Publications
254 results found
Lutz MP, Zimmerman RW, 2015, Effect of the interphase zone on the conductivity or diffusivity of a particulate composite using Maxwell's homogenization method, International Journal of Engineering Science, Vol: 98, Pages: 51-59, ISSN: 0090-6913
An analytical model is developed for the conductivity (diffusivity, permeability, etc.) of a material that contains a dispersion of spherical inclusions, each surrounded by an inhomogeneous interphase zone in which the conductivity varies radially according to a power law. The method of Frobenius series is used to obtain an exact solution for the problem of a single such inclusion in an infinite matrix. Two versions of the solution are developed, one of which is more computationally convenient for interphase zones that are less conductive than the pure matrix, and vice versa. Maxwell’s homogenization method is then used to estimate the effective macroscopic conductivity of the medium. The developed model is used to analyze some data from the literature on the ionic diffusivity of concrete. Use of the model in an inverse mode permits the estimation of the local diffusivity variation within the interphase, and in particular at the interface with the inclusion.
Nejati M, Paluszny A, Zimmerman RW, 2015, On the use of quarter-point tetrahedral finite elements in linear elastic fracture mechanics, Engineering Fracture Mechanics, Vol: 144, Pages: 194-221, ISSN: 0013-7944
This paper discusses the reproduction of the square root singularity in quarter-point tetrahedral (QPT) finite elements. Numerical results confirm that the stress singularity is modeled accurately in a fully unstructured mesh by using QPTs. A displacement correlation (DC) scheme is proposed in combination with QPTs to compute stress intensity factors (SIF) from arbitrary meshes, yielding an average error of 2–3%. This straightforward method is computationally cheap and easy to implement. The results of an extensive parametric study also suggest the existence of an optimum mesh-dependent distance from the crack front at which the DC method computes the most accurate SIFs.
Lang PS, Paluszny A, Zimmerman RW, 2015, Hydraulic sealing due to pressure solution contact zone growth in siliciclastic rock fractures, Journal of Geophysical Research: Solid Earth, Vol: 120, Pages: 4080-4101, ISSN: 2169-9356
Thermo-hydro-mechanical–chemical simulations at the pore scale are conducted to study the hydraulic sealing of siliciclastic rock fractures as contact zones grow driven by pressure dissolution. The evolving fluid-saturated three-dimensional pore space of the fracture results from the elastic contact between self-affine, randomly rough surfaces in response to the effective confining pressure. A diffusion–reaction equation controls pressure solution over contact zones as a function of their emergent geometry and stress variations. Results show that three coupled processes govern the evolution of the fracture's hydraulic properties: (1) the dissolution-driven convergence of the opposing fracture walls acts to compact the pore space; (2) the growth of contact zones reduces the elastic compression of the pore space; and (3) the growth of contact zones leads to flow channeling and the presence of stagnant zones in the flow field. The dominant early-time compaction mechanism is the elastic compression of the fracture void space, but this eventually becomes overshadowed by the irreversible process of pressure dissolution. Growing contact zones isolate void space and cause an increasing disproportion between average and hydraulic aperture. This results in the loss of hydraulic conductivity when the mean aperture is a third of its initial value and the contact ratio approaches the characteristic value of one half. Convergence rates depend on small wavelength roughness initially, and on long wavelength roughness in the late time. The assumption of a characteristic roughness length scale, therefore, leads to a characteristic time scale with an underestimation of dissolution rates before, and an overestimation thereafter.
Defoort T, Salimzadeh S, Paluszny A, et al., 2015, A finite element geomechanical study of the brittle failure of a caprock due to deflation, Pages: 70-79
The deformation of an initially intact caprock, due to the depletion of an underlying reservoir during oil extraction, is geomechanically modeled in three dimensions using a fully coupled poro-elastic model, incorporating plastic damage and fracture models in the caprock. Fractures are represented explicitly in an arbitrary tetrahedral mesh. An isotropic damage model accounts for micro-fracture growth in response to the accumulation of plastic strain. Stress intensity factors, computed using the reduced virtual integration technique, assess potential fracture growth by measuring energy concentrations around the tips. The objectives are to evaluate the locations in the caprock, where damage and fracture propagation are most likely to occur. As a result of poro-elastic deformation during the onset of reservoir depletion, shear driven damage in fractures above and around the well are observed. Extension driven growth is observed in fractures located away from the well. Damage and fracture growth both potentially decrease the caprock integrity, and locally enhance the permeability.
Ambrose J, Zimmerman RW, 2015, Failure of anisotropic shales under triaxial compression and extension
Shales are highly anisotropic in their mechanical behavior. The strength ( σ 1) of anisotropic shales depends not only on the magnitude of the other two principal stresses ( σ 2, σ 3), but also on the bedding plane orientations (b) relative to the principal stresses. In this study, the role of the intermediate stress ( σ 2) on the strength of shale is evaluated using new data from triaxial compression and extension tests. To understand the failure behavior of shales, we have carried out triaxial compression tests ( σ 1 > σ 2 = s 3) on two organic rich mudstones, at different confining stresses and loading angles. We first fit the triaxial compression data with Jaeger's plane-of-weakness model, and find that the model is able to represent the strength behavior of anisotropic shales reasonably well. We then carried out five triaxial extension tests ( σ 1 = σ 2 > s 3) for a high strength-anisotropy shale, and two extension tests for a low strength-anisotropy shale. Results from the compression and extension tests for failure along the weak plane shows that the role of σ 2 is not significant for weak plane failure. However, for the low strength-anisotropy shale, the failure strength of the intact rock (i.e., at β = 0o and 90o) for compression and extension tests were significantly different. This indicates that for intact rock failure, the role of σ 2 is important and cannot be ignored.
Paluszny A, Nejati M, Zimmerman RW, 2015, A numerical model for fracture propagation leading to primary fragmentation in block caving mines, Pages: 1-15
A numerical method is proposed to propagate multiple discrete fractures leading to primary fragmentation in a mine that is being worked using block caving. Deformation is computed using the finite element method, fractures are represented explicitly, and the mine domain is discretized by an unstructured mesh. Bedding planes are represented by systematically varying the elastic modulus of the rock and by defining horizontal weakness planes. Fractures and matrix are represented using parametric surfaces, and tips are defined by their boundary curves. Tip advance is controlled by a failure criterion, and a criterion for propagation direction and magnitude, based on the evaluation of the modal stress intensity factors. A novel domain integral approach is applied to accurately compute stress intensity factors (K) ahead of fracture tips in three dimensions. The method does not require a structured volumetric mesh structure around the crack tip, as integration is performed over a series of virtual surface domains along the crack front. The method is efficient, as it makes direct use of automatically generated, arbitrary tetrahedral meshes, and approximates stress intensity factors (KI, KII, KIII) along each crack front using Interaction-integrals. As opposed to the JIntegral, the method does not decompose K a-posteriori, but instead uses an auxiliary field to directly compute modal K. When using this method, numerical approximations of K do not exhibit dependence on the mesh layout, and require meshes that can generally be ten times coarser than are required by displacement- and stress-based methods. Volumetric meshing requires only, on average, 17% of each computation step. Thus, cracks do not follow any pre-existing mesh structure, and the method is well suited for high-density fracture datasets. The method is demonstrated for primary fragmentation of a mine area covering 110 initial draw points, immediately beneath a 2m high undercut. Displacement is constrained at all
Singh G, Zimmerman RW, 2014, Modification of Griffith-McClintock-Walsh model for crack growth under compression to incorporate stick-slip along the crack faces, INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES, Vol: 72, Pages: 311-318, ISSN: 1365-1609
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- Citations: 11
Singh G, Kermode JR, De Vita A, et al., 2014, Validity of linear elasticity in the crack-tip region of ideal brittle solids, INTERNATIONAL JOURNAL OF FRACTURE, Vol: 189, Pages: 103-110, ISSN: 0376-9429
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- Citations: 18
Lang PS, Paluszny A, Zimmerman RW, 2014, Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions, Journal of Geophysical Research: Solid Earth, Vol: 119, Pages: 6288-6307, ISSN: 2169-9356
The reduction from three‐ to two‐dimensional analysis of the permeability of a fractured rock mass introduces errors in both the magnitude and direction of principal permeabilities. This error is numerically quantified for porous rock by comparing the equivalent permeability of three‐dimensional fracture networks with the values computed on arbitrarily extracted planar trace maps. A method to compute the full permeability tensor of three‐dimensional discrete fracture and matrix models is described. The method is based on the element‐wise averaging of pressure and flux, obtained from a finite element solution to the Laplace problem, and is validated against analytical expressions for periodic anisotropic porous media. For isotropic networks of power law size‐distributed fractures with length‐correlated aperture, two‐dimensional cut planes are shown to underestimate the magnitude of permeability by up to 3 orders of magnitude near the percolation threshold, approaching an average factor of deviation of 3 with increasing fracture density. At low‐fracture densities, percolation may occur in three dimensions but not in any of the two‐dimensional cut planes. Anisotropy of the equivalent permeability tensor varies accordingly and is more pronounced in two‐dimensional extractions. These results confirm that two‐dimensional analysis cannot be directly used as an approximation of three‐dimensional equivalent permeability. However, an alternative expression of the excluded area relates trace map fracture density to an equivalent three‐dimensional fracture density, yielding comparable minimum and maximum permeability. This formulation can be used to approximate three‐dimensional flow properties in cases where only two‐dimensional analysis is available.
Ambrose J, Zimmerman RW, Suarez-Rivera R, 2014, Failure of shales under triaxial compressive stress, Pages: 258-268
Some rocks, such as shales, are highly anisotropic in their mechanical behavior. In such rocks, the value of the maximum principal stress that causes shear failure depends not only on the confining stress, but also on the angle β between the maximum principal stress and the normal vector to the bedding plane. Triaxial compression experiments were carried out on two types of organic-rich mudstones at different bedding angles β and confining pressures σ3. Two triaxial compression datasets from experiments and 10 datasets from the literature were fit to the Pariseau and the Jaeger plane-of-weakness (JPW) models. Results show that Pariseau's model is more accurate for 10 of the 12 anisotropic rocks, whereas the JPW model is more accurate for the other two rocks, which were both rocks that had a low degree of strength anisotropy. Post-test examination of computerized tomography (CT) and thin-section images shows that for highly laminated organic-rich shales, there is a transition regime of angles β lying between angles of about 10°<β<35°, wherein the failure surface follows an irregular path that may jump between the weak plane and intact rock. In this regime, the strength of the rock is lower than the strength predicted by the JPW model.
De La Porte JJ, Zimmerman RW, Kossack CA, 2014, Modelling heavy oil viscosity during thermal stimulation using the free volume theory, Pages: 3242-3258
Large errors in oil viscosity predictions result in large production rate errors during numerical simulation, due to a first-order dependency of flow rates on viscosity. Questions that arise during thermal simulation studies of heavy oil are (1) which viscosity-temperature model could be sufficiently well based on molecular physics such that viscosity prediction, as a function of temperature, would be possible if only oil composition is available; (2) in which temperature range do viscosity predictions need to be most accurate so as to ensure most accurate recovery predictions - The high or the low end? This work will provide simulation engineers with additional tools and information to address these questions, and more accurately model production of heavy oil under thermal stimulation, by providing a viscosity model based on physical properties of molecular structure and thermodynamic behavior, and additionally, will show that the priority temperature range depends on the thermal recovery method. The Free Volume Model (FVM), based on the concept of the 'available free space to which a molecule can move under shear stress', is applied in this work to three different heavy oils to calculate viscosity as a function of temperature. The model was first extended for application to extra-long chain molecules up to ChH130 by de la Porte (2012) and de la Porte and Kossack (2014); the present work will provide users with guidelines to estimate the FVT molecular characteristics for a resin-asphaltene heavy pseudo- component. Furthermore, the range of temperatures at which accurate viscosity prediction is essential for more accurate oil recovery predictions is investigated for various recovery methods, such as cyclic steam stimulation (CSS), line-drive steam stimulation (SLD), and steam-assisted gravity-drainage (SAGD). Analytical models are used to predict the sensitivity to the viscosity error in a specific temperature range, followed by numerical simulation to confirm the f
Paluszny A, Zimmerman RW, Potjewyd, et al., 2014, Finite Element-Based Numerical Modeling of Fracture Propagation due to the Plunge of a Spherical Indenter, Publisher: American Rock Mechanics Association
AbstractNumerical simulations have been conducted to model the deformation, damage, and fracture growth caused by the plunge of a spherical drill bit insert into a brittle rock. The deformation of the rock, which is initially homogeneous and isotropic, is modeled using the finite element method. Fracture geometry evolves as a function of fracture growth, and the rock domain is continuously re-meshed to capture this geometric change. Contact forces are applied radially over the contact area as a function of the depth of the plunge. A series of simulations is presented, having varying initial flaw distributions, and which capture the fracture pattern formation during the progressive indentation of the insert into the rock. The ensuing patterns depict the formation of horizontal and Hertzian fractures. A large fracture density is created around the contact area. The complexity of the internal fracture structure is less apparent at the surface of the deformed rock, as compared to the internal fracture pattern. Fracturing leads to the formation of surface chips in the form of tilted elliptical domains parallel to the rock surface. Early stages of chipping are not always apparent from the fracture pattern at the surface of the rock. Results are in good agreement with experimental observations.
Tang X, Paluszny A, Zimmerman RW, 2014, An impulse-based energy tracking method for collision resolution, Computer Methods in Applied Mechanics and Engineering, Vol: 278, Pages: 160-185, ISSN: 0045-7825
Abstract Discrete element methods can be based on either penalties or impulses to resolve collisions. A generic impulse based method, the energy tracking method (ETM), is described to resolve collisions between multiple non-convex bodies in three dimensions. As opposed to the standard sequential impulse method (SQM) and simultaneous impulse method (SMM), which also apply impulses to avoid penetration, the energy tracking method changes the relative velocity between two colliding bodies iteratively yet simultaneously. Its main novelty is that impulses are applied gradually at multi-point contacts, and energy changes at the contact points are tracked to ensure conservation. Three main steps are involved in the propagation of the impulses during the single- and multi-contact resolution: compression, restitution-related energy loss, and separation. Numerical tests show that the energy tracking method captures the energy conservation property of perfectly elastic single- and multi-point collisions. ETM exhibits improved angular velocity estimation, as compared to SMM and SQM, as demonstrated by two numerical examples that model multi-point contact between box-shaped objects. Angles of repose estimated for multi-object pack repositioning of spheres, cubes, and crosses are in good agreement with the reported experimental values.
David EC, Zimmerman RW, 2013, Model for frequency-dependence of elastic wave velocities in porous rocks, Pages: 2431-2440
A model is proposed for the frequency dependence of elastic wave velocities in porous rocks using the spheroidal geometry for the pores. The model is based on the assumption that the rock contains a distribution of « closable» cracks having small aspect ratios, and one family of «non-closable» pores. At a given wave frequency, some pores obey the Gassmann equation and others are isolated, with a critical aspect ratio demarcating the two families that depens on frequency and fluid viscosity. An effective medium model is used to add the compliances of the individual pores, so as to yield effective moduli. The model also allows for calculation of «intrinsic» seismic attenuation by applying the Kramers-Kronig relations to the velocities. By considering the crack closure process, the model is capable of describing the frequency dispersion of both the compressional and shear velocities at each pressure. The predictions, for some sandstones datasets taken from the literature, show that P and S-wave velocities generally increase in a relatively similar manner with frequency, and that dispersion of both velocities rapidly decreases with pressure. Attenuation values are consistent with typical values found in the literature. © 2013 American Society of Civil Engineers.
Paluszny A, Tang XH, Zimmerman RW, 2013, Fracture and impulse based finite-discrete element modeling of fragmentation, COMPUTATIONAL MECHANICS, Vol: 52, Pages: 1071-1084, ISSN: 0178-7675
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- Citations: 42
David EC, Fortin J, Schubnel A, et al., 2013, Laboratory measurements of low- and high-frequency elastic moduli in Fontainebleau sandstone, GEOPHYSICS, Vol: 78, Pages: D367-D377, ISSN: 0016-8033
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- Citations: 48
Tang XH, Paluszny A, Zimmerman RW, 2013, Energy conservative property of impulse-based methods for collision resolution, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Vol: 95, Pages: 529-540, ISSN: 0029-5981
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- Citations: 28
Paluszny A, Zimmerman RW, 2013, Numerical fracture growth modeling using smooth surface geometric deformation, ENGINEERING FRACTURE MECHANICS, Vol: 108, Pages: 19-36, ISSN: 0013-7944
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- Citations: 26
Zhao Z, Rutqvist J, Leung C, et al., 2013, Impact of stress on solute transport in a fracture network: A comparison study, Journal of Rock Mechanics and Geotechnical Engineering, Vol: 5, Pages: 110-123, ISSN: 1674-7755
This paper compares numerical modeling of the effect of stress on solute transport (advection and matrix diffusion) in fractured rocks in which fracture apertures are correlated with fracture lengths. It is mainly motivated by the performance and safety assessments of underground radioactive waste repositories. Five research teams used different approaches to model stress/deformation, flow and transport processes, based on either discrete fracture network or equivalent continuum models. The simulation results derived by various teams generally demonstrated that rock stresses could significantly influence solute transport processes through stress-induced changes in fracture apertures and associated changes in permeability. Reasonably good agreement was achieved regarding advection and matrix diffusion given the same fracture network, while some observed discrepancies could be explained by different mechanical or transport modeling approaches. © 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.
Tang X, Paluszny A, Zimmerman RW, 2013, A Study of the Influence of Fragmentation in Ore-Pass Hang-up Phenomena, Publisher: American Rock Mechanics Association
Abstract: Fragmentation strongly influences the interlocking hang-up phenomena, a common occurrence in conjunction with cohesive arching around draw points in block caving systems. This work presents a brief numerical study of the influence of fragmentation on interlocking hang-up phenomena. Fragment interaction and breakup are simulated numerically by combining the impulse-based energy tracking method (ETM) and the finite element method (FEM) in three dimensions. Numerical tests with varying size of ore fragments are carried out. The breakage of rock fragments is modeled during the entire simulation and the influence of fragmentation is investigated in terms of productivity and the efficiency of draw point extraction. Simulation results with fragmentation are compared to non-fragmentation numerical tests. It is observed that with fragmentation, 1.93% and 2.57% more volume of ore fragments are extracted before hang-up when the initial diameter of ore fragments is 5.775 m and 7.5 m, respectively.
Nejati M, Paluszny A, Zimmerman RW, 2013, Theoretical and Numerical Modeling of Rock Hysteresis Based on Sliding of Microcracks, 47th U.S. Rock Mechanics/Geomechanics Symposium, Publisher: American Rock Mechanics Association, Pages: 573-581
Nonlinearity and hysteresis are two key features of elastic rock deformation. This behavior can be attributed to the presence of cracks and crack-like voids. The hysteretic behavior of rocks is related to the concept of unrecovered energy. Two main processes lead to the existence of unrecovered energy in the sliding crack model: (i) the work of frictional forces and (ii) the strain energy trapped in the solid. In this paper, a theoretical and numerical analysis will be presented to extend the work of David et al. [1] to consider 3D penny-shaped cracks. A 3D finite element analysis is used to evaluate the sliding crack model numerically. In this approach, the penalty method is used to simulate the contact behavior of the crack faces. The stick-slip condition of the crack faces is simulated by employing the constitutive frictional law of Amontons. The results show that no residual strain is developed in the body containing randomly oriented cracks if one assumes a uniform stress over all the crack cells. The energy loss is therefore equal to the work of frictional forces on the crack faces.
Leung CTO, Hoch AR, Zimmerman RW, 2012, Comparison of discrete fracture network and equivalent continuum simulations of fluid flow through two-dimensional fracture networks for the DECOVALEX-2011 project, MINERALOGICAL MAGAZINE, Vol: 76, Pages: 3179-3190, ISSN: 0026-461X
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- Citations: 13
David EC, Zimmerman RW, 2012, Pore structure model for elastic wave velocities in fluid-saturated sandstones, JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH, Vol: 117, ISSN: 2169-9313
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- Citations: 114
Leung CTO, Zimmerman RW, 2012, Estimating the Hydraulic Conductivity of Two-Dimensional Fracture Networks Using Network Geometric Properties, TRANSPORT IN POROUS MEDIA, Vol: 93, Pages: 777-797, ISSN: 0169-3913
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- Citations: 93
David EC, Brantut N, Schubnel A, et al., 2012, Sliding crack model for nonlinearity and hysteresis in the uniaxial stress-strain curve of rock, INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES, Vol: 52, Pages: 9-17, ISSN: 1365-1609
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- Citations: 156
Zimmerman RW, Paluszny A, 2012, Some New Developments in Modelling the Failure, Fracture and Fragmentation of Rocks, Publisher: International Society for Rock Mechanics
ABSTRACTIn this paper, several new developments regarding the failure, fracture and fragmentation of rocks will be discussed. The first topic discussed is the development of true-triaxial failure criteria that involve all three principal stresses. The next topic is a new approach to modelling the propagation of cracks and fractures using accurate local calculations of the stress intensity factor. Lastly, a method for fracture-driven rock fragmentation with a velocity-dependent propagation law is discussed.
Wong HS, Zimmerman RW, Buenfeld NR, 2012, Estimating the permeability of cement pastes and mortars using image analysis and effective medium theory, Cem. Concr. Res., Vol: 42, Pages: 476-483
Paluszny A, Tang XH, Zimmerman RW, 2012, A Multi-modal Approach to 3D Fracture And Fragmentation of Rock Using Impulse-Based Dynamics And the Finite Element Method, Publisher: American Rock Mechanics Association
ABSTRACT:A numerical method combining the finite element method (FEM) and impulse-based dynamics is proposed for the simulation of 3D fracture and fragmentation. As opposed to existing methods, fragments are not represented as a conglomeration of primitive shapes; instead, their geometry is represented using solid modeling techniques. This allows for continuum-mechanics-based fracture propagation analysis to be carried out within each fragment, with fragment interaction and movement simulated using impulse-based dynamics. This approach models multi-body interaction of non-convex 3D objects which fall, collide, and fragment using impulse-based dynamics, as opposed to a penalty-based method. Instead, object trajectories are used to estimate time-of-impact, and contact between bodies is modeled by collisions at contact locations. This approach allows material properties to be explicitly defined at the macro-scale. A 3D fracture engine models fracture propagation in the individual 3D continua based on local stress intensity factor measurements using the reduced virtual integration technique, as well as decoupled geometry and mesh representation, and on the evaluation of local failure and propagation criteria. Fractures that reach free boundaries lead to further fragmentation. The framework, presented as a multi-modal toolkit, is suitable for meso-scale simulations, and is demonstrated by a mining-specific block caving application. 1. INTRODUCTIONFragmentation simulation involves capturing two main processes: damage and cracking of single bodies, and dynamics/collision between fragments. The analysis of damage and cracking in single bodies includes challenges such as defining initial material properties and rock heterogeneities, crack nucleation, and propagation of multiple cracks. Modeling collisions between fragments includes capturing processes such as collision detection, force transfer due to impact and compression, and energy loss during collision. Challenges inclu
Mathias SA, de Miguel GJGM, Thatcher KE, et al., 2011, Pressure Buildup During CO<sub>2</sub> Injection into a Closed Brine Aquifer, TRANSPORT IN POROUS MEDIA, Vol: 89, Pages: 383-397, ISSN: 0169-3913
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- Citations: 73
David EC, Zimmerman RW, 2011, Elastic moduli of solids containing spheroidal pores, INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, Vol: 49, Pages: 544-560, ISSN: 0020-7225
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- Citations: 53
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