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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 propertiesSystematic 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.Systematic design of tetra-petals auxetic structures with stiffness constraint
http://hdl.handle.net/10985/15085
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/10985/150852019-01-01T00:00:00ZWANG, 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.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.