scholarly journals Linking snow microstructure to its macroscopic elastic stiffness tensor: A numerical homogenization method and its application to 3‐D images from X‐ray tomography

2015 ◽  
Vol 42 (19) ◽  
pp. 8031-8041 ◽  
Author(s):  
A. Wautier ◽  
C. Geindreau ◽  
F. Flin
Keyword(s):  
Elastic Stiffness ◽  
Homogenization Method ◽  
Numerical Homogenization ◽  
Stiffness Tensor ◽  
X Ray ◽  
Elastic Stiffness Tensor ◽  
Snow Microstructure

Effect of variations in microstructure on clay elastic anisotropy

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. MR73-MR82 ◽  
Author(s):  
Colin M. Sayers ◽  
Lennert D. den Boer
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Elastic Anisotropy ◽  
Rock Physics ◽  
Elastic Stiffness ◽  
Single Domain ◽  
Model Parameters ◽  
Stiffness Tensor ◽  
Elastic Stiffness Tensor ◽  
Clay Platelets

Rock physics provides a crucial link between seismic and reservoir properties, but it requires knowledge of the elastic properties of rock components. Whereas the elastic properties of most rock components are known, the anisotropic elastic properties of clay are not. Scanning electron microscopy studies of clay in shales indicate that individual clay platelets vary in orientation but are aligned locally. We present a simple model of the elastic properties of a region (domain) of locally aligned clay platelets that accounts for the volume fraction, aspect ratio, and elastic-stiffness tensor of clay platelets, as well as the effective elastic properties of the interplatelet medium. Variations in clay anisotropy are quantified by examining the effects of varying model parameters upon the effective transverse-isotropic (TI) elastic-stiffness tensor of a domain. Statistics of these distributions and correlations between stiffnesses and anisotropy parameters enable the most probable sets of stiffnesses to be identified for rock physics calculations. The mean of these distributions is on the order of twice the mode for in-plane stiffnesses ([Formula: see text], [Formula: see text], [Formula: see text]), but it is of the same order as the mode for out-of-plane stiffnesses ([Formula: see text], [Formula: see text], [Formula: see text]). Despite random sampling, well-defined relations emerge, consistent with similar shale relations reported in the literature. Expressing these relations in terms of [Formula: see text] for a single domain of aligned clay platelets facilitates their general application. In the limit that the volume fraction approaches unity, the elastic stiffnesses thus derived reproduce those of the clay mineral assumed as platelets. Given the elastic-stiffness tensor of a single domain of aligned clay platelets, the effective TI elastic-stiffness tensor of clay is obtained by integrating over the clay-platelet orientation-distribution function.

scholarly journals Combining AFM and Acoustic Probes to Reveal Changes in the Elastic Stiffness Tensor of Living Cells

2014 ◽  
Vol 107 (7) ◽  
pp. 1502-1512 ◽  
Author(s):  
Nadja Nijenhuis ◽  
Xuegen Zhao ◽  
Alex Carisey ◽  
Christoph Ballestrem ◽  
Brian Derby
Keyword(s):  
Elastic Stiffness ◽  
Living Cells ◽  
Stiffness Tensor ◽  
Elastic Stiffness Tensor

scholarly journals Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

2017 ◽  
Vol 11 (3) ◽  
pp. 1465-1485 ◽  
Author(s):  
Antoine Wautier ◽  
Christian Geindreau ◽  
Frédéric Flin
Keyword(s):  
Laboratory Tests ◽  
Mechanical Response ◽  
Numerical Homogenization ◽  
X Ray ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Definition Of ◽  
Snow Microstructure ◽  
Homogenization Problems ◽  
Snow Samples

Abstract. While the homogenization of snow elastic properties has been widely reported in the literature, homogeneous rate-dependent behavior responsible for the densification of the snowpack has hardly ever been upscaled from snow microstructure. We therefore adapt homogenization techniques developed within the framework of elasticity to the study of snow viscoplastic behavior. Based on the definition of kinematically uniform boundary conditions, homogenization problems are applied to 3-D images obtained from X-ray tomography, and the mechanical response of snow samples is explored for several densities. We propose an original post-processing approach in terms of viscous dissipated powers in order to formulate snow macroscopic behavior. Then, we show that Abouaf models are able to capture snow viscoplastic behavior and we formulate a homogenized constitutive equation based on a density parametrization. Eventually, we demonstrate the ability of the proposed models to account for the macroscopic mechanical response of snow for classical laboratory tests.

scholarly journals Modified Eshelby tensor for an anisotropic matrix with interfacial damage

2018 ◽  
Vol 24 (6) ◽  
pp. 1749-1762 ◽  
Author(s):  
Sangryun Lee ◽  
Jinyeop Lee ◽  
Seunghwa Ryu
Keyword(s):  
Spherical Inclusion ◽  
Elastic Stiffness ◽  
Eshelby Tensor ◽  
Algebraic Expression ◽  
Stiffness Tensor ◽  
Interfacial Damage ◽  
Element Analysis ◽  
Linear Spring ◽  
Elastic Stiffness Tensor ◽  
Order Identity

We derive a simple tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities (the fourth-order identity tensor, the elastic stiffness tensor, and the Eshelby tensor) and two scalar quantities (the inclusion radius and interfacial spring constant), when the interfacial damage is modelled as a linear-spring layer of vanishing thickness. We validate the expression for a triclinic crystal involving 21 independent elastic constants against finite element analysis.

scholarly journals Elastic Coefficients of β-HMX as Functions of Pressure and Temperature from Molecular Dynamics

Crystals ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 1123
Author(s):  
Andrey Pereverzev ◽  
Tommy Sewell
Keyword(s):  
Molecular Dynamics ◽  
Elastic Stiffness ◽  
Cauchy Stress ◽  
Stiffness Tensor ◽  
Fixed Temperature ◽  
Equilibrium Stress ◽  
Strain Components ◽  
Elastic Stiffness Tensor ◽  
Derivatives Of ◽  
Elastic Coefficients

The isothermal second-order elastic stiffness tensor and isotropic moduli of β-1,3,5,7- tetranitro-1,3,5,7-tetrazoctane (β-HMX) were calculated, using the P21/n space group convention, from molecular dynamics for hydrostatic pressures ranging from 10−4 to 30 GPa and temperatures ranging from 300 to 1100 K using a validated all-atom flexible-molecule force field. The elastic stiffness tensor components were calculated as derivatives of the Cauchy stress tensor components with respect to linear strain components. These derivatives were evaluated numerically by imposing small, prescribed finite strains on the equilibrated β-HMX crystal at a given pressure and temperature and using the equilibrium stress tensors of the strained cells to obtain the derivatives of stress with respect to strain. For a fixed temperature, the elastic coefficients increase substantially with increasing pressure, whereas, for a fixed pressure, the elastic coefficients decrease as temperature increases, in accordance with physical expectations. Comparisons to previous experimental and computational results are provided where possible.

Sign in / Sign up

Export Citation Format

Share Document