The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
S Doll - One of the best experts on this subject based on the ideXlab platform.
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extension of the solid shell concept for application to large elastic and large elastoplastic deformations
International Journal for Numerical Methods in Engineering, 2000Co-Authors: R Hauptmann, Karl Schweizerhof, S DollAbstract:In the present contribution we extend a previously proposed so-called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modi cations necessary for hyper-elastic or elastoplastic material laws are discussed. These modi cations concern the right Cauchy–Green Tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modi ed Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright ? 2000 John Wiley & Sons, Ltd.
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Extension of the ‘solid‐shell’ concept for application to large elastic and large elastoplastic deformations
International Journal for Numerical Methods in Engineering, 2000Co-Authors: R Hauptmann, Karl Schweizerhof, S DollAbstract:In the present contribution we extend a previously proposed so-called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modi cations necessary for hyper-elastic or elastoplastic material laws are discussed. These modi cations concern the right Cauchy–Green Tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modi ed Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright ? 2000 John Wiley & Sons, Ltd.
R Hauptmann - One of the best experts on this subject based on the ideXlab platform.
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extension of the solid shell concept for application to large elastic and large elastoplastic deformations
International Journal for Numerical Methods in Engineering, 2000Co-Authors: R Hauptmann, Karl Schweizerhof, S DollAbstract:In the present contribution we extend a previously proposed so-called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modi cations necessary for hyper-elastic or elastoplastic material laws are discussed. These modi cations concern the right Cauchy–Green Tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modi ed Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright ? 2000 John Wiley & Sons, Ltd.
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Extension of the ‘solid‐shell’ concept for application to large elastic and large elastoplastic deformations
International Journal for Numerical Methods in Engineering, 2000Co-Authors: R Hauptmann, Karl Schweizerhof, S DollAbstract:In the present contribution we extend a previously proposed so-called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modi cations necessary for hyper-elastic or elastoplastic material laws are discussed. These modi cations concern the right Cauchy–Green Tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modi ed Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright ? 2000 John Wiley & Sons, Ltd.
Philippe G. Ciarlet - One of the best experts on this subject based on the ideXlab platform.
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Expression of Dirichlet boundary conditions in terms of the Cauchy–Green Tensor field
Comptes Rendus Mathematique, 2013Co-Authors: Philippe G. Ciarlet, Cristinel MardareAbstract:Abstract In a previous work, it was shown how the Cauchy–Green Tensor field C : = ∇ Φ T ∇ Φ ∈ W 2 , s ( Ω ; S > 3 ) , s > 3 / 2 , can be considered as the sole unknown in the homogeneous Dirichlet problem of nonlinear elasticity posed over a domain Ω ⊂ R 3 , instead of the deformation Φ ∈ W 3 , s ( Ω ; R 3 ) in the usual approach. The purpose of this Note is to show that the same approach applies as well to the Dirichlet–Neumann problem. To this end, we show how the boundary condition Φ = Φ 0 on a portion Γ 0 of the boundary of Ω can be recast, again as boundary conditions on Γ 0 , but this time expressed only in terms of the new unknown C ∈ W 2 , s ( Ω ; S > 3 ) .
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Continuity of a Deformation in H^1 as a Function of Its Cauchy-Green Tensor in L^1
Journal of Nonlinear Science, 2004Co-Authors: Philippe G. Ciarlet, C. MardareAbstract:Let $\Omega$ be a bounded Lipschitz domain in $\BBbR^n$. The Cauchy-Green, or metric, Tensor field associated with a deformation of the set $\Omega$, i.e., a smooth-enough orientation-preserving mapping $\bTh\colon\Omega\to\BBbR^n$, is the $n\times n$ symmetric matrix field defined by $\bnabla\bTheta^T(x)\bnabla\bTheta(x)$ at each point $x\in\Omega$. We show that, under appropriate assumptions, the deformations depend continuously on their Cauchy-Green Tensors, the topologies being those of the spaces $\bH^1(\Omega)$ for the deformations and $\bL^1(\Omega)$ for the Cauchy-Green Tensors. When $n=3$ and $\Omega$ is viewed as a reference configuration of an elastic body, this result has potential applications to nonlinear three-dimensional elasticity, since the stored energy function of a hyperelastic material depends on the deformation gradient field $\bnabla\bTheta$ through the Cauchy-Green Tensor.
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Continuity of a Deformation as a Function of its Cauchy-Green Tensor
Archive for Rational Mechanics and Analysis, 2003Co-Authors: Philippe G. Ciarlet, Florian LaurentAbstract:If the Riemann-Christoffel Tensor associated with a field C of class
C. Mardare - One of the best experts on this subject based on the ideXlab platform.
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Continuity of a Deformation in H^1 as a Function of Its Cauchy-Green Tensor in L^1
Journal of Nonlinear Science, 2004Co-Authors: Philippe G. Ciarlet, C. MardareAbstract:Let $\Omega$ be a bounded Lipschitz domain in $\BBbR^n$. The Cauchy-Green, or metric, Tensor field associated with a deformation of the set $\Omega$, i.e., a smooth-enough orientation-preserving mapping $\bTh\colon\Omega\to\BBbR^n$, is the $n\times n$ symmetric matrix field defined by $\bnabla\bTheta^T(x)\bnabla\bTheta(x)$ at each point $x\in\Omega$. We show that, under appropriate assumptions, the deformations depend continuously on their Cauchy-Green Tensors, the topologies being those of the spaces $\bH^1(\Omega)$ for the deformations and $\bL^1(\Omega)$ for the Cauchy-Green Tensors. When $n=3$ and $\Omega$ is viewed as a reference configuration of an elastic body, this result has potential applications to nonlinear three-dimensional elasticity, since the stored energy function of a hyperelastic material depends on the deformation gradient field $\bnabla\bTheta$ through the Cauchy-Green Tensor.
Karl Schweizerhof - One of the best experts on this subject based on the ideXlab platform.
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extension of the solid shell concept for application to large elastic and large elastoplastic deformations
International Journal for Numerical Methods in Engineering, 2000Co-Authors: R Hauptmann, Karl Schweizerhof, S DollAbstract:In the present contribution we extend a previously proposed so-called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modi cations necessary for hyper-elastic or elastoplastic material laws are discussed. These modi cations concern the right Cauchy–Green Tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modi ed Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright ? 2000 John Wiley & Sons, Ltd.
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Extension of the ‘solid‐shell’ concept for application to large elastic and large elastoplastic deformations
International Journal for Numerical Methods in Engineering, 2000Co-Authors: R Hauptmann, Karl Schweizerhof, S DollAbstract:In the present contribution we extend a previously proposed so-called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modi cations necessary for hyper-elastic or elastoplastic material laws are discussed. These modi cations concern the right Cauchy–Green Tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modi ed Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright ? 2000 John Wiley & Sons, Ltd.