite, especially in the longitudinal direction of the nanotube. The conventional rule-of-mixture predicts a much larger value than MD simulation for the nanocomposite.

Nano-scale Chemistry of Complex Self-Assembled Nanostructures in Epitaxial SiGe Films

ABSTRACTHeteroepitaxy of SiGe alloys on Si (001) under certain growth conditions has previously been shown to cause self-assembly of nanostructures called Quantum Dot Molecules, QDMs, where pyramidal pits and 3D islands cooperatively form. QDMs have potential applications to nanologic device architectures such as Quantum Cellular Automata that relies on localization of charges inside islands to create bi-stable logic states. In order to determine the applicability of QDMs to such structures it is necessary to understand the nano-scale chemistry of QDMs because the chemistry affects local bandgap which in turn affects a QDM’s charge confinement property. We investigate the nanoscale chemistry of QDMs in the Si0.7Ge0.3/Si (100) system using Auger Electron Spectroscopy (AES). Our AES analysis indicates that compressively strained QDM pit bases are the most Ge rich regions in a QDM. The segregation of Ge to these locations cannot be explained by strain energy minimization.

A Molecular Dynamics Simulation Study of the Mechanical Properties of Carbon-Nanotube Reinforced Polystyrene Composite

In recent years, polymer/carbon nanotube composites have attracted increased attention because the polymer properties have significantly improved. In this paper, a single walled carbon nanotube (SWCNT) is used to reinforce polystyrene matrix. Molecular dynamics (MD) simulations are used to study two periodic systems - a long CNT-reinforced polystyrene composite and amorphous polystyrene matrix itself. The axial and transverse elastic moduli of the amorphous polystyrene matrix and nanocomposites are evaluated using constant-strain energy minimization method. The results from MD simulations are compared with corresponding rule-of-mixture predictions. The simulation results show that CNTs significantly improve the stiffness of polystyrene/CNT composite, especially in the longitudinal direction of the nanotube. Polystyrene posses a strong attractive interaction with the surface of the SWCNT and therefore play an important role in providing effective adhesion. The conventional rule-of-mixture predicts a smaller value than MD simulation where there are strong interfacial interactions. Here the authors report a study on the interfacial characteristics of a CNT-PS composite system through MD simulations and continuum mechanics.