scholarly journals A numerical method to estimate the effective elastic moduli of rocks from two- and three-dimensional digital images of rock core samples

2017 ◽  
pp. 416-433
Author(s):  
Г.В. Решетова ◽  
Т.С. Хачкова
Keyword(s):  
Numerical Method ◽  
Elastic Moduli ◽  
Digital Images ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Effective Elastic Moduli ◽  
Effective Parameters ◽  
Static State ◽  
Core Samples ◽  
Static Conditions

Представлен численный алгоритм оценки упругих свойств образцов горной породы по дву- и трехмерным компьютерным томограммам. Метод основан на принципе эквивалентности энергии деформаций, вызываемых однородными граничными статическими условиями, имитирующими физический эксперимент. На этой основе определяется эффективный тензор податливости представительного объема неоднородной среды. Особенностью алгоритма является новая схема расчета статического напряженно-деформированного состояния образца методом установления решения соответствующей задачи динамической теории упругости. Приводятся результаты численных расчетов. Предложенный метод верифицировался на однородных образцах с заданными свойствами, а также для слоистых материалов, для которых доказана справедливость построения эффективных параметров по методу Шенберга. В заключение приведены эффективные параметры для трехмерного образца кернового материала. A numerical method to estimate the effective elastic moduli of rocks from two- and three-dimensional digital images of rock core samples is proposed. The method is based on the energy equivalence principle for deformations caused by the homogeneous boundary static conditions that simulate a physical experiment. On this basis, the effective compliance tensor of a representative volume of an inhomogeneous medium is determined. A specific feature of the proposed algorithm is a new scheme for calculating the stress-strain static state of a sample by solving the corresponding problem of dynamic elasticity theory using the relaxation method. The obtained numerical results are discussed. The proposed method is verified using homogeneous samples with specified properties as well as for layered materials with effective parameters obtained according to the Schoenberg method. In conclusion, the effective parameters for a three-dimensional core sample are presented.

Mechanics of Three-Dimensional Printed Lattices for Biomedical Devices

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Paul F. Egan ◽  
Isabella Bauer ◽  
Kristina Shea ◽  
Stephen J. Ferguson
Keyword(s):  
Elastic Moduli ◽  
Nutrient Transport ◽  
Three Dimensional ◽  
Integrated Design ◽  
Mechanical Efficiency ◽  
Lattice Structures ◽  
Effective Elastic Moduli ◽  
Biomedical Devices ◽  
Fully Integrated ◽  
Polyjet Printing

Advances in three-dimensional (3D) printing are enabling the design and fabrication of tailored lattices with high mechanical efficiency. Here, we focus on conducting experiments to mechanically characterize lattice structures to measure properties that inform an integrated design, manufacturing, and experiment framework. Structures are configured as beam-based lattices intended for use in novel spinal cage devices for bone fusion, fabricated with polyjet printing. Polymer lattices with 50% and 70% porosity were fabricated with beam diameters of 0.4–1.0mm, with measured effective elastic moduli from 28MPa to 213MPa. Effective elastic moduli decreased with higher lattice porosity, increased with larger beam diameters, and were highest for lattices compressed perpendicular to their original build direction. Cages were designed with 50% and 70% lattice porosities and included central voids for increased nutrient transport, reinforced shells for increased stiffness, or both. Cage stiffnesses ranged from 4.1kN/mm to 9.6kN/mm with yielding after 0.36–0.48mm displacement, thus suggesting their suitability for typical spinal loads of 1.65kN. The 50% porous cage with reinforced shell and central void was particularly favorable, with an 8.4kN/mm stiffness enabling it to potentially function as a stand-alone spinal cage while retaining a large open void for enhanced nutrient transport. Findings support the future development of fully integrated design approaches for 3D printed structures, demonstrated here with a focus on experimentally investigating lattice structures for developing novel biomedical devices.

Effective elastic moduli of metal honeycombs manufactured using selective laser melting

2020 ◽  
Vol 26 (5) ◽  
pp. 971-980 ◽  
Author(s):  
Rafid Hussein ◽  
Sudharshan Anandan ◽  
Myranda Spratt ◽  
Joseph W. Newkirk ◽  
K. Chandrashekhara ◽  
...  
Keyword(s):  
Strain Energy ◽  
Elastic Moduli ◽  
Three Dimensional ◽  
Analytical Models ◽  
Effective Elastic Moduli ◽  
Effective Moduli ◽  
Content Type ◽  
Out Of Plane ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Purpose Honeycomb cellular structures exhibit unique mechanical properties such as high specific strength, high specific stiffness, high energy absorption and good thermal and acoustic performance. This paper aims to use numerical modeling to investigate the effective elastic moduli, in-plane and out-of-plane, for thick-walled honeycombs manufactured using selective laser melting (SLM). Design/methodology/approach Theoretical predictions were performed using homogenization on a sample scale domain equivalent to the as-manufactured dimensions. A Renishaw AM 250 machine was used to manufacture hexagonal honeycomb samples with wall thicknesses of 0.2 to 0.5 mm and a cell size of 3.97 mm using 304 L steel powder. The SLM-manufactured honeycombs and cylindrical test coupons were tested using flatwise and edgewise compression. Three-dimensional finite element and strain energy homogenization were conducted to determine the effective elastic properties, which were validated by the current experimental outcomes and compared to analytical models from the literature. Findings Good agreement was found between the results of the effective Young’s moduli ratios numerical modeling and experimental observations. In-plane effective elastic moduli were found to be more sensitive to geometrical irregularity compared to out-of-plane effective moduli, which was confirmed by the analytical models. Also, it was concluded that thick-walled SLM manufactured honeycombs have bending-dominated in-plane compressive behavior and a stretch-dominated out-of-plane compressive behavior, which matched well with the simulation and numerical models predictions. Originality/value This work uses three-dimensional finite element and strain energy homogenization to evaluate the effective moduli of SLM manufactured honeycombs.

Three-Dimensional Effective Elastic Moduli for Multi-Directional Hybrid Filament-Wound Cylindrical Shell with Lining

2011 ◽  
Vol 121-126 ◽  
pp. 539-544
Author(s):  
Wen Jun Ruan ◽  
Qing Ping Yang ◽  
Guang Lei Xu ◽  
Hao Wang
Keyword(s):  
Cylindrical Shell ◽  
Elastic Moduli ◽  
Plate Theory ◽  
Three Dimensional ◽  
Effective Elastic Moduli ◽  
Hybrid Fiber ◽  
Filament Wound ◽  
Glass Carbon ◽  
Filament Wound Composite ◽  
Wound Composite

A method based on laminated plate theory is presented for estimating three-dimensional effective elastic moduli of multi-directional hybrid filament-wound composite cylindrical shell with lining. The method introduces a factor of hybrid effects. The effective elastic moduli of glass/epoxy fiber-wound tube with lining and glass/carbon/epoxy hybrid fiber-wound tube with lining are predicted by present method respectively. It is shown that the method is simple and accurate.

Three-Dimensional Effective Elastic Moduli for Multidirectional Filament-Wound Tube with Lining

2011 ◽  
Vol 194-196 ◽  
pp. 1823-1829 ◽  
Author(s):  
Guang Lei Xu ◽  
Wen Jun Ruan ◽  
Hao Wang ◽  
Qing Ping Yang ◽  
Jia Wen Liu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Elastic Moduli ◽  
Three Dimensional ◽  
Thin Wall ◽  
Effective Elastic Moduli ◽  
Element Analysis ◽  
Reinforced Composite ◽  
Filament Wound ◽  
Laminate Theory

A method based on laminate theory is presented for estimating three-dimensional effective elastic moduli of multidirectional filament-wound fibre-reinforced composite thin-wall tube with lining. The effective elastic moduli of glass fibre wound tube with lining are calculated. In contrast with finite element analysis, effective elastic moduli estimated by this method are accurate.

scholarly journals A three-dimensional model for rain-wind induced vibration of stay cables in cable-stayed bridges

2020 ◽  
Vol 14 (1) ◽  
pp. 15-27
Author(s):  
Nguyen Thi Hai Nhu ◽  
Tran Anh Binh ◽  
Ha Manh Hung
Keyword(s):  
Elastic Moduli ◽  
Heterogeneous Media ◽  
Effective Properties ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Main Idea ◽  
Data Driven ◽  
Effective Elastic Moduli ◽  
Three Dimensional Model ◽  
Data Driven Approach

The most rigorous effective medium approximations for elastic moduli are elaborated for matrix composites made from an isotropic continuous matrix and isotropic inclusions associated with simple shapes such as circles or spheres. In this paper, we focus specially on the effective elastic moduli of the heterogeneous composites with arbitrary inclusion shapes. The main idea of this paper is to replace those inhomogeneities by simple equivalent circular (spherical) isotropic inclusions with modified elastic moduli. Available simple approximations for the equivalent circular (spherical) inclusion media then can be used to estimate the effective properties of the original medium. The data driven technique is employed to estimate the properties of equivalent inclusions and the Extended Finite Element Method is introduced to modeling complex inclusion shapes. Robustness of the proposed approach is demonstrated through numerical examples with arbitrary inclusion shapes. Keywords: data driven approach; equivalent inclusion, effective elastic moduli; heterogeneous media; artificial neural network.

scholarly journals The time domain numerical method of three-dimensional conductors including radiation with lumped parameter circuit

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Souma Jinno ◽  
Shuji Kitora ◽  
Hiroshi Toki ◽  
Masayuki Abe
Keyword(s):  
Numerical Method ◽  
Time Domain ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
New Formalism ◽  
Vector Potentials ◽  
Lumped Parameter ◽  
Radiation Theory ◽  
Stable Solutions ◽  
The Time Domain

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

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