An Improved Analytical Model for the Elastic Constants of Auxetic and Conventional Hexagonal Honeycombs

2011 ◽  
Vol 30 (6) ◽  
pp. 287-310 ◽  
Author(s):  
Joseph N. Grima ◽  
Daphne Attard ◽  
Brian Ellul ◽  
Ruben Gatt
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Elastic Constants ◽  
Finite Thickness ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Cellular Solids ◽  
Significant Extent ◽  
The Subject ◽  
Insight Into

Cellular solids, in particular hexagonal honeycombs have been the subject of numerous studies in the last decades in view of their extensive use in many applications. In particular, there have been various studies aimed at expressing the mechanical properties of honeycombs in terms of the geometrical parameters used to describe the structure of such honeycombs. Despite improvements over the first established model, finite element simulations performed in this work on honeycombs having ribs with a realistic thickness-to-length ratio suggest that the mechanical properties for such systems differ from those predicted by current models, sometimes to a very significant extent. In view of this, we analyse in detail the deformed structures in an attempt to gain insight into how and the extent to which the shape of the ligaments, in particular its thickness and mode of connection affects deformation in conventional and re-entrant hexagonal honeycombs. Based on these observations, we propose a modified version of the previous analytical models that take into consideration the finite thickness of the ligaments.

Evaluation methods for predicting the elastic constants of C/Epoxy plain-weave composites by considering the realistic mesostructures

2018 ◽  
Vol 53 (2) ◽  
pp. 197-208 ◽  
Author(s):  
Shan-yuan Jiang ◽  
Hao Wang ◽  
Zhong-wei Wang
Keyword(s):  
Mechanical Properties ◽  
Elastic Constants ◽  
Stochastic Theory ◽  
Textile Composites ◽  
Analytical Models ◽  
Plane Shear ◽  
Elliptical Cross ◽  
Variable Metric ◽  
Plain Weave ◽  
Feature Parameters

Variabilities of mesostructures existing in textile composites can affect their mechanical properties. Most of the deterministic mechanical models are based on the assumptions of ideal Representative Volume Element, which cannot predict the mechanical properties accurately. Two analytical models predicting the elastic constants of C/Epoxy plain-weave composites by considering the realistic mesostructures are presented in this paper. These models utilize the variable metric stochastic theory to introduce the fluctuations of yarn feature parameters (yarn path and elliptical cross-section parameters) into the model of macro elastic properties. C/Epoxy plain-weave composite is taken as an example to quantify the influences of realistic yarn feature parameters on the elastic constants of the composite. The predicted elastic constants by analytical models and finite element method are verified by the results of mechanical experiments. It can be concluded that for C/Epoxy plain-weave composite the stochastic fluctuations of yarn feature parameters reduce in-plane elastic moduli by a maximum of 4%, and increase the in-plane shear modulus and Poisson’s ratio by a maximum of 15% and 33%, respectively.

A 2-legged XY parallel flexure motion stage with minimised parasitic rotation

2014 ◽  
Vol 228 (17) ◽  
pp. 3156-3169 ◽  
Author(s):  
Guangbo Hao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Design Approach ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Element Analysis ◽  
Motion Range ◽  
Cross Axis

XY compliant parallel manipulators (aka XY parallel flexure motion stages) have been used as diverse applications such as atomic force microscope scanners due to their proved advantages such as eliminated backlash, reduced friction, reduced number of parts and monolithic configuration. This paper presents an innovative stiffness centre based approach to design a decoupled 2-legged XY compliant parallel manipulator in order to better minimise the inherent parasitic rotation and have a more compact configuration. This innovative design approach makes all of the stiffness centres, associated with the passive prismatic (P) modules, overlap at a point that all of the applied input forces can go through. A monolithic compact and decoupled XY compliant parallel manipulator with minimised parasitic rotation is then proposed using the proposed design approach based on a 2-PP kinematically decoupled translational parallel manipulator. Its load–displacement and motion range equations are derived, and geometrical parameters are determined for a specified motion range. Finite element analysis comparisons are also implemented to verify the analytical models with analysis of the performance characteristics including primary stiffness, cross-axis coupling, parasitic rotation, input and output motion difference and actuator nonisolation effect. Compared with the existing XY compliant parallel manipulators obtained using 4-legged mirror-symmetric constraint arrangement, the proposed XY compliant parallel manipulators based on stiffness centre approach mainly benefits from fewer legs resulting in reduced size, simpler modelling as well as smaller lost motion. Compared with existing 2-legged designs with the conventional arrangement, the present design has smaller parasitic rotation, which has been proved from the finite element analysis results.

scholarly journals Interaction between Edge-Crack and Aggregate in Silicate-Based Composite

2017 ◽  
Vol 17 (2) ◽  
pp. 59-64
Author(s):  
Lucie Malíková ◽  
Jan Klusák
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Edge Crack ◽  
Matrix Material ◽  
Interfacial Transition Zone ◽  
Bending Test ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Three Point Bending

Abstract The paper deals with investigation of the interaction between an edge-crack and an aggregate in a silicate-based composite, because adding of aggregates into basic matrix material can improve the fracture mechanical properties of the material significantly. In this work, the three-point-bending test is modelled by means of the finite element method and the dependences of fracture parameters on various material and geometrical parameters of the aggregate and the interfacial transition zone are studied. The results are discussed thoroughly.

The static response of axisymmetric conical shells exhibiting bistable behavior

2021 ◽  
pp. 1-24
Author(s):  
Yair Luxenburg ◽  
Sefi Givli
Keyword(s):  
Finite Element ◽  
Radial Displacement ◽  
Functional Dependence ◽  
Building Blocks ◽  
Rigid Rotation ◽  
Finite Element Simulations ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Bistable Behavior ◽  
Conical Shells

Abstract Belleville springs are widely used in variety of mechanical systems. Recent advances in the field of multi-stable structures suggest that these conical axisymmetric washers may be extremely useful as bistable building-blocks for multi-stable architected metamaterials. In this paper, we examine the ability of existing analytical models to accurately predict the bistable behavior of Belleville springs, namely a non-monotonous force-displacement relation with two branches of positive stiffness separated by a branch of negative stiffness. By comparing to results of finite-element simulations, we find that current analytical models may suffer from significant inaccuracies associated with the assumption of rigid rotation. According to this assumption, adopted by all analytical models of Belleville springs, the cross-section of the spring rotates without bending, i.e. maintains zero curvature as the spring deforms. Motivated by this insight, we relax the rigid-rotation assumption and approximate the radial displacement field by a linear relation in terms of the distance from the spring axis. We find, based on extensive finite-element simulations, that the functional dependence of the radial displacement on the geometry of the springs is indifferent to the stage of deformation and can be expressed in terms of three geometrical parameters. These findings enable us to derive closed-form expressions that are simple and straight-forward to use, yet are significantly more accurate than existing analytical models.

Mechanical Properties of Open-Cell Cellular Structures With Rhombic Dodecahedron Cells

2010 ◽  
Author(s):  
Sahab Babaee ◽  
Babak Haghpanah Jahromi ◽  
Amin Ajdari ◽  
Hamid Nayeb-Hashemi ◽  
Ashkan Vaziri
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Single Unit ◽  
Cellular Structure ◽  
Three Dimensional ◽  
Small Deformation ◽  
Unit Cell ◽  
Analytical Models ◽  
Open Cell ◽  
Principal Directions

We present a series of analytical models and finite element results (FE) for special 3-D open cellular foam to determine the effective material properties of a 3D rhombic dedecahedron open-cell cellular structure. The analytical approach is based on minimizing the total energy associated with small deformation of a single unit cell of the cellular structure. The finite element models were developed for both a single unit cell and three dimensional foam structure and used to obtain the mechanical properties in all three principal directions.

scholarly journals Wrinkling of a stiff thin film bonded to a pre-strained, compliant substrate with finite thickness

2016 ◽  
Vol 472 (2192) ◽  
pp. 20160339 ◽  
Author(s):  
Yinji Ma ◽  
Yeguang Xue ◽  
Kyung-In Jang ◽  
Xue Feng ◽  
John A. Rogers ◽  
...  
Keyword(s):  
Thin Film ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Thickness ◽  
Analytical Models ◽  
Thickness Effect ◽  
Element Analysis ◽  
Compliant Substrate ◽  
Tensile Stiffness ◽  
The Finite Element Analysis

A stiff thin film bonded to a pre-strained, compliant substrate wrinkles into a sinusoidal form upon release of the pre-strain. Many analytical models developed for the critical pre-strain for wrinkling assume that the substrate is semi-infinite. This critical pre-strain is actually much smaller than that for a substrate with finite thickness (Ma Y et al. 2016 Adv. Funct. Mater. ( doi:10.1002/adfm.201600713 )). An analytical solution of the critical pre-strain for a system of a stiff film bonded to a pre-strained, finite-thickness, compliant substrate is obtained, and it agrees well with the finite-element analysis. The finite-thickness effect is significant when the substrate tensile stiffness cannot overwhelm the film tensile stiffness.

scholarly journals Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 993
Author(s):  
Naeim Ghavidelnia ◽  
Mahdi Bodaghi ◽  
Reza Hedayati
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Element Model ◽  
Industrial Applications ◽  
Poisson's Ratio ◽  
Geometrical Parameters ◽  
Mechanical Metamaterials ◽  
Strength And Stiffness ◽  
The One

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson’s ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts—one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler–Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson’s ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson’s ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson’s ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.

scholarly journals Computational Approach in Formulating Mechanical Characteristics of 3D Star Honeycomb Auxetic Structure

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Mozafar Shokri Rad ◽  
Zaini Ahmad ◽  
Amran Alias
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Element Model ◽  
Honeycomb Structure ◽  
Geometrical Parameters ◽  
Theoretical Formulation ◽  
Design Guideline ◽  
Structural Cell ◽  
Auxetic Materials ◽  
Structural Applications

Auxetic materials exhibit a unique characteristic due to the altered microstructure. Different structures have been used to model these materials. This paper treats a development of finite element model and theoretical formulation of 3D star honeycomb structure of these materials. Various shape parameters of the structural cell were evaluated with respect to the basic mechanical properties of the cell. Finite element and analytical approach for various geometrical parameters were numerically used to formulate the characteristics of the material. The study aims at quantifying mechanical properties for any domain in which auxetic material is of interest for variations in geometrical parameters. It is evident that mechanical properties of the material could be controlled by changing the base wall angle of the configuration. The primary outcome of the study is a design guideline for the use of 3D star honeycomb auxetic cellular structure in structural applications.

scholarly journals Size Effect on the Elastic Mechanical Properties of Beech and Its Application in Finite Element Analysis of Wood Structures

Forests ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 783 ◽  
Author(s):  
Wengang Hu ◽  
Hui Wan ◽  
Huiyuan Guan
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Elastic Constants ◽  
Wood Specimen ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Element Analysis ◽  
Cross Sectional ◽  
Wood Structures

Elastic constants of wood are fundamental parameters used in finite element analysis of wood structures. However, few studies and standards regulate the dimensions of sample used to measure elastic constants of wood. The size effect on mechanical properties (i.e., elastic constants and proportional limit stresses) of European beech (Fagus sylvatica L.) wood was studied with five different sizes samples. The data of experiments were inputted into a finite element model of self-designed chair and the loading capacity of chair was investigated by finite element method (FEM) and experiment. The results showed that nonlinear relationships were found between proportional limit stresses, cross-sectional area, and height of specimen by response surface method with R2 greater than 0.72 in longitudinal, radial, and tangential directions. Elastic moduli and shear moduli increased with the height of specimen when cross-sectional area was kept constant, and decreased with an increased cross-sectional area of specimen, when the height was a constant, while the trends of Poisson’s ratio were not as expected. The comparisons between experiment and FEM suggested that the accuracy of FEM simulation increase with the raise of width-height ratio (≤1) of specimens used to determine the elastic constants. It is recommended to use small cubic wood specimen to determine the elastic mechanical properties used for finite element analysis of beech wood structures. Further research to find optimized wood specimen dimensions to get mechanical properties for FEM is quite necessary.

Sign in / Sign up

Export Citation Format

Share Document