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http://hdl.handle.net/10985/7983
Towards gigantic RVE sizes for 3D stochastic fibrous networks
DIRRENBERGER, Justin; FOREST, Samuel; JEULIN, Dominique
The size of representative volume element (RVE) for 3D stochastic fibrous media is investigated. A statistical RVE size determination method is applied to a specific model of random microstructure: Poisson fibers. The definition of RVE size is related to the concept of integral range. What happens in microstructures exhibiting an infinite integral range? Computational homogenization for thermal and elastic properties is performed through finite elements, over hundreds of realizations of the stochastic microstructural model, using uniform and mixed boundary conditions. The generated data undergoes statistical treatment, from which gigantic RVE sizes emerge. The method used for determining RVE sizes was found to be operational, even for pathological media, i.e., with infinite integral range, interconnected percolating porous phase and infinite contrast of properties
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/79832014-01-01T00:00:00ZDIRRENBERGER, JustinFOREST, SamuelJEULIN, DominiqueThe size of representative volume element (RVE) for 3D stochastic fibrous media is investigated. A statistical RVE size determination method is applied to a specific model of random microstructure: Poisson fibers. The definition of RVE size is related to the concept of integral range. What happens in microstructures exhibiting an infinite integral range? Computational homogenization for thermal and elastic properties is performed through finite elements, over hundreds of realizations of the stochastic microstructural model, using uniform and mixed boundary conditions. The generated data undergoes statistical treatment, from which gigantic RVE sizes emerge. The method used for determining RVE sizes was found to be operational, even for pathological media, i.e., with infinite integral range, interconnected percolating porous phase and infinite contrast of propertiesScalar-based strain gradient plasticity theory to model size-dependent kinematic hardening effects
http://hdl.handle.net/10985/19875
Scalar-based strain gradient plasticity theory to model size-dependent kinematic hardening effects
JEBAHI, Mohamed; FOREST, Samuel
A common belief in phenomenological strain gradient plasticity modeling is that including the gradient of scalar variables in the constitutive setting leads to size-dependent isotropic hardening, whereas the gradient of second-order tensors induces size-dependent kinematic hardening. The present paper shows that it is also possible to produce size-dependent kinematic hardening using scalar-based gradient theory. For this purpose, a new model involving the gradient of the equivalent plastic strain is developed and compared with two reference scalar-based and tensor-based theories. Theoretical investigations using simple monotonic loading conditions are first presented to assess the ability of the proposed model to solve some issues related to existing scalar-based gradient theories. Simulations under cyclic loading conditions are then provided to investigate the nature of the resulting hardening. These simulations show that the proposed model is capable of producing size-dependent kinematic hardening effects at more affordable costs, compared to existing tensor-based strain gradient plasticity theories.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/198752021-01-01T00:00:00ZJEBAHI, MohamedFOREST, SamuelA common belief in phenomenological strain gradient plasticity modeling is that including the gradient of scalar variables in the constitutive setting leads to size-dependent isotropic hardening, whereas the gradient of second-order tensors induces size-dependent kinematic hardening. The present paper shows that it is also possible to produce size-dependent kinematic hardening using scalar-based gradient theory. For this purpose, a new model involving the gradient of the equivalent plastic strain is developed and compared with two reference scalar-based and tensor-based theories. Theoretical investigations using simple monotonic loading conditions are first presented to assess the ability of the proposed model to solve some issues related to existing scalar-based gradient theories. Simulations under cyclic loading conditions are then provided to investigate the nature of the resulting hardening. These simulations show that the proposed model is capable of producing size-dependent kinematic hardening effects at more affordable costs, compared to existing tensor-based strain gradient plasticity theories.Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization
http://hdl.handle.net/10985/12036
Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization
WANG, Zhen-Pei; POH, Leong Hien; DIRRENBERGER, Justin; ZHU, Yilin; FOREST, Samuel
An important feature that drives the auxetic behaviour of the star-shaped auxetic structures is the hinge-functional connection at the vertex connections. This feature poses a great challenge for manufacturing and may lead to significant stress concentrations. To overcome these problems, we introduced smoothed petal-shaped auxetic structures, where the hinges are replaced by smoothed connections. To accommodate the curved features of the petal-shaped auxetics, a parametrisation modelling scheme using multiple NURBS patches is proposed. Next, an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance. To ensure a minimum thickness for each member, a geometry sizing constraint is imposed via piece-wise bounding polynomials. This geometry sizing constraint, in the context of isogeometric shape optimization, is particularly interesting due to the non-interpolatory nature of NURBS basis. The effective Poisson ratio is used directly as the objective function, and an adjoint sensitivity analysis is carried out. The optimized designs – smoothed petal auxetic structures – are shown to achieve low negative Poisson’s ratios, while the difficulties of manufacturing the hinges are avoided. For the case with six petals, an in-plane isotropy is achieved.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/120362017-01-01T00:00:00ZWANG, Zhen-PeiPOH, Leong HienDIRRENBERGER, JustinZHU, YilinFOREST, SamuelAn important feature that drives the auxetic behaviour of the star-shaped auxetic structures is the hinge-functional connection at the vertex connections. This feature poses a great challenge for manufacturing and may lead to significant stress concentrations. To overcome these problems, we introduced smoothed petal-shaped auxetic structures, where the hinges are replaced by smoothed connections. To accommodate the curved features of the petal-shaped auxetics, a parametrisation modelling scheme using multiple NURBS patches is proposed. Next, an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance. To ensure a minimum thickness for each member, a geometry sizing constraint is imposed via piece-wise bounding polynomials. This geometry sizing constraint, in the context of isogeometric shape optimization, is particularly interesting due to the non-interpolatory nature of NURBS basis. The effective Poisson ratio is used directly as the objective function, and an adjoint sensitivity analysis is carried out. The optimized designs – smoothed petal auxetic structures – are shown to achieve low negative Poisson’s ratios, while the difficulties of manufacturing the hinges are avoided. For the case with six petals, an in-plane isotropy is achieved.Computational Homogenization of Architectured Materials
http://hdl.handle.net/10985/14978
Computational Homogenization of Architectured Materials
DIRRENBERGER, Justin; FOREST, Samuel; JEULIN, Dominique
Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/149782019-01-01T00:00:00ZDIRRENBERGER, JustinFOREST, SamuelJEULIN, DominiqueArchitectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials.An alternative way to describe thermodynamically-consistent higher-order dissipation within strain gradient plasticity
http://hdl.handle.net/10985/22795
An alternative way to describe thermodynamically-consistent higher-order dissipation within strain gradient plasticity
JEBAHI, Mohamed; FOREST, Samuel
In the context of strain gradient plasticity (SGP), description of higher-order dissipation is the subject of extensive on-going discussions. In most existing SGP theories including thermodynamically-consistent higher-order dissipation, higher-order dissipative processes are described based on the decomposition of the higher-order stresses into recoverable and unrecoverable parts. This higher-order stress decomposition represents the basis of the so-called non-incremental (Gurtin-type) SGP theories, which are the most commonly used in the literature. As formulated, these theories satisfy the thermodynamic requirement of non-negative dissipation. However, they generally lead to unusual effects for some boundary value problems, such as the occurrence of elastic gaps under non-proportional loading conditions. The present work proposes an alternative way to describe higher-order dissipative effects, with an illustration within strain gradient crystal plasticity (SGCP) framework. Inspired by rheological models in series like Maxwell model, the higher-order stress decomposition is replaced by a decomposition of the plastic slip gradients into recoverable and unrecoverable parts. Effects of this decomposition technique are studied and compared with those obtained using higher-order stress decomposition. Capabilities of such a technique to deal with elastic gaps are also investigated.
Sat, 01 Oct 2022 00:00:00 GMThttp://hdl.handle.net/10985/227952022-10-01T00:00:00ZJEBAHI, MohamedFOREST, SamuelIn the context of strain gradient plasticity (SGP), description of higher-order dissipation is the subject of extensive on-going discussions. In most existing SGP theories including thermodynamically-consistent higher-order dissipation, higher-order dissipative processes are described based on the decomposition of the higher-order stresses into recoverable and unrecoverable parts. This higher-order stress decomposition represents the basis of the so-called non-incremental (Gurtin-type) SGP theories, which are the most commonly used in the literature. As formulated, these theories satisfy the thermodynamic requirement of non-negative dissipation. However, they generally lead to unusual effects for some boundary value problems, such as the occurrence of elastic gaps under non-proportional loading conditions. The present work proposes an alternative way to describe higher-order dissipative effects, with an illustration within strain gradient crystal plasticity (SGCP) framework. Inspired by rheological models in series like Maxwell model, the higher-order stress decomposition is replaced by a decomposition of the plastic slip gradients into recoverable and unrecoverable parts. Effects of this decomposition technique are studied and compared with those obtained using higher-order stress decomposition. Capabilities of such a technique to deal with elastic gaps are also investigated.Multiscale modeling of the elasto-plastic behavior of architectured and nanostructured Cu-Nb composite wires and comparison with neutron diffraction experiments
http://hdl.handle.net/10985/17970
Multiscale modeling of the elasto-plastic behavior of architectured and nanostructured Cu-Nb composite wires and comparison with neutron diffraction experiments
GU, T.; MEDY, J. R.; KLOSEK, Vincent; CASTELNAU, Olivier; FOREST, Samuel; HERVÉ-LUANCO, Eveline; LECOUTURIER-DUPOUY, F.; PROUDHON, Henry; RENAULT, Pierre Olivier; THILLY, Ludovic; VILLECHAISE, Patrick
Nanostructured and architectured copper niobium composite wires are excellent candidates for the generation of intense pulsed magnetic fields ( 100T) as they combine both high strength and high electrical conductivity. Multi-scaled Cu-Nb wires are fabricated by accumulative drawing and bundling (a severe plastic deformation technique), leading to a multiscale, architectured, and nanostructured microstructure exhibiting a strong fiber crystallographic texture and elongated grain shape along the wire axis. This paper presents a comprehensive study of the effective elastoplastic behavior of this composite material by using two different approaches to model the microstructural features: full-field finite elements and mean-field modeling. As the material exhibits several characteristic scales, an original hierarchical strategy is proposed based on iterative scale transition steps from the nanometric grain scale to the millimetric macro-scale. The best modeling strategy is selected to estimate reliably the effective elasto-plastic behavior of Cu-Nb wires with minimum computational time. Finally, for the first time, the models are confronted to tensile tests and in-situ neutron diffraction experimental data with a good agreement.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/179702019-01-01T00:00:00ZGU, T.MEDY, J. R.KLOSEK, VincentCASTELNAU, OlivierFOREST, SamuelHERVÉ-LUANCO, EvelineLECOUTURIER-DUPOUY, F.PROUDHON, HenryRENAULT, Pierre OlivierTHILLY, LudovicVILLECHAISE, PatrickNanostructured and architectured copper niobium composite wires are excellent candidates for the generation of intense pulsed magnetic fields ( 100T) as they combine both high strength and high electrical conductivity. Multi-scaled Cu-Nb wires are fabricated by accumulative drawing and bundling (a severe plastic deformation technique), leading to a multiscale, architectured, and nanostructured microstructure exhibiting a strong fiber crystallographic texture and elongated grain shape along the wire axis. This paper presents a comprehensive study of the effective elastoplastic behavior of this composite material by using two different approaches to model the microstructural features: full-field finite elements and mean-field modeling. As the material exhibits several characteristic scales, an original hierarchical strategy is proposed based on iterative scale transition steps from the nanometric grain scale to the millimetric macro-scale. The best modeling strategy is selected to estimate reliably the effective elasto-plastic behavior of Cu-Nb wires with minimum computational time. Finally, for the first time, the models are confronted to tensile tests and in-situ neutron diffraction experimental data with a good agreement.Propagating material instabilities in planar architectured materials
http://hdl.handle.net/10985/19142
Propagating material instabilities in planar architectured materials
VIARD, Antoine-Emmanuel; DIRRENBERGER, Justin; FOREST, Samuel
Under tension low carbon steel exhibits inhomogeneous plastic deformation. This instability called Piobert-Lüders banding creates fronts of localized strain that propagate in the structure. To date, Lüders banding has been studied experimentally and numerically only in simple geometries like sheets, tubes and normalized fracture mechanics specimens. This paper focuses on architectured materials and specifically lattice structures which can be defined as a tessellation of unit-cells periodically distributed in space. This class of advanced materials draws new mechanical properties from its inner architecture. We investigate the effect of the architecture on the global behavior of the structure. Especially, how bands interact with the lattice and how to control initiation and propagation of localized strain using the architecture. An elastoplastic material model is used in order to simulate the Piobert-Lüders band formation and propagation. The model also considers a large deformation framework for elastoplasticity with periodic boundary conditions in order to represent the architectured material. Initiation and propagation of material instabilities depend on the geometry as well as its on the relative orientation with respect to the loading direction. Propagating and non-propagating behaviors are identified for the Piobert-Lüders bands and related to the different types of geometry. Material instabilities affect the mechanical behavior of the structure as far as they are governed by the architecture. These conclusions are compared to experimental results from tensile tests on laser-architectured specimens made of ARMCO steel.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/191422020-01-01T00:00:00ZVIARD, Antoine-EmmanuelDIRRENBERGER, JustinFOREST, SamuelUnder tension low carbon steel exhibits inhomogeneous plastic deformation. This instability called Piobert-Lüders banding creates fronts of localized strain that propagate in the structure. To date, Lüders banding has been studied experimentally and numerically only in simple geometries like sheets, tubes and normalized fracture mechanics specimens. This paper focuses on architectured materials and specifically lattice structures which can be defined as a tessellation of unit-cells periodically distributed in space. This class of advanced materials draws new mechanical properties from its inner architecture. We investigate the effect of the architecture on the global behavior of the structure. Especially, how bands interact with the lattice and how to control initiation and propagation of localized strain using the architecture. An elastoplastic material model is used in order to simulate the Piobert-Lüders band formation and propagation. The model also considers a large deformation framework for elastoplasticity with periodic boundary conditions in order to represent the architectured material. Initiation and propagation of material instabilities depend on the geometry as well as its on the relative orientation with respect to the loading direction. Propagating and non-propagating behaviors are identified for the Piobert-Lüders bands and related to the different types of geometry. Material instabilities affect the mechanical behavior of the structure as far as they are governed by the architecture. These conclusions are compared to experimental results from tensile tests on laser-architectured specimens made of ARMCO steel.Systematic design of tetra-petals auxetic structures with stiffness constraint
http://hdl.handle.net/10985/14755
Systematic design of tetra-petals auxetic structures with stiffness constraint
WANG, Zhen-Pei; POH, Leong Hien; ZHU, Yilin; DIRRENBERGER, Justin; FOREST, Samuel
This paper focuses on a systematic isogeometric design approach for the optimal petal form and size characterization of tetra-petals auxetics, considering both plane stress and plane strain conditions. The underlying deformation mechanism of a tetra-petals auxetic is analyzed numerically with respect to several key parameters. Design optimizations are performed systematically to give bounding graphs for the minimum Poisson's ratio achievable with different stiffness constraints. Tunable design studies with targeted effective Poisson's ratio, shear modulus and stiffness are demonstrated. Potential application for functionally graded lattice structures is presented. Numerical and experimental verifications are provided to verify the designs. The out-of-plane buckling phenomenon in tension for thin auxetics with re-entrant features is illustrated experimentally to draw caution to results obtained using plane stress formulations for designing such structures.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/147552019-01-01T00:00:00ZWANG, Zhen-PeiPOH, Leong HienZHU, YilinDIRRENBERGER, JustinFOREST, SamuelThis paper focuses on a systematic isogeometric design approach for the optimal petal form and size characterization of tetra-petals auxetics, considering both plane stress and plane strain conditions. The underlying deformation mechanism of a tetra-petals auxetic is analyzed numerically with respect to several key parameters. Design optimizations are performed systematically to give bounding graphs for the minimum Poisson's ratio achievable with different stiffness constraints. Tunable design studies with targeted effective Poisson's ratio, shear modulus and stiffness are demonstrated. Potential application for functionally graded lattice structures is presented. Numerical and experimental verifications are provided to verify the designs. The out-of-plane buckling phenomenon in tension for thin auxetics with re-entrant features is illustrated experimentally to draw caution to results obtained using plane stress formulations for designing such structures.On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation
http://hdl.handle.net/10985/23663
On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation
AMOUZOU-ADOUN, Yaovi Armand; JEBAHI, Mohamed; FIVEL, Marc; FOREST, Samuel; LECOMTE, Jean-Sebastien; SCHUMAN, Christophe; ABED-MERAIM, Farid
Although presenting attractive features in dealing with small-scale size effects, strain gradient plasticity (SGP) theories can lead to uncommon phenomena for some boundary value problems. Almost all non-incremental (Gurtin-type) SGP theories including thermodynamically-consistent higher-order dissipation predict elastic gaps under certain non-proportional loading conditions. An elastic gap is defined as a finite change in the equivalent yield stress after an infinitesimal change in the strain conditions, at the occurrence of the non-proportional loading source. The existence of such gaps in reality is largely questioned and represents a major source of uncertainty preventing the development of robust SGP theories for real small-scale applications. Using 3D discrete dislocation dynamics (3D-DDD), the present paper aims at investigating size effects within micron-scale single crystal structures under various non-proportional loading conditions, including tension-compression-passivation, bending-passivation and tension-bending. An in-depth investigation of the occurrence of elastic gaps under these conditions, which are known to entail such gaps when using classical non-incremental SGP theories, is conducted. The obtained 3D-DDD results reproduce well known experimentally confirmed size effects like Hall-Petch effect, Asaro’s type III kinematic hardening and reversible plasticity. However, no evidence of the phenomenon of elastic gaps is found, which constitutes a first indication that this phenomenon may not exist in reality. The simulations are performed on face-centered cubic (FCC) Nickel single grains with cuboid shapes ranging from 2 microns to 15 microns and different orientations.
Sat, 01 Apr 2023 00:00:00 GMThttp://hdl.handle.net/10985/236632023-04-01T00:00:00ZAMOUZOU-ADOUN, Yaovi ArmandJEBAHI, MohamedFIVEL, MarcFOREST, SamuelLECOMTE, Jean-SebastienSCHUMAN, ChristopheABED-MERAIM, Farid Although presenting attractive features in dealing with small-scale size effects, strain gradient plasticity (SGP) theories can lead to uncommon phenomena for some boundary value problems. Almost all non-incremental (Gurtin-type) SGP theories including thermodynamically-consistent higher-order dissipation predict elastic gaps under certain non-proportional loading conditions. An elastic gap is defined as a finite change in the equivalent yield stress after an infinitesimal change in the strain conditions, at the occurrence of the non-proportional loading source. The existence of such gaps in reality is largely questioned and represents a major source of uncertainty preventing the development of robust SGP theories for real small-scale applications. Using 3D discrete dislocation dynamics (3D-DDD), the present paper aims at investigating size effects within micron-scale single crystal structures under various non-proportional loading conditions, including tension-compression-passivation, bending-passivation and tension-bending. An in-depth investigation of the occurrence of elastic gaps under these conditions, which are known to entail such gaps when using classical non-incremental SGP theories, is conducted. The obtained 3D-DDD results reproduce well known experimentally confirmed size effects like Hall-Petch effect, Asaro’s type III kinematic hardening and reversible plasticity. However, no evidence of the phenomenon of elastic gaps is found, which constitutes a first indication that this phenomenon may not exist in reality. The simulations are performed on face-centered cubic (FCC) Nickel single grains with cuboid shapes ranging from 2 microns to 15 microns and different orientations.