Effect of Volume Element Geometry on Convergence to a Representative Volume

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
Katherine Acton ◽  
Connor Sherod ◽  
Bahador Bahmani ◽  
Reza Abedi
Keyword(s):  
Material Property ◽  
Effective Properties ◽  
Probability Distributions ◽  
Voronoi Tessellation ◽  
Strength Properties ◽  
Volume Element ◽  
Small Scale ◽  
Material Strength ◽  
Representative Volume ◽  
Proportional Limit Stress

To accurately simulate fracture, it is necessary to account for small-scale randomness in the properties of a material. Apparent properties of statistical volume element (SVE) can be characterized below the scale of a representative volume element (RVE). Apparent properties cannot be defined uniquely for an SVE, in the manner that unique effective properties can be defined for an RVE. Both constitutive behavior and material strength properties in SVE must be statistically characterized. The geometrical partitioning method can be critically important in affecting the probability distributions of mesoscale material property parameters. Here, a Voronoi tessellation-based partitioning scheme is applied to generate SVE. Resulting material property distributions are compared with those from SVE generated by square partitioning. The proportional limit stress of the SVE is used to approximate SVE strength. Superposition of elastic results is used to obtain failure strength distributions from boundary conditions at variable angles of loading.

Mesoscale Material Strength Characterization for Use in Fracture Modeling

2018 ◽  
Author(s):  
Katherine Acton ◽  
Bahador Bahmani ◽  
Reza Abedi
Keyword(s):  
Material Property ◽  
Effective Properties ◽  
Probability Distributions ◽  
Voronoi Tessellation ◽  
Strength Properties ◽  
Small Scale ◽  
Material Strength ◽  
Fracture Modeling ◽  
Strength Characterization ◽  
Proportional Limit Stress

To accurately simulate fracture, it is necessary to account for small-scale randomness in the properties of a material. Apparent properties of Statistical Volume Elements (SVE), can be characterized below the scale of a Representative Volume Element (RVE). Apparent properties cannot be defined uniquely for an SVE, in the manner that unique effective properties can be defined for an RVE. Both constitutive behavior and material strength properties in SVE must be statistically characterized. The geometrical partitioning method can be critically important in affecting the probability distributions of mesoscale material property parameters. Here, a Voronoi tessellation based partitioning scheme is applied to generate SVE. Resulting material property distributions are compared with those from SVE generated by square partitioning. The proportional limit stress of the SVE is used to approximate SVE strength. Superposition of elastic results is used to obtain failure strength distributions from boundary conditions at variable angles of loading.

Crystal Plasticity Simulation of the Bauschinger Effect of Polycrystalline AA7075 through a Texture-Based Representative Volume Element Model

2014 ◽  
Vol 553 ◽  
pp. 22-27
Author(s):  
Ling Li ◽  
Lu Ming Shen ◽  
Gwénaëlle Proust
Keyword(s):  
Finite Element ◽  
Representative Volume Element ◽  
Crystal Plasticity ◽  
Bauschinger Effect ◽  
Voronoi Tessellation ◽  
Strain Curve ◽  
Element Model ◽  
Volume Element ◽  
Model Parameters ◽  
Representative Volume

A texture-based representative volume element (TBRVE) model is developed for the three-dimensional crystal plasticity (CP) finite element simulations of the Bauschinger effect (BE) of polycrystalline aluminium alloy 7075 (AA7075). In the simulations, the grain morphology is created using the Voronoi tessellation method with the material texture systematically discretised from experiment. A modified CP constitutive model, which takes into account the backstress, is used to simulate the BE during cyclic loading. The model parameters are calibrated using the first cycle stress-strain curve and used to predict the mechanical response to the cyclic saturation of AA7075. The results indicate that the proposed TBRVE CP finite element model can effectively capture the BE at the grain level.

scholarly journals Investigation on Alamparai Fort by Utilization of Organic Materials for Improvement of Stability of Heritage Structure

2021 ◽  
Author(s):  
Kotteeswaran Santhanam ◽  
Ravi Ramadoss
Keyword(s):  
Seismic Analysis ◽  
Strength Properties ◽  
Small Scale ◽  
Strength Analysis ◽  
Material Strength ◽  
Existing Structures ◽  
Seismic Modelling ◽  
Punch Test ◽  
Mortar Strength ◽  
The Stability

Abstract Heritage structures are valuable monuments to describe the culture and traditions of the country. These heritage structures get deformed in today's scenario by natural or artificial disasters. Hence, to preserve these heritage structures, restoration was introduced to restore the ancient building with new binding agents. Rehabilitation can take place only by analysing the properties of existing structures. Based on the existing structure properties, the alternative binding agent selected; can regain the same strength and shape of the heritage structures. Based on these, the restoration of Alamparai fort was performed by analysing the fort materials using mortar strength analysis by core-drilling, double punch test, and small-scale masonry test. The arch properties are also analysed by performing seismic analysis based on the mortar strength properties. The stability analysis of the organic and existing materials shows that Gur and haritaki is the best agent for restoring the fort. Hence, the mortar strength and seismic analysis of these materials performed using diagonal shear test and seismic modelling of the fort. The proposed material strength tests results indicate that the Gur and Haritaki is the best agent to restore the fort. The fort was restored with these materials; it survived in Nivar cyclone crossed on 26th November 2020.

On the size of representative volume element for Darcy law in random media

2006 ◽  
Vol 462 (2074) ◽  
pp. 2949-2963 ◽  
Author(s):  
X Du ◽  
M Ostoja-Starzewski
Keyword(s):  
Representative Volume Element ◽  
Random Media ◽  
Effective Properties ◽  
Finite Size ◽  
Hard Core ◽  
Volume Element ◽  
Dirichlet Boundary Conditions ◽  
Darcy Law ◽  
Representative Volume ◽  
Micro Channels

Most studies of effective properties of random heterogeneous materials are based on the assumption of the existence of a representative volume element (RVE), without quantitatively specifying its size L relative to that of the micro-heterogeneity d . In this paper, we study the finite-size scaling trend to RVE of the Darcy law for Stokesian flow in random porous media, without invoking any periodic structure assumptions, but only assuming the microstructure's statistics to be spatially homogeneous and ergodic. By analogy to the existing methodology in thermomechanics of random materials, we first formulate a Hill–Mandel condition for the Darcy flow velocity and pressure gradient fields. This dictates uniform Neumann and Dirichlet boundary conditions, which, with the help of two variational principles, lead to scale-dependent hierarchies on effective (RVE level) permeability. To quantitatively assess the scaling trend towards the RVE, these hierarchies are computed for various porosities of random disc systems, where the disc centres are generated by a planar hard-core Poisson point field. Overall, it turns out that the higher is the density of random discs—or, equivalently, the narrower are the micro-channels in the system—the smaller is the size of RVE pertaining to the Darcy law.

Mesoscale Models Characterizing Material Property Fields Used As a Basis for Predicting Fracture Patterns in Quasi-Brittle Materials

2017 ◽  
Author(s):  
Katherine A. Acton ◽  
Sarah C. Baxter ◽  
Bahador Bahmani ◽  
Philip L. Clarke ◽  
Reza Abedi
Keyword(s):  
Crack Propagation ◽  
Material Property ◽  
Mesoscale Model ◽  
Voronoi Tessellation ◽  
Brittle Materials ◽  
Material Behavior ◽  
Small Scale ◽  
Element Analysis ◽  
Stress Criterion ◽  
Fracture Patterns

To accurately predict fracture patterns in quasi-brittle materials, it is necessary to accurately characterize heterogeneity in the properties of a material microstructure. This heterogeneity influences crack propagation at weaker points. Also, inherent randomness in localized material properties creates variability in crack propagation in a population of nominally identical material samples. In order to account for heterogeneity in the strength properties of a material at a small scale (or “microscale”), a mesoscale model is developed at an intermediate scale, smaller than the size of the overall structure. A central challenge of characterizing material behavior at a scale below the representative volume element (RVE), is that the stress/strain relationship is dependent upon boundary conditions imposed. To mitigate error associated with boundary condition effects, statistical volume elements (SVE) are characterized using a Voronoi tessellation based partitioning method. A moving window approach is used in which partitioned Voronoi SVE are analysed using finite element analysis (FEA) to determine a limiting stress criterion for each window. Results are obtained for hydrostatic, pure and simple shear uniform strain conditions. A method is developed to use superposition of results obtained to approximate SVE behavior under other loading conditions. These results are used to determine a set of strength parameters for mesoscale material property fields. These random fields are then used as a basis for input in to a fracture model to predict fracture patterns in quasi-brittle materials.

scholarly journals Representative volume element based micromechanical modelling of rod shaped glass filled epoxy composites

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Aanchna Sharma ◽  
Yashwant Munde ◽  
Vinod Kushvaha
Keyword(s):  
Representative Volume Element ◽  
Poisson’S Ratio ◽  
Volume Fraction ◽  
Tensile Modulus ◽  
Volume Element ◽  
Poisson's Ratio ◽  
Epoxy Composites ◽  
Micromechanical Modeling ◽  
Representative Volume ◽  
Shaped Glass

AbstractIn this study, Representative Volume Element based micromechanical modeling technique has been implemented to assess the mechanical properties of glass filled epoxy composites. Rod shaped glass fillers having an aspect ratio of 80 were used for preparing the epoxy composite. The three-dimensional unit cell model of representative volume element was prepared with finite element analysis tool ANSYS 19 using the periodic square and hexagonal array with an assumption that there is a perfect bonding between the filler and the epoxy matrix. Results revealed that the tensile modulus increases and Poisson’s ratio decreases with increase in the volume fraction of the filler. To study the effect of filler volume fraction, the pulse echo techniques were used to experimentally measure the tensile modulus and Poisson’s ratio for 5% to 15% volume fraction of the filler. A good agreement was found between the RVE based predicted values and the experimental results.

Localization simulation of forming-induced residual stresses of composite using prescribed boundary

2021 ◽  
pp. 073168442094118
Author(s):  
Qi Wu ◽  
Hongzhou Zhai ◽  
Nobuhiro Yoshikawa ◽  
Tomotaka Ogasawara ◽  
Naoki Morita
Keyword(s):  
Residual Stresses ◽  
Representative Volume Element ◽  
Computational Cost ◽  
Volume Element ◽  
Thermoplastic Composite ◽  
Structural Deformation ◽  
Element Analysis ◽  
Micro Scale ◽  
Representative Volume ◽  
Localization Approach

A novel localization approach that seamlessly bridges the macro- and micro-scale models is proposed and used to model the forming-induced residual stresses within a representative volume element of a fiber reinforced composite. The approach uses a prescribed boundary that is theoretically deduced by integrating the asymptotic expansion of a composite and the equal strain transfer, thus rendering the simulation setting to be easier than conventional approaches. When the localization approach is used for the finite element analysis, the temperature and residual stresses within an ideal cubic representative volume element are precisely simulated, given a sandwiched thermoplastic composite is formed under one-side cooling condition. The simulation results, after being validated, show that the temperature gradient has an impact on the local residual stresses, especially on the in-plane normal stress transverse to the fiber, and consequently, influences the structural deformation. This newly designed localization approach demonstrates the advantages of enhanced precision and reduced computational cost owing to the fast modeling of the finely meshed representative volume element. This is beneficial for a detailed understanding of the actual residual stresses at the micro-scale.

Sign in / Sign up

Export Citation Format

Share Document