https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Sat, 18 Apr 2026 22:41:13 GMT 2026-04-18T22:41:13Z http://hdl.handle.net/10985/10849 Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials CHATZIGEORGIOU, George; CHARALAMBAKIS, Nicolas; CHEMISKY, Yves; MERAGHNI, Fodil The current work deals with periodic thermomechanical composite media, in which the material constituents are considered to obey the generalized standard materials laws. The aim is to provide a proper homogenization framework that takes into account both the equilibrium and the thermodynamics laws in microscale and macroscale levels. The study is based on the asymptotic expansion homogenization technique, which permits to deduce useful results about the general structure of microscale and macroscale energy potentials and constitutive laws. The paper also proposes an incremental, linearized formulation that allows to identify suitable thermomechanical tangent moduli for the macroscale problem. The capabilities of this framework are illustrated with numerical examples on multilayered composites. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/10985/10849 2016-01-01T00:00:00Z CHATZIGEORGIOU, George CHARALAMBAKIS, Nicolas CHEMISKY, Yves MERAGHNI, Fodil The current work deals with periodic thermomechanical composite media, in which the material constituents are considered to obey the generalized standard materials laws. The aim is to provide a proper homogenization framework that takes into account both the equilibrium and the thermodynamics laws in microscale and macroscale levels. The study is based on the asymptotic expansion homogenization technique, which permits to deduce useful results about the general structure of microscale and macroscale energy potentials and constitutive laws. The paper also proposes an incremental, linearized formulation that allows to identify suitable thermomechanical tangent moduli for the macroscale problem. The capabilities of this framework are illustrated with numerical examples on multilayered composites. http://hdl.handle.net/10985/10050 Dissipation inequality-based periodic homogenization of wavy materials TSALIS, Dimitrios; CHATZIGEORGIOU, George; TSAKMAKIS, Charalampos; CHARALAMBAKIS, Nicolas In this paper we present an internal variable-based homogenization of a composite made of wavy elastic-perfectly plastic layers. In the context of a strain-driven process, the macrostress and the effective yield surface are expressed in terms of the residual stresses, which act as hardening parameters in the effective behavior of the composite. Moreover, an approximate two-steps homogenization scheme useful for composites made of matrix with wavy inclusions is proposed and a comparison with one computational and one semi-analytical homogenization method is presented. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/10985/10050 2015-01-01T00:00:00Z TSALIS, Dimitrios CHATZIGEORGIOU, George TSAKMAKIS, Charalampos CHARALAMBAKIS, Nicolas In this paper we present an internal variable-based homogenization of a composite made of wavy elastic-perfectly plastic layers. In the context of a strain-driven process, the macrostress and the effective yield surface are expressed in terms of the residual stresses, which act as hardening parameters in the effective behavior of the composite. Moreover, an approximate two-steps homogenization scheme useful for composites made of matrix with wavy inclusions is proposed and a comparison with one computational and one semi-analytical homogenization method is presented. http://hdl.handle.net/10985/14235 A model of heterogeneous thermoviscoplastic material preserving uniform normal strains under combined compression, tension (or compression) and shearing. Instability and homogenization results CHATZIGEORGIOU, George; CHARALAMBAKIS, Nicolas In this paper, we present the special solution of the two-dimensional problem of a continuously graded composite made of thermovisco- rigid plastic materials under combined biaxial quasistatic compression and tension (or compression) and shear, that preserves prescribed uniform normal strains. The related reference initial-boundary value problem is fully defined and the corresponding solution is analyzed and computed numerically. In the context of a linearized instability analysis, critical conditions, as the critical shear banding angle, in terms of the loading level and material heterogeneities, are presented. In the context of non-linear instability, these results are examined and explained. Additionally, in the same context of non-linear analysis, the destabilizing mechanism, the onset of instability and the critical time for prescribed lower and upper bounds of equivalent strain-rate and upper bound of equivalent strain are defined and related to the lateral normal stress. The limitations of linearized analysis results are also revealed. Moreover, a semi-analytical homogenization scheme for a periodically-graded plate is presented. The related results are used for the derivation of a homogenized problem of a multilayered composite with continuously graded interlayers. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/14235 2019-01-01T00:00:00Z CHATZIGEORGIOU, George CHARALAMBAKIS, Nicolas In this paper, we present the special solution of the two-dimensional problem of a continuously graded composite made of thermovisco- rigid plastic materials under combined biaxial quasistatic compression and tension (or compression) and shear, that preserves prescribed uniform normal strains. The related reference initial-boundary value problem is fully defined and the corresponding solution is analyzed and computed numerically. In the context of a linearized instability analysis, critical conditions, as the critical shear banding angle, in terms of the loading level and material heterogeneities, are presented. In the context of non-linear instability, these results are examined and explained. Additionally, in the same context of non-linear analysis, the destabilizing mechanism, the onset of instability and the critical time for prescribed lower and upper bounds of equivalent strain-rate and upper bound of equivalent strain are defined and related to the lateral normal stress. The limitations of linearized analysis results are also revealed. Moreover, a semi-analytical homogenization scheme for a periodically-graded plate is presented. The related results are used for the derivation of a homogenized problem of a multilayered composite with continuously graded interlayers. http://hdl.handle.net/10985/17521 Mathematical homogenization of inelastic dissipative materials: a survey and recent progress CHARALAMBAKIS, Nicolas; CHATZIGEORGIOU, George; CHEMISKY, Yves; MERAGHNI, Fodil In this paper, a review of papers on mathematical homogenization of dissipative composites under small strains and on the interplay between homogenization procedure and dissipation due to mechanical work is presented. Moreover, a critical survey on the links between mathematical homogenization and computational homogenization is attempted. Sun, 01 Jan 2017 00:00:00 GMT http://hdl.handle.net/10985/17521 2017-01-01T00:00:00Z CHARALAMBAKIS, Nicolas CHATZIGEORGIOU, George CHEMISKY, Yves MERAGHNI, Fodil In this paper, a review of papers on mathematical homogenization of dissipative composites under small strains and on the interplay between homogenization procedure and dissipation due to mechanical work is presented. Moreover, a critical survey on the links between mathematical homogenization and computational homogenization is attempted. http://hdl.handle.net/10985/17469 Thermomechanical Behavior of Dissipative Composite Materials CHATZIGEORGIOU, George; CHARALAMBAKIS, Nicolas; CHEMISKY, Yves; MERAGHNI, Fodil This book presents theoretical and numerical tools for studying materials and structures under fully coupled thermomechanical conditions, with a special focus on composites. The authors cover many aspects of the modeling process and provide the reader with the knowledge required to: a) identify the conservation laws and thermodynamic principles that need to be respected by most solid materials; b) construct constitutive laws for various types of dissipative processes, both rate-independent and rate-dependent, by utilizing a rigorous thermodynamic framework; c) design robust numerical algorithms that permit accuracy and efficiency in the calculations of complicated constitutive laws; d) extend the theoretical and numerical investigation from homogeneous media to composites with periodic or random microstructure. The discussions and topics explored are useful for graduate students, as well as for young and advanced researchers, who wish to strengthen their knowledge of the application of thermodynamic principles on dissipative materials and homogenization theories for composites. Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/10985/17469 2018-01-01T00:00:00Z CHATZIGEORGIOU, George CHARALAMBAKIS, Nicolas CHEMISKY, Yves MERAGHNI, Fodil This book presents theoretical and numerical tools for studying materials and structures under fully coupled thermomechanical conditions, with a special focus on composites. The authors cover many aspects of the modeling process and provide the reader with the knowledge required to: a) identify the conservation laws and thermodynamic principles that need to be respected by most solid materials; b) construct constitutive laws for various types of dissipative processes, both rate-independent and rate-dependent, by utilizing a rigorous thermodynamic framework; c) design robust numerical algorithms that permit accuracy and efficiency in the calculations of complicated constitutive laws; d) extend the theoretical and numerical investigation from homogeneous media to composites with periodic or random microstructure. The discussions and topics explored are useful for graduate students, as well as for young and advanced researchers, who wish to strengthen their knowledge of the application of thermodynamic principles on dissipative materials and homogenization theories for composites. http://hdl.handle.net/10985/19175 Multiscale modeling accounting for inelastic mechanisms of fuzzy fiber composites with straight or wavy carbon nanotubes CHATZIGEORGIOU, George; MERAGHNI, Fodil; CHARALAMBAKIS, Nicolas; BENAARBIA, Adil This paper proposes a micromechanical approach aimed at identifying the response of unidirectional fuzzy fiber composites undergoing inelastic fields. Fuzzy fibers are reinforcement fibers coated with radially aligned straight or wavy carbon nanotubes grown through chemical deposition process (PVD or CVD). Due to this nature, the composite with fuzzy fibers is described by three scales: i) the microscale consisting of carbon nanotubes and their surrounding matrix, ii) the mesoscale containing the fiber, the nanocomposite and the matrix, and iii) the macroscale related to the overall fuzzy fiber composite. The developed framework considers for the mesoscopic scale an analytical formulation, based on the composite cylinders assemblage (CCA) method, combining the principles of the Transformation Field Analysis (TFA) technique. A numerical example that includes comparisons with full field homogenization strategies confirms the accuracy of the framework to predict the overall response, as well as the average local fields of the constituents. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/19175 2020-01-01T00:00:00Z CHATZIGEORGIOU, George MERAGHNI, Fodil CHARALAMBAKIS, Nicolas BENAARBIA, Adil This paper proposes a micromechanical approach aimed at identifying the response of unidirectional fuzzy fiber composites undergoing inelastic fields. Fuzzy fibers are reinforcement fibers coated with radially aligned straight or wavy carbon nanotubes grown through chemical deposition process (PVD or CVD). Due to this nature, the composite with fuzzy fibers is described by three scales: i) the microscale consisting of carbon nanotubes and their surrounding matrix, ii) the mesoscale containing the fiber, the nanocomposite and the matrix, and iii) the macroscale related to the overall fuzzy fiber composite. The developed framework considers for the mesoscopic scale an analytical formulation, based on the composite cylinders assemblage (CCA) method, combining the principles of the Transformation Field Analysis (TFA) technique. A numerical example that includes comparisons with full field homogenization strategies confirms the accuracy of the framework to predict the overall response, as well as the average local fields of the constituents. http://hdl.handle.net/10985/21675 Multiscale Modeling Approaches for Composites CHATZIGEORGIOU, George; MERAGHNI, Fodil; CHARALAMBAKIS, Nicolas Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples. The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then progresses to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green’s tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory. Sat, 01 Jan 2022 00:00:00 GMT http://hdl.handle.net/10985/21675 2022-01-01T00:00:00Z CHATZIGEORGIOU, George MERAGHNI, Fodil CHARALAMBAKIS, Nicolas Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples. The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then progresses to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green’s tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory. http://hdl.handle.net/10985/10840 Effective properties of multiphase composites made of elastic materials with hierarchical structure TSALIS, Dimitrios; BONNAY, Kevin; CHATZIGEORGIOU, George; CHARALAMBAKIS, Nicolas In this paper, the analytical solution of the multi - step homogenization problem for multi - rank composites with generalized periodicity made of elastic materials is presented. The proposed homogenization scheme may be combined with computational homogenization for solving more complex microstructures. Three numerical examples are presented, concerning locally periodic stratified materials, matrices with wavy layers and wavy fiber reinforced composites. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/10985/10840 2015-01-01T00:00:00Z TSALIS, Dimitrios BONNAY, Kevin CHATZIGEORGIOU, George CHARALAMBAKIS, Nicolas In this paper, the analytical solution of the multi - step homogenization problem for multi - rank composites with generalized periodicity made of elastic materials is presented. The proposed homogenization scheme may be combined with computational homogenization for solving more complex microstructures. Three numerical examples are presented, concerning locally periodic stratified materials, matrices with wavy layers and wavy fiber reinforced composites. http://hdl.handle.net/10985/11177 Effective behavior of thermo-elastic tubes with wavy layers TSALIS, Dimitrios; CHATZIGEORGIOU, George; CHARALAMBAKIS, Nicolas In the present article, the homogenization of a composite star-shaped tube with numerous thin, periodic, elastic wavy layers, is presented. The composite exhibits a multiscale periodicity allowing for a multistep asymptotic homogenization scheme starting from the finest scale. The scheme gives the complete effective thermoelastic behavior of the composite. By a numerical example of a two-phase composite with sinusoidal wavy walls, whose effective behavior is an orthotropic material, the above method is illustrated. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/10985/11177 2016-01-01T00:00:00Z TSALIS, Dimitrios CHATZIGEORGIOU, George CHARALAMBAKIS, Nicolas In the present article, the homogenization of a composite star-shaped tube with numerous thin, periodic, elastic wavy layers, is presented. The composite exhibits a multiscale periodicity allowing for a multistep asymptotic homogenization scheme starting from the finest scale. The scheme gives the complete effective thermoelastic behavior of the composite. By a numerical example of a two-phase composite with sinusoidal wavy walls, whose effective behavior is an orthotropic material, the above method is illustrated. http://hdl.handle.net/10985/11896 Multiscale modeling of periodic dissipative composites under thermomechanical loading conditions CHARALAMBAKIS, Nicolas; CHATZIGEORGIOU, George; CHEMISKY, Yves; MERAGHNI, Fodil The modern technological challenges on the engineering industry and the extensive advances in the materials science have caused a tremendous increase in the development of composites. Plenty of engineering and biomechanics applications demand smart materials and structures which combine high strength, multifunctionality and durability. At the same time, a crucial parameter in the choice of the most suitable composite material is the long lifetime during repeated loading cycles, thus fatigue is an essential parameter in design. To achieve the high demands in the modern applications, composite materials often operate under thermomechanical conditions that cause the appearance of dissipative phenomena like plasticity, viscoelasticity-viscoplasticity and damage. The present work deals with periodic composite media subjected to fully coupled thermomechanical loading. The material constituents of these composites are assumed to belong in the general class of generalized standard materials laws. The aim is to provide a proper homogenization framework that describes accurately the basic conservation laws in both microscopic and macroscopic levels. The study is based on the asymptotic expansion homogenization technique, which permits to deduce useful results about the energy potentials that characterize the material response in both scales. Moreover, the numerical implementation is based on an incremental, linearized formulation. This formulation allows to identify proper thermomechanical 3D tangent moduli for the macroscale problem and thus design an implicit computational scheme. Sun, 01 Jan 2017 00:00:00 GMT http://hdl.handle.net/10985/11896 2017-01-01T00:00:00Z CHARALAMBAKIS, Nicolas CHATZIGEORGIOU, George CHEMISKY, Yves MERAGHNI, Fodil The modern technological challenges on the engineering industry and the extensive advances in the materials science have caused a tremendous increase in the development of composites. Plenty of engineering and biomechanics applications demand smart materials and structures which combine high strength, multifunctionality and durability. At the same time, a crucial parameter in the choice of the most suitable composite material is the long lifetime during repeated loading cycles, thus fatigue is an essential parameter in design. To achieve the high demands in the modern applications, composite materials often operate under thermomechanical conditions that cause the appearance of dissipative phenomena like plasticity, viscoelasticity-viscoplasticity and damage. The present work deals with periodic composite media subjected to fully coupled thermomechanical loading. The material constituents of these composites are assumed to belong in the general class of generalized standard materials laws. The aim is to provide a proper homogenization framework that describes accurately the basic conservation laws in both microscopic and macroscopic levels. The study is based on the asymptotic expansion homogenization technique, which permits to deduce useful results about the energy potentials that characterize the material response in both scales. Moreover, the numerical implementation is based on an incremental, linearized formulation. This formulation allows to identify proper thermomechanical 3D tangent moduli for the macroscale problem and thus design an implicit computational scheme.