Determination of effective properties of granite rock: A numerical investigation

MRS Advances ◽  
2018 ◽  
Vol 3 (37) ◽  
pp. 2159-2168
Author(s):  
Rehema Ndeda ◽  
S. E. M Sebusang ◽  
R. Marumo ◽  
Erich O. Ogur
Keyword(s):  
Elastic Properties ◽  
Close Agreement ◽  
Effective Properties ◽  
Volume Element ◽  
The Finite Element Method ◽  
Effective Elastic Properties ◽  
Spherical Inclusions ◽  
Periodic Microstructures ◽  
Crack Profile

ABSTRACTMacroscopic strength of the rock depends on the behavior of the micro constituents, that is, the minerals, pores and crack profile. It is important to determine the effect of these constituents on the overall behavior of the rock. This study seeks to estimate the effective elastic properties of granite using the finite element method. A representative volume element (RVE) of suitable size with spherical inclusions of different distribution is subjected to loading and the effective elastic properties determined. The results are compared to those obtained from analytical methods. The elastic properties are obtained in both the axial and transverse direction to account for anisotropy. It is observed that there is congruence in the results obtained both analytically and numerically. The method of periodic microstructures exhibits close agreement with the numerical results.

A FINITE ELEMENT ANALYSIS OF EFFECTIVE THERMOELECTROELASTIC PROPERTIES OF COMPOSITES WITH A DOUBLY PERIODIC ARRAY OF PIEZOELECTRIC FIBERS

2009 ◽  
Vol 23 (06n07) ◽  
pp. 1689-1694 ◽  
Author(s):  
PENG YAN ◽  
CHIPING JIANG
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Cell Model ◽  
Periodic Array ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Uniform Temperature Field ◽  
Periodic Microstructures ◽  
Doubly Periodic Array ◽  
Electrical Loads

This work deals with modeling of 1-3 thermoelectroelastic composites with a doubly periodic array of piezoelectric fibers under arbitrary combination of mechanical, electrical loads and a uniform temperature field. The finite element method (FEM) based on a unit cell model is extended to take into account the thermoelectroelastic effect. The FE predictions of effective properties for several typical periodic microstructures are presented, and their influences on effective properties are discussed. A comparison with the Mori-Tanaka method is made to estimate the application scope of micromechanics. The study is useful for the design and assessment of composites.

Probability of Debonding and Effective Elastic Properties of Particle-Reinforced Composites

2017 ◽  
Vol 33 (6) ◽  
pp. 789-796 ◽  
Author(s):  
L. C. Bian ◽  
W. Liu ◽  
J. Pan
Keyword(s):  
Elastic Properties ◽  
Effective Properties ◽  
Effective Elastic Modulus ◽  
Reinforced Composites ◽  
Effective Elastic Properties ◽  
Linear Elastic ◽  
Mechanics Model ◽  
Equivalent Inclusion ◽  
Particle Reinforced Composites ◽  
Good Agreement

AbstractIn this paper, the effective properties of particle-reinforced composites with a weakened interphase are investigated. The particle and interphase are regarded as an equivalent-inclusion, and the interphase zone around the particle is modeled as a linear elastic spring layer. A modified micro-mechanics model is proposed to obtain the effective elastic modulus. Moreover, a statistical debonding criterion is proposed to characterize the varying probability of the evolution of interphase debonding. Numerical examples are considered to illustrate the effect of imperfect interphases on the effective properties of particle-reinforced composites. It is found that the effective elastic properties obtained in the present work are in a good agreement with the existing data from the literatures.

Digital rock physics and laboratory considerations on a high-porosity volcanic rock

2020 ◽  
Author(s):  
Laura L. Schepp ◽  
Benedikt Ahrens ◽  
Martin Balcewicz ◽  
Mandy Duda ◽  
Mathias Nehler ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Elastic Properties ◽  
Effective Properties ◽  
Rock Physics ◽  
Numerical Results ◽  
High Porosity ◽  
Effective Elastic Properties ◽  
Digital Rock Physics ◽  
Digital Rock ◽  
Laboratory Investigations

<p>Microtomographic imaging techniques and advanced numerical simulations are combined by digital rock physics (DRP) to obtain effective physical material properties. The numerical results are typically used to complement laboratory investigations with the aim to gain a deeper understanding of physical processes related to transport (e.g. permeability and thermal conductivity) and effective elastic properties (e.g. bulk and shear modulus). The present study focuses on DRP and laboratory techniques applied to a rock called reticulite, which is considered as an end-member material with respect to porosity, stiffness and brittleness of the skeleton. Classical laboratory investigations on effective properties, such as ultrasonic transmission measurements and uniaxial deformation experiments, are very difficult to perform on this class of high-porosity and brittle materials.</p><p>Reticulite is a pyroclastic rock formed during intense Hawaiian fountaining events. The open honeycombed network has a porosity of more than 80 % and consists of bubbles that are supported by glassy threads. The natural mineral has a strong analogy to fabricated open-cell foams. By comparing experimental with numerical results and theoretical estimates we demonstrate the potential of digital material methodology with respect to the investigation of porosity, effective elastic properties, thermal conductivity and permeability</p><p>We show that the digital rock physics workflow, previously applied to conventional rock types, yields reasonable results for a high-porosity rock and can be adopted for fabricated foam-like materials. Numerically determined effective properties of reticulite are in good agreement with the experimentally determined results. Depending on the fields of application, numerical methods as well as theoretical estimates can become reasonable alternatives to laboratory methods for high porous foam-like materials.</p>

Micromechanical modeling of 3D printable interpenetrating phase composites with tailorable effective elastic properties including negative Poisson's ratio

2017 ◽  
Vol 02 (04) ◽  
pp. 1750015 ◽  
Author(s):  
L. Ai ◽  
X.-L. Gao
Keyword(s):  
Elastic Properties ◽  
Effective Properties ◽  
Matrix Material ◽  
Micromechanical Model ◽  
Micromechanical Modeling ◽  
Tetragonal Symmetry ◽  
Geometrical Parameters ◽  
Fe Model ◽  
Effective Elastic Properties ◽  
Interpenetrating Phase Composites

3D printable two-phase interpenetrating phase composites (IPCs) are designed by embedding a 3D periodic re-entrant lattice structure (as the reinforcing phase) in a matrix phase. These IPCs display the cubic or tetragonal symmetry. A micromechanical model is developed to evaluate effective elastic properties of the IPCs. Effective Young's moduli, shear moduli and Poisson's ratios (PRs) of each IPC are determined from the effective stiffness and compliance matrices of the composite, which are obtained through a homogenization analysis using a unit cell-based finite element (FE) model incorporating periodic boundary conditions. The FE simulation results are also compared with those based on various analytical bounding techniques in micromechanics, including the Voigt–Reuss, Hashin–Shtrikman, and Tuchinskii bounds. The effective properties of the IPC can be tailored by adjusting five geometrical parameters, including two strut lengths, two re-entrant angles and one strut diameter, and elastic properties of the two constituent materials. The numerical results reveal that IPCs with a negative PR can be generated by using a compliant matrix material and large re-entrant angles. In addition, it is found that the two re-entrant angles can greatly affect other effective elastic properties of the IPC: the effective shear modulus can be enhanced, while the effective Young's modulus can be enhanced or compromised with the increase of the re-entrant angles. Furthermore, it is seen that by adjusting one of the two re-entrant angles or one of the two strut lengths, the material symmetry exhibited by the IPC can be changed from cubic to tetragonal.

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