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M B Rubin - One of the best experts on this subject based on the ideXlab platform.

  • a ten node Tetrahedral macro cosserat point Element mcpe part ii nonlinear elastic viscoplastic materials
    Finite Elements in Analysis and Design, 2019
    Co-Authors: M Hollenstein, M B Rubin
    Abstract:

    Abstract In Part I of this two-part paper, a Macro-Cosserat Point Element (MCPE) was developed based on a Lagrangian formulation of a ten node macro-Tetrahedral Element. The MCPE provides ten nodal forces as functions of ten nodal positions, similar to standard finite Elements. In previous work, it has been shown that a Eulerian formulation of plasticity can remove unphysical arbitrariness of the reference configuration, an intermediate configuration, total deformation measures and plastic deformation measures that are used in the standard Lagrangian formulation of plasticity. The main objective of this Part II is to develop a Eulerian formulation of the MCPE which is implemented for elastic-viscoplastic response. The resulting MCPE satisfies a nonlinear form of a patch test for plasticity. The examples in Parts I and II of this paper indicate that the MCPE is a robust Element that can be used with confidence for modeling general material response.

  • a ten node Tetrahedral macro cosserat point Element mcpe part i isotropic and anisotropic hyperelastic materials
    Finite Elements in Analysis and Design, 2019
    Co-Authors: M Hollenstein, M B Rubin
    Abstract:

    Abstract A Macro-Cosserat Point Element (MCPE) has been developed based on a ten node macro-Tetrahedral Element. The macro-Tetrahedral Element is divided into eight Tetrahedral sub-Elements, which are each modeled as a ten node Cosserat Point Element (CPE) with all nodes of the sub-Elements being kinematically linked to the ten nodes of the macro-Tetrahedral Element. The MCPE provides ten nodal forces as functions of ten nodal positions, similar to standard finite Elements. The MCPE is proposed as a new candidate for a general purpose, simple, robust Element that is versatile in the sense that it can be used to mesh complicated regions and can easily incorporate general constitutive models. Example problems show that the MCPE exhibits enhanced robustness relative to the full integration ten node tetrahedron. The cost for this robustness is moderate loss of accuracy of the MCPE for small deformations of coarsely meshed thin structures.

  • A ten node Tetrahedral Cosserat Point Element (CPE) for nonlinear isotropic elastic materials
    Computational Mechanics, 2013
    Co-Authors: M. Jabareen, E. Hanukah, M B Rubin
    Abstract:

    It is known that the standard full integration ten node Tetrahedral Element is inaccurate for thin nearly incompressible structures. Also, the commercial code ABAQUS recommends replacing this standard Element (C3D10) with an undocumented patented modified Element (C3D10M) for contact problems. The objective of this work is to develop a ten node Tetrahedral Cosserat Point Element (CPE) for nonlinear isotropic hyperelastic materials. Hyperelastic constitutive equations for the CPE are developed by treating the Element as a structure with a strain energy function that is restricted to satisfy a nonlinear form of the patch test. A number of examples are considered which demonstrate that the resulting CPE is accurate and robust, it does not exhibit the numerical stiffness for nearly incompressible materials observed for (C3D10) nor the unphysical instabilities observed for (C3D10M). Moreover, the CPE can be used for thin structures and three-dimensional bodies with a smooth transition from compressible to nearly incompressible material behavior.

M Hollenstein - One of the best experts on this subject based on the ideXlab platform.

  • a ten node Tetrahedral macro cosserat point Element mcpe part ii nonlinear elastic viscoplastic materials
    Finite Elements in Analysis and Design, 2019
    Co-Authors: M Hollenstein, M B Rubin
    Abstract:

    Abstract In Part I of this two-part paper, a Macro-Cosserat Point Element (MCPE) was developed based on a Lagrangian formulation of a ten node macro-Tetrahedral Element. The MCPE provides ten nodal forces as functions of ten nodal positions, similar to standard finite Elements. In previous work, it has been shown that a Eulerian formulation of plasticity can remove unphysical arbitrariness of the reference configuration, an intermediate configuration, total deformation measures and plastic deformation measures that are used in the standard Lagrangian formulation of plasticity. The main objective of this Part II is to develop a Eulerian formulation of the MCPE which is implemented for elastic-viscoplastic response. The resulting MCPE satisfies a nonlinear form of a patch test for plasticity. The examples in Parts I and II of this paper indicate that the MCPE is a robust Element that can be used with confidence for modeling general material response.

  • a ten node Tetrahedral macro cosserat point Element mcpe part i isotropic and anisotropic hyperelastic materials
    Finite Elements in Analysis and Design, 2019
    Co-Authors: M Hollenstein, M B Rubin
    Abstract:

    Abstract A Macro-Cosserat Point Element (MCPE) has been developed based on a ten node macro-Tetrahedral Element. The macro-Tetrahedral Element is divided into eight Tetrahedral sub-Elements, which are each modeled as a ten node Cosserat Point Element (CPE) with all nodes of the sub-Elements being kinematically linked to the ten nodes of the macro-Tetrahedral Element. The MCPE provides ten nodal forces as functions of ten nodal positions, similar to standard finite Elements. The MCPE is proposed as a new candidate for a general purpose, simple, robust Element that is versatile in the sense that it can be used to mesh complicated regions and can easily incorporate general constitutive models. Example problems show that the MCPE exhibits enhanced robustness relative to the full integration ten node tetrahedron. The cost for this robustness is moderate loss of accuracy of the MCPE for small deformations of coarsely meshed thin structures.

Byung Chai Lee - One of the best experts on this subject based on the ideXlab platform.

  • a 10 node Tetrahedral Element with condensed lagrange multipliers for the modified couple stress theory
    Computers & Structures, 2021
    Co-Authors: Jaehoon Choi, Byung Chai Lee, Gidong Sim
    Abstract:

    Abstract In this paper, a mixed Tetrahedral Element based on the Lagrange multiplier is newly developed for the modified couple stress theory. The limitations of the Lagrange multiplier method are that the total number of degrees of freedom is increased and that there are zeros in the diagonal term of the stiffness matrix. We developed a method to overcome the limitations by condensing out the Lagrange multipliers in the calculation of the Element stiffness. Higher-order rotation modes are introduced. As condensing out the rotation modes, the Lagrange multiplier is also condensed. The total number of degrees of freedom can be greatly reduced, maximizing computational efficiency. Through numerical examples, the convergence and efficiency of the proposed Elements were validated. The developed Element is expected to be used for the analysis of micro/nano-scale structures.

  • a four node c 0 Tetrahedral Element based on the node based smoothing technique for the modified couple stress theory
    Computational Mechanics, 2020
    Co-Authors: Jaehoon Choi, Gidong Sim, Byung Chai Lee
    Abstract:

    In this paper, a four-node $$C^{0}$$ Tetrahedral Element for the modified couple stress theory is proposed. Since the governing equations are the fourth-order differential equations, the first-order derivative of displacement or rotation should be approximated by a continuous function. In the proposed Element, nodal rotations are defined using the node-based smoothing technique. Continuous rotation fields are defined with the shape functions and nodal rotations. Both the displacement field and the rotation field are expressed solely in terms of the displacement degrees of freedom. The Element stiffness matrix is calculated using the newly defined rotation field. To prevent the increase of calculation cost due to increase of the bandwidth of the stiffness matrix, the preconditioned conjugate gradient method is introduced. The performance of the proposed Element is evaluated through various numerical examples.

  • development of a 4 node hybrid stress Tetrahedral Element using a node based smoothed finite Element method
    International Journal for Numerical Methods in Engineering, 2018
    Co-Authors: Jaehoon Choi, Byung Chai Lee
    Abstract:

    Summary In this paper, a new four-node hybrid stress Element is proposed using a node-based smoothing technique of Tetrahedral mesh. The conditions for hybrid stress field required are summarized and the field should be continuous for better performance of a constant-strain Tetrahedral Element. Nodal stress is approximated by the node-based smoothing technique and the stress field is interpolated with standard shape functions. This stress field is linear within each Element and continuous across Elements. The stress field is expressed by nodal displacements and no additional variables. The Element stiffness matrix is calculated using the Hellinger-Reissner functional, which guarantees the strain field from displacement field to be equal to that from the stress field in a weak sense. The performance of the proposed Element is verified by through several numerical examples.

Jaehoon Choi - One of the best experts on this subject based on the ideXlab platform.

  • a 10 node Tetrahedral Element with condensed lagrange multipliers for the modified couple stress theory
    Computers & Structures, 2021
    Co-Authors: Jaehoon Choi, Byung Chai Lee, Gidong Sim
    Abstract:

    Abstract In this paper, a mixed Tetrahedral Element based on the Lagrange multiplier is newly developed for the modified couple stress theory. The limitations of the Lagrange multiplier method are that the total number of degrees of freedom is increased and that there are zeros in the diagonal term of the stiffness matrix. We developed a method to overcome the limitations by condensing out the Lagrange multipliers in the calculation of the Element stiffness. Higher-order rotation modes are introduced. As condensing out the rotation modes, the Lagrange multiplier is also condensed. The total number of degrees of freedom can be greatly reduced, maximizing computational efficiency. Through numerical examples, the convergence and efficiency of the proposed Elements were validated. The developed Element is expected to be used for the analysis of micro/nano-scale structures.

  • a four node c 0 Tetrahedral Element based on the node based smoothing technique for the modified couple stress theory
    Computational Mechanics, 2020
    Co-Authors: Jaehoon Choi, Gidong Sim, Byung Chai Lee
    Abstract:

    In this paper, a four-node $$C^{0}$$ Tetrahedral Element for the modified couple stress theory is proposed. Since the governing equations are the fourth-order differential equations, the first-order derivative of displacement or rotation should be approximated by a continuous function. In the proposed Element, nodal rotations are defined using the node-based smoothing technique. Continuous rotation fields are defined with the shape functions and nodal rotations. Both the displacement field and the rotation field are expressed solely in terms of the displacement degrees of freedom. The Element stiffness matrix is calculated using the newly defined rotation field. To prevent the increase of calculation cost due to increase of the bandwidth of the stiffness matrix, the preconditioned conjugate gradient method is introduced. The performance of the proposed Element is evaluated through various numerical examples.

  • development of a 4 node hybrid stress Tetrahedral Element using a node based smoothed finite Element method
    International Journal for Numerical Methods in Engineering, 2018
    Co-Authors: Jaehoon Choi, Byung Chai Lee
    Abstract:

    Summary In this paper, a new four-node hybrid stress Element is proposed using a node-based smoothing technique of Tetrahedral mesh. The conditions for hybrid stress field required are summarized and the field should be continuous for better performance of a constant-strain Tetrahedral Element. Nodal stress is approximated by the node-based smoothing technique and the stress field is interpolated with standard shape functions. This stress field is linear within each Element and continuous across Elements. The stress field is expressed by nodal displacements and no additional variables. The Element stiffness matrix is calculated using the Hellinger-Reissner functional, which guarantees the strain field from displacement field to be equal to that from the stress field in a weak sense. The performance of the proposed Element is verified by through several numerical examples.

Hong Zheng - One of the best experts on this subject based on the ideXlab platform.

  • A mass lumping scheme for the 10-node Tetrahedral Element
    Engineering Analysis with Boundary Elements, 2019
    Co-Authors: Guohua Zhang, Yongtao Yang, Guanhua Sun, Hong Zheng
    Abstract:

    Abstract In the dynamic analysis with explicit time integration scheme, a lumped mass matrix (LMM) is always preferable than the consistent mass matrix (CMM), since the solving of large scale simultaneous algebraic equations can be avoided if a LMM is employed. In this study, a mass lumping scheme which is suitable for the 10-node Tetrahedral Element is proposed. A series of numerical examples show that the natural frequencies assessed from the proposed LMM are very close to those from CMM. In addition, the dynamic responses of structure predicted by the proposed LMM are in very good agreement with those from CMM if an implicit time integration scheme is adopted. More importantly, the proposed LMM is less sensitive to mesh distortion than the CMM. The proposed LMM can supersede the CMM at any cases.

  • a four node Tetrahedral Element with continuous nodal stress
    Computers & Structures, 2017
    Co-Authors: Yongtao Yang, Guanhua Sun, Hong Zheng
    Abstract:

    Abstract Formulation of a partition of unity (PU) based four-node Tetrahedral Element with continuous nodal stress (Tetr4-CNS) and its applications to the analysis of linear elasticity problems in three-dimension are presented in this paper. By simply using the same mesh as the classical Tetrahedral Element (Tetr4), Tetr4-CNS Element is able to obtain continuous nodal stress without recourse to stress smoothing operation in the post-processing process, and to construct high order global approximation without adding extra nodes or nodal DOFs. Moreover, it is free from the linear dependence problem which cripples many of the PU-based methods. A series of numerical tests are carried out to evaluate the performance of the Tetr4-CNS Element. The numerical results show that accuracy through the proposed Element is superior to that through Tetr4 Element and eight-node hexahedral Element (Hexa8). More importantly, the proposed Element has excellent mesh distortion tolerant capabilities.