Eduardo Lages - Academia.edu (original) (raw)

Papers by Eduardo Lages

Mecánica Computacional, 2010

Resumo. Neste trabalho é apresentada uma análise do acoplamento fluxo-deformação de meios porosos... more Resumo. Neste trabalho é apresentada uma análise do acoplamento fluxo-deformação de meios porosos, tendo como suporte teórico a formulação poroelástica de Biot. Em grande parte dos problemas de engenharia relacionados com meios porosos é possível encontrar casos em que o movimento de fluidos através dos poros influencia significativamente o seu comportamento mecânico. Nesses problemas, alterações na poropressão de solos e rochas indicam a ocorrência de fluxo, provocando alterações nas tensões efetivas e, consequentemente, deformações no meio. Com o objetivo de alcançar resultados mais significativos na análise de meios porosos, utiliza-se a Teoria da Poroelasticidade de Biot, que leva em consideração o acoplamento entre o comportamento mecânico dos grãos e o comportamento hidráulico do fluxo de fluido presente através dos poros. Como resultado, é apresentado o estudo do comportamento de rochas reservatório durante a etapa de produção de hidrocarboneto. A retirada do óleo pode provocar compactação e subsidência do reservatório, trazendo diversos impactos para todo o sistema de produção. A estratégia numérica acoplada desenvolvida é baseada na Teoria da Poroelasticidade de Biot, utilizando o Método dos Elementos Finitos. Algumas aplicações são mostradas de modo a comparar os resultados numéricos obtidos com dados encontrados na literatura.

Ocean Engineering, Jul 1, 2023

Social Science Research Network, 2023

International Journal of Thermal Sciences, 2022

Abstract Most of the available approaches for the prediction of effective thermal conductivity of... more Abstract Most of the available approaches for the prediction of effective thermal conductivity of composites are proposed for two-phase cases with inhomogeneities of simple geometry. Here, a procedure originally developed for two-phase composites is extended to obtain effective thermal conductivities of periodic composites with an arbitrary number of phases and geometric shapes of the inhomogeneities. The procedure is based on a generalization of the equivalent inclusion method for steady-state heat conduction, using Fourier series to represent the periodic fluctuating fields of the quantities involved in the problem. Applications to three-phase composites with different microstructural features are presented and discussed in detail. The model predictions are compared with analytical and numerical results obtained from other homogenization procedures, as well as with available experimental data. These comparisons show a very good performance of the model regardless of the volume fraction of the inhomogeneities, enabling it to be presented as an interesting alternative to the limited number of existing approaches for evaluating the effective thermal conductivity of multiphase/multi-inclusion periodic composites.

Applied Mathematical Modelling, Jul 1, 2023

DOAJ (DOAJ: Directory of Open Access Journals), Jul 1, 2021

No projeto de pavimentos de concreto simples da PCA (1984), empregam-se tabelas e ábacos para ver... more No projeto de pavimentos de concreto simples da PCA (1984), empregam-se tabelas e ábacos para verificar a fadiga da placa de concreto e a erosão do subleito/sub-base. Caso um desses critérios não seja atendido, ou se constate o atendimento dos critérios com margem de segurança elevada, repetese o cálculo para um novo conjunto de parâmetros, sendo usual o ajuste da espessura da placa. Concebe-se um algoritmo computacional para minimizar o custo da placa do pavimento, que combina a espessura da placa com a resistência característica à tração na flexão do concreto. Adota-se o guia da AUSTROADS (2010), por reunir explicitamente as equações analíticas envolvidas no processo de verificação dos critérios em pauta. Um exemplo numérico é apresentado e discutido, o qual evidencia que o ajuste combinado da espessura da placa com a resistência do concreto possibilita a definição de projetos mais otimizados frente àqueles em que se ajusta apenas a espessura.

Revista IBRACON de Estruturas e Materiais, 2021

Reinforced concrete short corbels are components characterized to represent typical conditions of... more Reinforced concrete short corbels are components characterized to represent typical conditions of geometrical and static discontinuity. In general, the classical bending theory is not valid for their design. With the strut and tie method, a model of a self-balanced truss, a strategy of representation of the principal stress flow appears as a representation of the trajectories of the main stresses in these components. Within the context of obtaining the strut and tie models, topology optimization is an indicated technique for an automated process. Combined with a numerical analysis based on finite elements, the SIMP (Solid Isotropic Material with Penalization) method formulation, which is defined with the criterion of minimum strain energy restricted by the volumetric fraction, is used for the development of the models with the ABAQUS® v. 6.14.1 software. Therefore, with the material distribution posterior to the optimization and the validation based on normative codes, it is demonst...

SPE Journal, 2020

The mobility of salt rocks may cause problems, such as stuck pipe, high torque, casing collapse, ... more The mobility of salt rocks may cause problems, such as stuck pipe, high torque, casing collapse, and hole closure, promoting enormous losses in different areas. The drilling mud weight generates a hydrostatic pressure that serves as a counterpressure to the displacement of the salt. Sometimes this measure is not enough, leading to the backreaming operation, which reconditions the diameter of the wellbore to its original state. Given the importance of backreaming during drilling operations in salt rocks, its incorporation into computational tools is necessary. Through the finite element method (FEM), we developed a program to identify and simulate the effects of the backreaming operations in vertical wells in the presence of salt layers. We proposed a simulator that associates 1D axisymmetric multilayers with unit thickness through a coupling strategy between them, considering a lesser number of degrees of freedom when compared to conventional 2D modeling. We checked the performance of multilayers strategy when compared with 2D axisymmetric modeling of the hole closure problem in the commercial software ABAQUSV R (Dassault Systèmes, Vélizy-Villacoublay, France); for the radial displacement histories, the multilayer strategy presented similarity with ABAQUS for cases that consider interaction, with the advantage of a low computational cost provided by the 1D formulation. We demonstrated the modeling of backreaming through the proposed tool.

Latin American Journal of Solids and Structures, 2020

Topology optimization is a well-suited method to establish the best material distribution inside ... more Topology optimization is a well-suited method to establish the best material distribution inside an analysis domain. It is common to observe some numerical instabilities in its gradient-based version, such as the checkerboard pattern, mesh dependence, and local minima. This research demonstrates the generalized finite-volume theory's checkerboard-free property by performing topology optimization algorithms without filtering techniques. The formation of checkerboard regions is associated with the finite element method's displacement field assumptions, where the equilibrium and continuity conditions are satisfied through the element nodes. On the other hand, the generalized finite-volume theory satisfies the continuity conditions between common faces of adjacent subvolumes, which is more likely from the continuum mechanics point of view. Also, the topology optimization algorithms based on the generalized finite-volume theory are performed using a mesh independent filter that regularizes the subvolume sensitivities, providing optimum topologies that avoid the mesh dependence and length scale issues.

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Applied Mathematical Modelling, 2021

Applied Mathematical Modelling, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Revista IBRACON de Estruturas e Materiais, 2019

Several factors influence the stability of concrete structures, such as building height, structur... more Several factors influence the stability of concrete structures, such as building height, structural components’ rigidity, bracing system, beam-wall connection rigidity, among others. Global structural stability is evaluated according to NBR 6118/2014 by the α e γz parameters. This article aims to evaluate the global structural stability concrete structures considering the eccentricity of the beam-wall connections. With the aid of software Abaqus© and TQS©, reticulated models were analyzed to evaluate the contribution of the eccentricity of the beam-wall connections on the global stability and the rigidity of the connections. The geometric nonlinear effects were disregarded in these analyses. The stability parameters from NBR6118/2014 were evaluated in the frame models, as well as the flexibilization criteria from the TQS© software, LEPMOL e REDMOL. The results of the displacement analysis show an increase of 26.45%, comparing the centered connection to the more eccentric connection.

Proceedings of the 7th International Symposium on Solid Mechanics, 2019

Revista IBRACON de Estruturas e Materiais, 2019

An analytical study aiming the design of cylindrical liquid storage tanks resting on deformable f... more An analytical study aiming the design of cylindrical liquid storage tanks resting on deformable foundations is developed in this work. The soil under the tanks is modeled as an elastic linear medium. The cylindrical wall is considered rigidly connected to the plate foundation. Here, concrete tanks are emphasized, although the study can be extended to other construction materials. For the analysis of the design forces acting on the tanks, efficient and simplified approximate expressions are derived based on rigorous analytical theories for thin shells and circular plate on elastic foundations. To verify the proposed approximate expressions and investigate the influence of the foundation deformability on displacements and design forces, parametric analyses of concrete tanks with different soil stiffness values are presented. The results illustrate the strong influence of the foundation stiffness on the tank design quantities and a very good performance of the simplified expressions.

Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019

This paper presents a semi-analytical micromechanical model for evaluation of effective thermal c... more This paper presents a semi-analytical micromechanical model for evaluation of effective thermal conductivity of composite materials with periodic microstructure. The model is based on the equivalent inclusion thermal problem and utilizes Fourier series for representation of periodic functions involved in the material homogenization approach. Two main objectives can be highlighted in the work. The first of them is the derivation of the thermal micromechanical model, which consists in an extension of a formulation originally derived for homogenization of elastic heterogeneous solids. The second objective consists in a detailed investigation on the performance of the model, considering convergence of results and efficiency of strategies employed for the approximate solution of the thermal homogenization problem. Analyses on the complexity of transformation temperature gradient functions are also included in this investigation. The results obtained for two examples of periodic composites with different microstructural architectures are presented and discussed in detail.

Risers verticais complacentes (CVAR) consistem em uma alternativa relativamente recente para expl... more Risers verticais complacentes (CVAR) consistem em uma alternativa relativamente recente para exploração de petróleo em águas ultra-profundas. A geometria do arranjo CVAR se apresenta predominantemente vertical com um offset horizontal entre o topo e a base. Sua configuração característica é obtida a partir da utilização de um trecho com revestimento de peso adicional na parte mais superior do riser e outro trecho com flutuadores, neste caso na região mais inferior. A disposição desses trechos ao longo da estrutura proporciona o aumento da tração ao longo do riser, mantendo os trechos verticais e atenuando a dinâmica da linha. O offset entre o topo e a base bem como a diferença de flutuação na região intermediária do riser geram uma leve curvatura nessa região. O dimensionamento do arranjo CVAR é determinado pela definição de 7 variáveis: diâmetro dos flutuadores, comprimento do trecho de flutuadores, espessura do revestimento pesado, comprimento do trecho de revestimento pesado, pos...

This work presents a study on strain and stress distributions in two-dimensional panels constitut... more This work presents a study on strain and stress distributions in two-dimensional panels constituted by elastic composite materials considering effects of physical and geometrical nonlinearities. The analyses are carried out by a new nonlinear model which is based on the parametric finite-volume theory. The model is incremental and uses a total Lagragian formulation that employs the Second Piola-Kirchhoff tensor and Green-Lagrange tensor as stress and strain measurements, respectively. The composite material and its constituents are assumed as linear or nonlinear elastic. The analyzed examples include two-dimensional panels with circular and elliptic inclusions presenting a large range of mismatch ratios for their Young’s moduli. In particular, stress concentrations in panels of functionally graded materials with circular and elliptic holes are analyzed. The study presents the distributions of stresses and strains over the matrices and inclusions of the composite materials. Results o...

International Journal of Solids and Structures, 2012

This contribution is motivated by the recent IJSS article titled ''Formulation of the High-Fideli... more This contribution is motivated by the recent IJSS article titled ''Formulation of the High-Fidelity Generalized Method of Cells with Arbitrary Cell Geometry for Refined Micromechanics and Damage in Composites'' by Haj-Ali and Aboudi. In the present discussion, we critically compare these authors' approach with the Parametric Finite-Volume Direct Averaging Micromechanics (FVDAM) theory developed in a sequence of papers dating to 2004. We show that the extension proposed by Haj-Ali and Aboudi follows the framework of the parametric FVDAM theory, and not the original HFGMC model as claimed. Just as importantly, we demonstrate that the proposed extension is fundamentally flawed as it violates accepted principles which every mechanics theory must satisfy, namely correct reducibility and coordinate frame indifference. Direct comparison of predictions generated by the parametric FVDAM theory, the proposed extension called HFGMC with arbitrary cell geometry and finite-element method demonstrates no need for the extension carried out in the specific manner proposed by Haj-Ali and Aboudi, which in fact produces inferior results.

Mecánica Computacional, 2010

Resumo. Neste trabalho é apresentada uma análise do acoplamento fluxo-deformação de meios porosos... more Resumo. Neste trabalho é apresentada uma análise do acoplamento fluxo-deformação de meios porosos, tendo como suporte teórico a formulação poroelástica de Biot. Em grande parte dos problemas de engenharia relacionados com meios porosos é possível encontrar casos em que o movimento de fluidos através dos poros influencia significativamente o seu comportamento mecânico. Nesses problemas, alterações na poropressão de solos e rochas indicam a ocorrência de fluxo, provocando alterações nas tensões efetivas e, consequentemente, deformações no meio. Com o objetivo de alcançar resultados mais significativos na análise de meios porosos, utiliza-se a Teoria da Poroelasticidade de Biot, que leva em consideração o acoplamento entre o comportamento mecânico dos grãos e o comportamento hidráulico do fluxo de fluido presente através dos poros. Como resultado, é apresentado o estudo do comportamento de rochas reservatório durante a etapa de produção de hidrocarboneto. A retirada do óleo pode provocar compactação e subsidência do reservatório, trazendo diversos impactos para todo o sistema de produção. A estratégia numérica acoplada desenvolvida é baseada na Teoria da Poroelasticidade de Biot, utilizando o Método dos Elementos Finitos. Algumas aplicações são mostradas de modo a comparar os resultados numéricos obtidos com dados encontrados na literatura.

Ocean Engineering, Jul 1, 2023

Social Science Research Network, 2023

International Journal of Thermal Sciences, 2022

Abstract Most of the available approaches for the prediction of effective thermal conductivity of... more Abstract Most of the available approaches for the prediction of effective thermal conductivity of composites are proposed for two-phase cases with inhomogeneities of simple geometry. Here, a procedure originally developed for two-phase composites is extended to obtain effective thermal conductivities of periodic composites with an arbitrary number of phases and geometric shapes of the inhomogeneities. The procedure is based on a generalization of the equivalent inclusion method for steady-state heat conduction, using Fourier series to represent the periodic fluctuating fields of the quantities involved in the problem. Applications to three-phase composites with different microstructural features are presented and discussed in detail. The model predictions are compared with analytical and numerical results obtained from other homogenization procedures, as well as with available experimental data. These comparisons show a very good performance of the model regardless of the volume fraction of the inhomogeneities, enabling it to be presented as an interesting alternative to the limited number of existing approaches for evaluating the effective thermal conductivity of multiphase/multi-inclusion periodic composites.

Applied Mathematical Modelling, Jul 1, 2023

DOAJ (DOAJ: Directory of Open Access Journals), Jul 1, 2021

No projeto de pavimentos de concreto simples da PCA (1984), empregam-se tabelas e ábacos para ver... more No projeto de pavimentos de concreto simples da PCA (1984), empregam-se tabelas e ábacos para verificar a fadiga da placa de concreto e a erosão do subleito/sub-base. Caso um desses critérios não seja atendido, ou se constate o atendimento dos critérios com margem de segurança elevada, repetese o cálculo para um novo conjunto de parâmetros, sendo usual o ajuste da espessura da placa. Concebe-se um algoritmo computacional para minimizar o custo da placa do pavimento, que combina a espessura da placa com a resistência característica à tração na flexão do concreto. Adota-se o guia da AUSTROADS (2010), por reunir explicitamente as equações analíticas envolvidas no processo de verificação dos critérios em pauta. Um exemplo numérico é apresentado e discutido, o qual evidencia que o ajuste combinado da espessura da placa com a resistência do concreto possibilita a definição de projetos mais otimizados frente àqueles em que se ajusta apenas a espessura.

Revista IBRACON de Estruturas e Materiais, 2021

Reinforced concrete short corbels are components characterized to represent typical conditions of... more Reinforced concrete short corbels are components characterized to represent typical conditions of geometrical and static discontinuity. In general, the classical bending theory is not valid for their design. With the strut and tie method, a model of a self-balanced truss, a strategy of representation of the principal stress flow appears as a representation of the trajectories of the main stresses in these components. Within the context of obtaining the strut and tie models, topology optimization is an indicated technique for an automated process. Combined with a numerical analysis based on finite elements, the SIMP (Solid Isotropic Material with Penalization) method formulation, which is defined with the criterion of minimum strain energy restricted by the volumetric fraction, is used for the development of the models with the ABAQUS® v. 6.14.1 software. Therefore, with the material distribution posterior to the optimization and the validation based on normative codes, it is demonst...

SPE Journal, 2020

The mobility of salt rocks may cause problems, such as stuck pipe, high torque, casing collapse, ... more The mobility of salt rocks may cause problems, such as stuck pipe, high torque, casing collapse, and hole closure, promoting enormous losses in different areas. The drilling mud weight generates a hydrostatic pressure that serves as a counterpressure to the displacement of the salt. Sometimes this measure is not enough, leading to the backreaming operation, which reconditions the diameter of the wellbore to its original state. Given the importance of backreaming during drilling operations in salt rocks, its incorporation into computational tools is necessary. Through the finite element method (FEM), we developed a program to identify and simulate the effects of the backreaming operations in vertical wells in the presence of salt layers. We proposed a simulator that associates 1D axisymmetric multilayers with unit thickness through a coupling strategy between them, considering a lesser number of degrees of freedom when compared to conventional 2D modeling. We checked the performance of multilayers strategy when compared with 2D axisymmetric modeling of the hole closure problem in the commercial software ABAQUSV R (Dassault Systèmes, Vélizy-Villacoublay, France); for the radial displacement histories, the multilayer strategy presented similarity with ABAQUS for cases that consider interaction, with the advantage of a low computational cost provided by the 1D formulation. We demonstrated the modeling of backreaming through the proposed tool.

Latin American Journal of Solids and Structures, 2020

Topology optimization is a well-suited method to establish the best material distribution inside ... more Topology optimization is a well-suited method to establish the best material distribution inside an analysis domain. It is common to observe some numerical instabilities in its gradient-based version, such as the checkerboard pattern, mesh dependence, and local minima. This research demonstrates the generalized finite-volume theory's checkerboard-free property by performing topology optimization algorithms without filtering techniques. The formation of checkerboard regions is associated with the finite element method's displacement field assumptions, where the equilibrium and continuity conditions are satisfied through the element nodes. On the other hand, the generalized finite-volume theory satisfies the continuity conditions between common faces of adjacent subvolumes, which is more likely from the continuum mechanics point of view. Also, the topology optimization algorithms based on the generalized finite-volume theory are performed using a mesh independent filter that regularizes the subvolume sensitivities, providing optimum topologies that avoid the mesh dependence and length scale issues.

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Applied Mathematical Modelling, 2021

Applied Mathematical Modelling, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Revista IBRACON de Estruturas e Materiais, 2019

Several factors influence the stability of concrete structures, such as building height, structur... more Several factors influence the stability of concrete structures, such as building height, structural components’ rigidity, bracing system, beam-wall connection rigidity, among others. Global structural stability is evaluated according to NBR 6118/2014 by the α e γz parameters. This article aims to evaluate the global structural stability concrete structures considering the eccentricity of the beam-wall connections. With the aid of software Abaqus© and TQS©, reticulated models were analyzed to evaluate the contribution of the eccentricity of the beam-wall connections on the global stability and the rigidity of the connections. The geometric nonlinear effects were disregarded in these analyses. The stability parameters from NBR6118/2014 were evaluated in the frame models, as well as the flexibilization criteria from the TQS© software, LEPMOL e REDMOL. The results of the displacement analysis show an increase of 26.45%, comparing the centered connection to the more eccentric connection.

Proceedings of the 7th International Symposium on Solid Mechanics, 2019

Revista IBRACON de Estruturas e Materiais, 2019

An analytical study aiming the design of cylindrical liquid storage tanks resting on deformable f... more An analytical study aiming the design of cylindrical liquid storage tanks resting on deformable foundations is developed in this work. The soil under the tanks is modeled as an elastic linear medium. The cylindrical wall is considered rigidly connected to the plate foundation. Here, concrete tanks are emphasized, although the study can be extended to other construction materials. For the analysis of the design forces acting on the tanks, efficient and simplified approximate expressions are derived based on rigorous analytical theories for thin shells and circular plate on elastic foundations. To verify the proposed approximate expressions and investigate the influence of the foundation deformability on displacements and design forces, parametric analyses of concrete tanks with different soil stiffness values are presented. The results illustrate the strong influence of the foundation stiffness on the tank design quantities and a very good performance of the simplified expressions.

Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019

This paper presents a semi-analytical micromechanical model for evaluation of effective thermal c... more This paper presents a semi-analytical micromechanical model for evaluation of effective thermal conductivity of composite materials with periodic microstructure. The model is based on the equivalent inclusion thermal problem and utilizes Fourier series for representation of periodic functions involved in the material homogenization approach. Two main objectives can be highlighted in the work. The first of them is the derivation of the thermal micromechanical model, which consists in an extension of a formulation originally derived for homogenization of elastic heterogeneous solids. The second objective consists in a detailed investigation on the performance of the model, considering convergence of results and efficiency of strategies employed for the approximate solution of the thermal homogenization problem. Analyses on the complexity of transformation temperature gradient functions are also included in this investigation. The results obtained for two examples of periodic composites with different microstructural architectures are presented and discussed in detail.

Risers verticais complacentes (CVAR) consistem em uma alternativa relativamente recente para expl... more Risers verticais complacentes (CVAR) consistem em uma alternativa relativamente recente para exploração de petróleo em águas ultra-profundas. A geometria do arranjo CVAR se apresenta predominantemente vertical com um offset horizontal entre o topo e a base. Sua configuração característica é obtida a partir da utilização de um trecho com revestimento de peso adicional na parte mais superior do riser e outro trecho com flutuadores, neste caso na região mais inferior. A disposição desses trechos ao longo da estrutura proporciona o aumento da tração ao longo do riser, mantendo os trechos verticais e atenuando a dinâmica da linha. O offset entre o topo e a base bem como a diferença de flutuação na região intermediária do riser geram uma leve curvatura nessa região. O dimensionamento do arranjo CVAR é determinado pela definição de 7 variáveis: diâmetro dos flutuadores, comprimento do trecho de flutuadores, espessura do revestimento pesado, comprimento do trecho de revestimento pesado, pos...

This work presents a study on strain and stress distributions in two-dimensional panels constitut... more This work presents a study on strain and stress distributions in two-dimensional panels constituted by elastic composite materials considering effects of physical and geometrical nonlinearities. The analyses are carried out by a new nonlinear model which is based on the parametric finite-volume theory. The model is incremental and uses a total Lagragian formulation that employs the Second Piola-Kirchhoff tensor and Green-Lagrange tensor as stress and strain measurements, respectively. The composite material and its constituents are assumed as linear or nonlinear elastic. The analyzed examples include two-dimensional panels with circular and elliptic inclusions presenting a large range of mismatch ratios for their Young’s moduli. In particular, stress concentrations in panels of functionally graded materials with circular and elliptic holes are analyzed. The study presents the distributions of stresses and strains over the matrices and inclusions of the composite materials. Results o...

International Journal of Solids and Structures, 2012

This contribution is motivated by the recent IJSS article titled ''Formulation of the High-Fideli... more This contribution is motivated by the recent IJSS article titled ''Formulation of the High-Fidelity Generalized Method of Cells with Arbitrary Cell Geometry for Refined Micromechanics and Damage in Composites'' by Haj-Ali and Aboudi. In the present discussion, we critically compare these authors' approach with the Parametric Finite-Volume Direct Averaging Micromechanics (FVDAM) theory developed in a sequence of papers dating to 2004. We show that the extension proposed by Haj-Ali and Aboudi follows the framework of the parametric FVDAM theory, and not the original HFGMC model as claimed. Just as importantly, we demonstrate that the proposed extension is fundamentally flawed as it violates accepted principles which every mechanics theory must satisfy, namely correct reducibility and coordinate frame indifference. Direct comparison of predictions generated by the parametric FVDAM theory, the proposed extension called HFGMC with arbitrary cell geometry and finite-element method demonstrates no need for the extension carried out in the specific manner proposed by Haj-Ali and Aboudi, which in fact produces inferior results.