Prediction Of Effective Elastic Properties Research Articles

Integrated Petrophysical Evaluation and Rock Physics Modeling of Broom Creek Deep Saline Aquifer for Geological CO2 Storage

Fossil fuels, such as coal and hydrocarbons, are major drivers of global warming and are primarily responsible for worldwide greenhouse gas emissions, including carbon dioxide CO2. The storage of CO2 in deep saline reservoirs is acknowledged as one of the top practical and promising methods to reduce CO2 emissions and meet climate goals. The North Dakota Industrial Commission (NDIC) recently approved the fourth Class VI permit for a carbon capture and storage project in the Williston basin of North Dakota for the geological CO2 storage in the Broom Creek formation. The current research aimed to conduct a comprehensive petrophysical characterization and rock physics modeling of the Broom Creek deep saline reservoir to unravel the mineralogical distribution and to understand the variations in petrophysical and elastic properties across the formation. This study utilized geophysical well logs, routine core analysis, and advanced core analysis to evaluate the Broom Creek formation. Multimineral petrophysical analysis calibrated with X-ray diffraction results reveals that this formation primarily comprises highly porous clean sandstone intervals with low-porosity interspersed with dolomite, anhydrite, and silt/clay layers. The formation exhibits varying porosities up to 0.3 and Klinkenberg air permeabilities up to ∼2600 mD. The formation water resistivity using Archie’s equation is approximately 0.055 ohm-m at 150 °F, corresponding to around 63,000 ppm NaCl salinity, which is consistent with prior data. The pore throat distribution in the samples from clean sandstone intervals is primarily situated in the macro-mega scales. However, the presence of anhydrite and dolomite impedes both porosity and pore throat sizes. The accurate prediction of effective elastic properties was achieved by developing a rock physics template. Dry rock moduli were modeled using Hill’s average, while Berryman’s self-consistent scheme was employed for modeling saturated moduli.

Automatic generation of 3D micromechanical finite element model with periodic boundary conditions to predict elastic properties of bamboo fibre-reinforced composites

This study presents an automatic algorithm to generate a three-dimensional (3D) micromechanical finite element (FE) model to predict elastic behaviours of biocomposites reinforced with unidirectional (UD) continuous natural fibres such as bamboo fibres. The developed algorithm constructs a virtual FE framework by generating stochastic Representative Volume Elements (RVEs) of fibre-reinforced composites incorporating random fibre arrangement and random assignment of fibre radii. It also applies various loading scenarios and periodic boundary conditions to simulate elastic behaviours accurately. The algorithm generates 3D periodic RVEs by introducing boundary and corner fibres. All the 3D RVE models, representing different fibre-reinforced composites, various loading cases, and periodic boundary conditions, are automatically created using Python scripting with the Abaqus FE solver. The accuracy of the algorithm and virtual FE test model is validated through comparisons with analytical models and experimental results. The effects of different types of fibre radius assignment, fibre volume fraction, and fibre periodicity on the prediction of effective elastic properties are investigated. The study also establishes correlations between all elastic constants of bamboo fibre-reinforced composites and the fibre volume fraction.

Integrated wavelet-learning method for macroscopic mechanical properties prediction of concrete composites with hierarchical random configurations

In this research, a novel integrated wavelet-learning approach with high-accuracy and efficient prediction capability is developed to predict the effective elastic properties of concrete composites with hierarchical random configurations and heterogeneous elasticity in multiple spatial scales. The significant contributions of this work include: (1) The random structural heterogeneities and material uncertainties of concrete composites in meso-scale and micro-scale are modeled on the basis of modified authors’ previous researches and Weibull probabilistic model separately. (2) Innovative stochastic three-scale asymptotic homogenization method (STAHM), background grid technique and padding strategy are presented to thoroughly acquire the doubly random geometry and material features of concrete composites with hierarchical random configurations for constructing concrete material databases. (3) The wavelet transform is utilized to preprocess the high-dimensional data features of the material databases, and the wavelet coefficients are employed as the novel input neurons for efficiently establishing more plain wavelet-neural networks that possess increasing capacity and resisting noise for approximating mappings of high complexity and nonlinearity. The numerical experiments and achieved results demonstrate that the integrated wavelet-learning approach is robust for the high-accuracy and efficient prediction of effective elastic properties of concrete materials with random heterogeneity patterns in multiple spatial scales.

A new constitutive model to predict effective elastic properties of plain weave fabric composites

In this study, a new constitutive model has been developed to predict the elastic behavior of plain weave textile composites, using the finite element (FE) method. The geometric conditions and basic assumptions of this model are based on the basics of a continuum theory developed for the plane curved composites. In this model, the mechanical properties of the weave region and pure matrix region is calculated separately and then imported for the FE analysis. This new constitutive model is used to implement the mechanical properties of weave region in the representative volume element (RVE). The constitutive relations are implemented as user-material subroutine code (UMAT) in ABAQUS FE software. The results of FE analysis have been compared with experimental results and other data available in the literature. These comparisons confirmed the capability of the presented model for the prediction of effective elastic properties of plain weave fabric composites.

Prediction of effective elastic properties of a polypropylene component by an enhanced multiscale simulation of the injection molding process

In the injection molding process of semi-crystalline polymers, the melt undergoes a complex deformation and cooling history which results in an inhomogeneous distribution of spherulites in the component. To evaluate these inhomogeneities in an isotactic polypropylene (α-iPP) part, an integrated multi-scale simulation approach has been developed in Laschet et al. (2017a). This approach combines a macroscale mold filling and heat transfer analysis with a crystallization model at the microscale and a two-scale homogenization scheme in order to calculate microstructure dependent elastic properties of the PP component. This approach is extended here by adding some features improving the local Hooke matrix predictions. A link between Molecular Dynamics (MD) simulations and the homogenization scheme is achieved in order to obtain unknown properties of the pure amorphous and crystalline phases. Next, the accuracy of the crystallization model is improved by considering not only isothermal but also athermal nucleation. The spherulite growth is now evaluated by a continuous cellular growth algorithm. Then, several numerical improvements have been integrated in the homogenization tool. The main ones are the implementation of stabilized mixed finite elements to handle accurately the quasi-incompressibility of the amorphous phase and the application of periodic boundary conditions via a master-slave projection algorithm. Eventually, the distribution of effective mechanical properties over the component thickness is compared for different crystallization scenarios with measured elastic moduli.

Elastic properties of sands, Part 2: Implementation of contact‐based model to determine the elasticity of the grains from ultrasonic measurements

ABSTRACTThe prediction of effective elastic properties of a granular medium using ultrasonic data based on contact models has been studied widely in both laboratory experiments and numerical simulations. In contrast, a calculation of the elastic properties of the constituent grains using similar data by inverting the equations from those models is a rather new concept. To do so, we have developed a controlled experiment technique that includes a uniaxial compaction test and measures ultrasonic velocities of four unconsolidated quartz sand samples with different sorting and grain shapes. We observe that both P‐ and S‐wave velocities are significantly influenced by the microstructure or internal arrangement of the grains. Well sorted and more spherical and rounded samples show higher velocities than the poorly sorted and less spherical and rounded samples. A microstructural parameter – namely coordination number – we have calculated from high resolution micro computed tomography images provides a good match between the model and dynamic effective bulk moduli of the sand pack. Combining this coordination number with a frictional parameter calculated from the measured velocity ratios has been very effective to fit the model with the dynamic effective shear moduli. Using these two key parameters along with the experiment results in the contact model we have been able to obtain the elastic parameters of the quartz sand grains in the sample. Elastic parameters obtained thus are very close to the actual values of the quartz grains found in the literature. This technique can be useful in hard rock mineral exploration where missing core samples or an absence of well logs can be replaced by laboratory measurements of powders to find the elasticity or velocities of the rocks. Moreover, the elastic properties of the solid phase calculated using this technique can be used as input parameters for the fluid substitution and rock physics characterization of unconsolidated reservoir sands.

Prediction of effective elastic properties of fiber reinforced composites using fiber orientation tensors

The main objective of this work is to give an answer to the question: is it sufficient to consider only the second-order fiber orientation tensor as microstructure variable describing the orientation distribution of short-fiber reinforced composites (SFRCs) in the prediction of effective elastic properties? This question is addressed in the context of SFRCs on the one hand with an overall transversal symmetric orientation distribution of fibers and, hence, effective transversally isotropic properties, and on the other hand with experimentally determined microstructure data using micro-computed tomography. Applying the maximum entropy principle, it is shown, how the fiber orientation distribution function (FODF) can be estimated by relying on the second and/or the fourth-order orientation tensor, only. Both estimates are used within the self-consistent and the interaction direct derivate approach to calculate the effective linear elastic properties. It is shown, that the predicted stiffness tensors significantly depend on the estimation of the FODF. Relative deviations of up to 20% in terms of stiffnesses and up to 46% in terms of Young's modulus are observed. For the experimentally determined microstructure, small deviations of up to 4.3% are found.

Finite element prediction of effective elastic properties of interpenetrating phase composites with architectured 3D sheet reinforcements

• A new type of 3D interpenetrating phase composite (IPC) is introduced. • Effective elastic properties are predicted using FEM. • 3D triply periodic minimal surfaces are used as solid shell reinforcements in IPC. • The effect of the architecture of 3D solid shell architectures is investigated. • Manufacturability of the proposed IPC through 3D printing is shown. In this paper, novel triply periodic minimal surfaces (TPMS) are converted into three-dimensional solid-sheet networks and used as reinforcements within a matrix material creating interpenetrating phase composites (IPC). Schwarz P (P), Schwarz D (D), Schwarz CLP (CLP), Schoen I-WP (IWP), Neovius C(P) (Neovius), Schoen G (Gyroid), Fischer and Koch S (S) TPMS architectures are investigated. The IPCs with the TPMS architectures are modeled using the finite element method, and their effective elastic properties (uniaxial, shear, and bulk moduli, anisotropy index, Poisson's ratio) are evaluated and compared with those of traditional composites (particulate and fibrous). The effects of the TPMS architecture, its volume fraction, and contrast in elastic properties between the two phases in the IPC are studied. Foam (cellular solid) is obtained if one of the phases in the proposed IPC is removed and its elastic properties are also estimated. It is shown that the TPMS architecture significantly affects effective elastic moduli when the contrast is high. The IWP-type IPC and foam give largest uniaxial and bulk moduli.

Stiffness constants prediction of nanocomposites using a periodic 3D‐FEM model

AbstractPredictive models, which enable the prediction of nanocomposite properties from their morphologies and account for polymer orientation, could greatly assist the exploitation of this new class of materials in more diversified and demanding market fields. This article focuses on the prediction of effective elastic properties (Young's moduli) of polymer nanocomposite films (copolyamide‐6/nanoclay) using 3D analytical (based on the Mori‐Tanaka theory) and 3D finite element (FE) models. The analytical model accounts for the orientation of polymer chains induced by drawing. 3D FE model exploits the representative volume element concept and accounts for the nanocomposite morphology as determined from transmission electron microscopy experiments. Model predictions were compared with experimental results obtained for nanocomposite films produced by means a pilot‐scale film blowing equipment and collected at different draw ratios. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012

Microstructure modelling and prediction of effective elastic properties of 3D multiphase and multilayer braided composite

This paper is focused on the microstructure modelling and evaluation of effective elastic properties of three-dimensional multiphase and multilayer braided composite. Regarding the multiscale characteristics of the composite, the microstructure modelling is carried out sequentially from fibre to tow scale. The geometrical configuration of the microstructure is first analysed, and mathematical relations among different geometrical parameters are derived on each scale. Second, effective elastic properties are obtained based on the sequential homogenisation from fibre to tow scale. A strain energy based method is proposed to evaluate effective elastic properties with specific boundary conditions imposed on the microstructure. Numerical results obtained by the proposed method and the microstructure model show a good agreement with the results measured experimentally.

Topology optimization of material microstructures using strain energy-based prediction of effective elastic properties

An alternative strain energy method is proposed for the prediction of effective elastic properties of orthotropic materials in this paper. The method is implemented in the topology optimization procedure to design cellular solids. A comparative study is made between the strain energy method and the well-known homogenization method. Numerical results show that both methods agree well in the numerical prediction and sensitivity analysis of effective elastic tensor when homogeneous boundary conditions are properly specified. Two dimensional and 3 dimensional microstructures are optimized for maximum stiffness designs by combining the proposed method with the dual optimization algorithm of convex programming. Satisfactory results are obtained for a variety of design cases.

Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures

An alternative strain energy method is proposed for the prediction of effective elastic properties of orthotropic materials in this paper. The method is implemented in the topology optimization procedure to design cellular solids. A comparative study is made between the strain energy method and the well-known homogenization method. Numerical results show that both methods agree well in the numerical prediction and sensitivity analysis of effective elastic tensor when homogeneous boundary conditions are properly specified. Two dimensional and three dimensional microstructures are optimized for maximum stiffness designs by combining the proposed method with the dual optimization algorithm of convex programming. Satisfactory results are obtained for a variety of design cases.

Size effect on elastic properties of random composites

In addition to the prediction of effective elastic properties of random media, the statistical variations of these properties for finite size specimens are of practical interest. From finite element method calculations on simulated 2D random media, size effects are studied and modelled. They enable us to draw practical conclusions for finite element applications to elastic random media.