scholarly journals Minimum energy bounds on longitudinal elastic constants of transversely isotropic unidirectional composites

2020 ◽  
Vol 476 (2239) ◽  
pp. 20190752
Author(s):  
Duc-Chinh pham
Keyword(s):  
Elastic Constants ◽  
Minimum Energy ◽  
Young Modulus ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Arithmetic Average ◽  
Energy Bounds ◽  
Cylindrical Phase ◽  
Elastic Composites ◽  
Energy Principles

We consider the n -component transversely isotropic unidirectional elastic composites, the longitudinal axis of which is parallel to those of the transversely isotropic components as well as the generators of the cylindrical phase boundaries between them. From the minimum energy and complementary energy principles, with appropriate constant strain and piece-wise constant stress trial fields, optimization and iteration techniques, a set of bounds for the macroscopic (effective) longitudinal elastic constants of the composites (including the simple lower arithmetic average estimate for longitudinal Young modulus E eff  ≥  E V ) are constructed. Numerical examples are provided to illustrate the obtained results.

Determination of Elastic Constants for Human Femurs

1979 ◽  
Vol 101 (3) ◽  
pp. 193-197 ◽  
Author(s):  
V. G. Lappi ◽  
M. S. King ◽  
I. Le May
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Isotropic Material ◽  
Rotational Symmetry ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Transversely Isotropic Material ◽  
Axis Of Symmetry ◽  
Plane Of Isotropy

The elastic properties of the bone constituting human femurs have been determined from measurements of the velocities of ultrasonic compressional and shear waves through wet, embalmed bone samples. The bone has been shown to be a transversely isotropic material with the axis of symmetry parallel to the longitudinal axis of the bone. The values of the elastic constants were determined to be: c11=6860±330MPaE3=5500MPac12=2700±570MPaE1=4990MPac13=3760±1570MPaν31=0.39c33=8480±760MPaν12=0.20c44=2240±180MPaG31=2240MPa where the 3-axis is that of rotational symmetry and the 1- and 2-axes are in the plane of isotropy.

The Elastic Characterization of Composite Based on Ultrasonic Waves

2021 ◽  
Author(s):  
Y. H. Park ◽  
J. Dana
Keyword(s):  
Composite Materials ◽  
Fatigue Failure ◽  
Elastic Constants ◽  
Material Properties ◽  
Weight Ratio ◽  
Transversely Isotropic ◽  
Ultrasonic Waves ◽  
Material Strength ◽  
Isotropic Composite

Abstract Anisotropic composite materials have been extensively utilized in mechanical, automotive, aerospace and other engineering areas due to high strength-to-weight ratio, superb corrosion resistance, and exceptional thermal performance. As the use of composite materials increases, determination of material properties, mechanical analysis and failure of the structure become important for the design of composite structure. In particular, the fatigue failure is important to ensure that structures can survive in harsh environmental conditions. Despite technical advances, fatigue failure and the monitoring and prediction of component life remain major problems. In general, cyclic loadings cause the accumulation of micro-damage in the structure and material properties degrade as the number of loading cycles increases. Repeated subfailure loading cycles cause eventual fatigue failure as the material strength and stiffness fall below the applied stress level. Hence, the stiffness degradation measurement can be a good indication for damage evaluation. The elastic characterization of composite material using mechanical testing, however, is complex, destructive, and not all the elastic constants can be determined. In this work, an in-situ method to non-destructively determine the elastic constants will be studied based on the time of flight measurement of ultrasonic waves. This method will be validated on an isotropic metal sheet and a transversely isotropic composite plate.

scholarly journals Three-dimensional numerical simulation of mechanical properties of soil-tire mixture by discrete element method

2019 ◽  
Vol 92 ◽  
pp. 14011
Author(s):  
Mohsen Asadi ◽  
Ahmad Mahboubi
Keyword(s):  
Mechanical Properties ◽  
Shear Strength ◽  
Damping Ratio ◽  
Strain Curve ◽  
Young Modulus ◽  
Engineering Properties ◽  
Triaxial Tests ◽  
Sand Particle ◽  
Arithmetic Average ◽  
Harmonic Average

Soil engineering properties can be improved employing different methods. Among them is mixing soil with tire derived additives (TDA). TDAs generally increase some parameters of mixture such as damping ratio, permeability, ductility and also in some cases shear strength. Various properties of TDAs from mechanical properties to their geometry can affect the mixture behavior. In this paper using the YADE platform, simulations of triaxial tests on sand tire mixtures are presented. To take compressibility into consideration, each rubber crumb particle is made of several spheres connected elastically to each other. For sand particle generation the clump technique was employed. Shapes of both sand and rubber particles are inspired from real grains. As properties of sand and rubber are different, especially Young modulus, rubber sand interaction is considered as soft rigid contact. Therefor harmonic average and arithmetic average was used to compute contact Young modulus (and then stiffness). The model was validated by comparison of results of triaxial tests simulation on pure rubber sample with literature ones which both exhibited linear stress-strain curve. Then triaxial tests with different sand to rubber ratio were simulated to see whether harmonic average or arithmetic average gives the best match to literature. The results show shear strength reduces by decreasing of sand to rubber ratio. This is the same as what is reported in literature.

Do traveltimes in pulse‐transmission experiments yield anisotropic group or phase velocities?

Geophysics ◽  
1994 ◽  
Vol 59 (11) ◽  
pp. 1774-1779 ◽  
Author(s):  
Joe Dellinger ◽  
Lev Vernik
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Elastic Constants ◽  
Near Field ◽  
Frequency Dispersion ◽  
Transversely Isotropic ◽  
Sh Waves ◽  
Phase Velocities ◽  
Pulse Transmission ◽  
Transmission Technique

The elastic properties of layered rocks are often measured using the pulse through‐transmission technique on sets of cylindrical cores cut at angles of 0, 90, and 45 degrees to the layering normal (e.g., Vernik and Nur, 1992; Lo et al., 1986; Jones and Wang, 1981). In this method transducers are attached to the flat ends of the three cores (see Figure 1), the first‐break traveltimes of P, SV, and SH‐waves down the axes are measured, and a set of transversely isotropic elastic constants are fit to the results. The usual assumption is that frequency dispersion, boundary reflections, and near‐field effects can all be safely ignored, and that the traveltimes measure either vertical anisotropic group velocity (if the transducers are very small compared to their separation) or phase velocity (if the transducers are relatively wide compared to their separation) (Auld, 1973).

Elastic Constants of Composite Materials by an Inverse Determination Method Based on A Hybrid Genetic Algorithm

2010 ◽  
Vol 26 (3) ◽  
pp. 345-353 ◽  
Author(s):  
S.-F. Hwang ◽  
J.-C. Wu ◽  
Evgeny Barkanovs ◽  
Rimantas Belevicius
Keyword(s):  
Genetic Algorithm ◽  
Elastic Constants ◽  
Hybrid Genetic Algorithm ◽  
Transversely Isotropic ◽  
Determination Method ◽  
Element Analysis ◽  
Plane Shear ◽  
Effective Elastic Constants ◽  
Testing Data ◽  
Out Of Plane

AbstractA numerical method combining finite element analysis and a hybrid genetic algorithm is proposed to inversely determine the elastic constants from the vibration testing data. As verified from composite material specimens, the repeatability and accuracy of the proposed inverse determination method are confirmed, and it also proves that the concept of effective elastic constants is workable. Moreover, three different sets of assumptions to reduce the five independent elastic constants to four do not make clear difference on the obtained results by the proposed method. In addition, to obtain robust values of the five elastic constants for a transversely isotropic material, it is recommended to use the out-of-plane Poisson's ratio instead of the out-of-plane shear modulus as the fifth one.

Elastic Moduli and Elastic Constants of Alloy AuCuSi With FCC Structure Under Pressure

2019 ◽  
Vol 38 (2019) ◽  
pp. 264-272 ◽  
Author(s):  
Nguyen Quang Hoc ◽  
Bui Duc Tinh ◽  
Nguyen Duc Hien
Keyword(s):  
Elastic Constants ◽  
Elastic Moduli ◽  
Nearest Neighbor ◽  
Young Modulus ◽  
Numerical Results ◽  
Main Metal ◽  
Substitution Alloy ◽  
Rigidity Modulus ◽  
The Mean ◽  
Fcc Structure

AbstractThis paper studies on the dependence of the mean nearest neighbor distance, the Young modulus E, the bulk modulus K, the rigidity modulus G and the elastic constants C11, C12, C44 on temperature, pressure, the concentration of substitution atoms and the concentration of interstitial atoms for alloy AuCuSi (substitution alloy AuCu with interstitial atom Si) with FCC structure by the way of the statistical moment method (SMM). The numerical results for alloy AuCuSi are compared with the numerical results for main metal Au, substitution alloy AuCu, interstitial alloy AuSi, other calculated results and experiments.

Specimen Specific Multiscale Model for the Anisotropic Elastic Properties of Human Cortical Bone Tissue

2007 ◽  
Author(s):  
Justin M. Deuerling ◽  
Weimin Yue ◽  
Alejandro A. Espinoza ◽  
Ryan K. Roeder
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Structural Information ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Orientation Distribution ◽  
Tissue Properties ◽  
Apatite Crystals ◽  
Micromechanical Models ◽  
Anisotropic Elastic

The elastic constants of cortical bone are orthotropic or transversely isotropic depending on the anatomic origin of the tissue. Micromechanical models have been developed to predict anisotropic elastic properties from structural information. Many have utilized microstructural features such as osteons, cement lines and Haversian canals to model the tissue properties [1]. Others have utilized nanoscale features to model the mineralized collagen fibril [2]. Quantitative texture analysis using x-ray diffraction techniques has shown that elongated apatite crystals exhibit a preferred orientation in the longitudinal axis of the bone [3]. The orientation distribution of apatite crystals provides fundamental information influencing the anisotropy of the extracellular matrix (ECM) but has not been utilized in existing micromechanical models.

scholarly journals Bounding of Flow and Transport Analysis in Heterogeneous Saturated Porous Media: A Minimum Energy Dissipation Principle for the Bounding and Scale-Up

Hydrology ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 33 ◽  
Author(s):  
Nelson ◽  
Williams
Keyword(s):  
Porous Media ◽  
Energy Dissipation ◽  
Heterogeneous System ◽  
Minimum Energy ◽  
Scale Up ◽  
Heterogeneous Porous Media ◽  
Porous Media Flow ◽  
Rotational Flow ◽  
Energy Principles

We apply minimum kinetic energy principles from classic mechanics to heterogeneous porous media flow equations to derive and evaluate rotational flow components to determine bounding homogenous representations. Kelvin characterized irrotational motions in terms of energy dissipation and showed that minimum dynamic energy dissipation occurs if the motion is irrotational; i.e., a homogeneous flow system. For porous media flow, reductions in rotational flow represent heterogeneity reductions. At the limit, a homogeneous system, flow is irrotational. Using these principles, we can find a homogenous system that bounds a more complex heterogeneous system. We present mathematics for using the minimum energy principle to describe flow in heterogeneous porous media along with reduced special cases with the necessary bounding and associated scale-up equations. The first, simple derivation involves no boundary differences and gives results based on direct Kelvin-type minimum energy principles. It provides bounding criteria, but yields only a single ultimate scale-up. We present an extended derivation that considers differing boundaries, which may occur between scale-up elements. This approach enables a piecewise less heterogeneous representation to bound the more heterogeneous system. It provides scale-up flexibility for individual model elements with differing sizes, and shapes and supports a more accurate representation of material properties. We include a case study to illustrate bounding with a single direct scale-up. The case study demonstrates rigorous bounding and provides insight on using bounding flow to help understand heterogeneous systems. This work provides a theoretical basis for developing bounding models of flow systems. This provides a means to justify bounding conditions and results.

An energy-based approach for modelling the behaviour of packaging material during processing

2004 ◽  
Vol 218 (1) ◽  
pp. 105-118 ◽  
Author(s):  
B J Hicks ◽  
C Berry ◽  
G Mullineux ◽  
C J McPherson ◽  
A J Medl
Keyword(s):  
Theoretical Model ◽  
Minimum Energy ◽  
Packaging Material ◽  
Parametric Models ◽  
Machine Material ◽  
Software Model ◽  
Energy Principles ◽  
Improved Methods ◽  
Material Interaction ◽  
Modelling Approach

This paper deals with the investigation of improved methods for considering machine-material interaction during the design and production of packaging machinery. Minimum energy principles are used to create a theoretical model of the response of the packaging material during processing. The complex non-linear properties of the packaging material are encapsulated in parametric models generated through analysis of the physical measurement of the changing properties during processing. These two techniques are incorporated into a software model that represents the behaviour of a skillet during the erection process. This software model considers the material, the pack design and the machine system. The overall modelling approach is validated by comparison with a physical system, which shows a good correlation with the theoretical model.

Sign in / Sign up

Export Citation Format

Share Document