The Experts below are selected from a list of 402024 Experts worldwide ranked by ideXlab platform
Mingjue Zhou - One of the best experts on this subject based on the ideXlab platform.
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A singular element of shape-free hybrid Stress-Function finite elements in anisotropic materials
Theoretical and Applied Fracture Mechanics, 2019Co-Authors: Mingjue Zhou, Yan Shang, Weiya Jin, Shuiqing Zhou, Chen ChenAbstract:Abstract In this paper, the analytical solutions of the Stress Function around crack tip in the 2D anisotropic material are proposed. Further, a new singular element based on hybrid Stress-Function (HSF) model is developed and tested. Compared with other well-known methods, such new scheme exhibits two advantages: (i) for the singular element, the shape and the number of nodes can be flexibly adjusted as required; (ii) high precision for Stress intensity factors (SIF) can be obtained due to the advantages of the HSF method, with very small computational cost. It demonstrates that the proposed scheme is an effective technique for dealing with crack problems.
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a quasi static crack propagation simulation based on shape free hybrid Stress Function finite elements with simple remeshing
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Mingjue Zhou, Song Cen, Yi BaoAbstract:In this paper, a new shape-free multi-node singular hybrid Stress-Function (HSF) element and a shape-free 8-node plane HSF element proposed recently are employed to simulate the quasi-static 2D crack propagation problem. Compared with other well-known methods, such new scheme exhibits four advantages: (i) for the singular element, the shape and the number of nodes can be flexibly adjusted as required; (ii) high precision for Stress intensity factors (SIF) can be obtained due to the advantages of the HSF method; (iii) only simple remeshing with a very coarse mesh is needed for each simulation step; (iv) unstructured mesh containing extremely distorted elements can be used without losing precision. It demonstrates that the proposed scheme is an effective technique for dealing with crack propagation problems. 2014 Elsevier B.V. All rights reserved.
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8 and 12 node plane hybrid Stress Function elements immune to severely distorted mesh containing elements with concave shapes
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Song Cen, Mingjue ZhouAbstract:Abstract By simply improving the first version of hybrid Stress element method proposed by Pian, several 8- and 12-node plane quadrilateral elements, which are immune to severely distorted mesh containing elements with concave shapes, are successfully developed. Firstly, instead of the Stresses, the Stress Function ϕ is regarded as the Functional variable and introduced into the complementary energy Functional. Then, the fundamental analytical solutions (in global Cartesian coordinates) of ϕ are taken as the trial Functions for 2D finite element models, and meanwhile, the corresponding unknown Stress-Function constants are introduced. Thus, the resulting Stress fields must be more reasonable because both the equilibrium and the compatibility relations can be satisfied. Thirdly, by using the principle of minimum complementary energy, these unknown Stress-Function constants can be expressed in terms of the displacements along element boundaries, which can be interpolated directly by the element nodal displacements. Finally, the complementary energy Functional can be rewritten in terms of element nodal displacement vector, and thus, the element stiffness matrix of such hybrid Stress-Function (HS-F) element is obtained. This technique establishes a universal frame for developing reasonable hybrid Stress elements based on the principle of minimum complementary energy. And the first hybrid Stress element proposed by Pian is just a special case within this frame. Following above procedure, two 8-node and two 12-node quadrilateral plane elements are constructed by employing different fundamental analytical solutions of Airy Stress Function. Numerical results show that, the 8-node and 12-node models can produce the exact solutions for pure bending and linear bending problems, respectively, even the element shape degenerates into triangle and concave quadrangle. Furthermore, these elements do not possess any spurious zero energy mode and rotational frame dependence.
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Shape-free finite element method: The plane hybrid Stress-Function (HS-F) element method for anisotropic materials
Science China Physics Mechanics and Astronomy, 2011Co-Authors: Song Cen, Guo-hua Zhou, Mingjue ZhouAbstract:The sensitivity problem to mesh distortion and the low accuracy problem of the Stress solutions are two inherent difficulties in the finite element method. By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy Stress Function ϕ of the anisotropic materials, 8- and 12-node plane quadrilateral hybrid Stress-Function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy. Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and Stress solutions than those obtained from other models. They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle. It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate Stress solutions.
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A 4-node hybrid Stress-Function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions
Computers & Structures, 2011Co-Authors: Song Cen, Mingjue ZhouAbstract:A simple but robust 4-node hybrid Stress-Function (HS-F) membrane element with drilling degrees of freedom is developed based on the principle of minimum complementary energy. Its Stress fields are derived from the first seven fundamental analytical solutions of the Airy Stress Function. The assumed displacements along element boundaries employ compatible mode of Allman for which the nodal drilling degrees of freedom are considered. Numerical results show that the proposed new element, denoted as HSF-Q4@q-7@b, exhibits much improved numerical accuracy and robust performance. In particular, the element performs well even when the element shape degenerates into a triangle or concave quadrangle.
Song Cen - One of the best experts on this subject based on the ideXlab platform.
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a novel shape free plane quadratic polygonal hybrid Stress Function element
Mathematical Problems in Engineering, 2015Co-Authors: Peilei Zhou, Song CenAbstract:A novel plane quadratic shape-free hybrid Stress-Function (HS-F) polygonal element is developed by employing the principle of minimum complementary energy and the fundamental analytical solutions of the Airy Stress Function. Without construction of displacement interpolation Function, the formulations of the new model are much simpler than those of the displacement-based polygonal elements and can be degenerated into triangular or quadrilateral elements directly. In particular, it is quite insensitive to various mesh distortions and even can keep precision when element shape is concave. Furthermore, the element does not show any spurious zero energy modes. Numerical examples show the excellent performance of the new element, denoted by HSF-AP-19β, in both displacement and Stress solutions.
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a quasi static crack propagation simulation based on shape free hybrid Stress Function finite elements with simple remeshing
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Mingjue Zhou, Song Cen, Yi BaoAbstract:In this paper, a new shape-free multi-node singular hybrid Stress-Function (HSF) element and a shape-free 8-node plane HSF element proposed recently are employed to simulate the quasi-static 2D crack propagation problem. Compared with other well-known methods, such new scheme exhibits four advantages: (i) for the singular element, the shape and the number of nodes can be flexibly adjusted as required; (ii) high precision for Stress intensity factors (SIF) can be obtained due to the advantages of the HSF method; (iii) only simple remeshing with a very coarse mesh is needed for each simulation step; (iv) unstructured mesh containing extremely distorted elements can be used without losing precision. It demonstrates that the proposed scheme is an effective technique for dealing with crack propagation problems. 2014 Elsevier B.V. All rights reserved.
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8 and 12 node plane hybrid Stress Function elements immune to severely distorted mesh containing elements with concave shapes
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Song Cen, Mingjue ZhouAbstract:Abstract By simply improving the first version of hybrid Stress element method proposed by Pian, several 8- and 12-node plane quadrilateral elements, which are immune to severely distorted mesh containing elements with concave shapes, are successfully developed. Firstly, instead of the Stresses, the Stress Function ϕ is regarded as the Functional variable and introduced into the complementary energy Functional. Then, the fundamental analytical solutions (in global Cartesian coordinates) of ϕ are taken as the trial Functions for 2D finite element models, and meanwhile, the corresponding unknown Stress-Function constants are introduced. Thus, the resulting Stress fields must be more reasonable because both the equilibrium and the compatibility relations can be satisfied. Thirdly, by using the principle of minimum complementary energy, these unknown Stress-Function constants can be expressed in terms of the displacements along element boundaries, which can be interpolated directly by the element nodal displacements. Finally, the complementary energy Functional can be rewritten in terms of element nodal displacement vector, and thus, the element stiffness matrix of such hybrid Stress-Function (HS-F) element is obtained. This technique establishes a universal frame for developing reasonable hybrid Stress elements based on the principle of minimum complementary energy. And the first hybrid Stress element proposed by Pian is just a special case within this frame. Following above procedure, two 8-node and two 12-node quadrilateral plane elements are constructed by employing different fundamental analytical solutions of Airy Stress Function. Numerical results show that, the 8-node and 12-node models can produce the exact solutions for pure bending and linear bending problems, respectively, even the element shape degenerates into triangle and concave quadrangle. Furthermore, these elements do not possess any spurious zero energy mode and rotational frame dependence.
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Shape-free finite element method: The plane hybrid Stress-Function (HS-F) element method for anisotropic materials
Science China Physics Mechanics and Astronomy, 2011Co-Authors: Song Cen, Guo-hua Zhou, Mingjue ZhouAbstract:The sensitivity problem to mesh distortion and the low accuracy problem of the Stress solutions are two inherent difficulties in the finite element method. By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy Stress Function ϕ of the anisotropic materials, 8- and 12-node plane quadrilateral hybrid Stress-Function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy. Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and Stress solutions than those obtained from other models. They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle. It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate Stress solutions.
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A 4-node hybrid Stress-Function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions
Computers & Structures, 2011Co-Authors: Song Cen, Mingjue ZhouAbstract:A simple but robust 4-node hybrid Stress-Function (HS-F) membrane element with drilling degrees of freedom is developed based on the principle of minimum complementary energy. Its Stress fields are derived from the first seven fundamental analytical solutions of the Airy Stress Function. The assumed displacements along element boundaries employ compatible mode of Allman for which the nodal drilling degrees of freedom are considered. Numerical results show that the proposed new element, denoted as HSF-Q4@q-7@b, exhibits much improved numerical accuracy and robust performance. In particular, the element performs well even when the element shape degenerates into a triangle or concave quadrangle.
Manfred H Wagner - One of the best experts on this subject based on the ideXlab platform.
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from linear viscoelasticity to elongational flow of polydisperse linear and branched polymer melts the hierarchical multi mode molecular Stress Function model
Polymer, 2016Co-Authors: Esmaeil Narimissa, Manfred H WagnerAbstract:Abstract We developed a novel Hierarchical Multi-mode Molecular Stress Function (HMMSF) model for polydisperse polymer melts, which implements the basic ideas of (i) hierarchical relaxation, (ii) dynamic dilution, and (iii) interchain tube pressure. Here, the capability of this approach is demonstrated by comparison of predictions of the HMMSF model with uniaxial extensional viscosity data of sixteen different grades of high and low density polyethylene melts, as well as two different polystyrene melts with defined topology. The modelling is solely based on the linear-viscoelastic relaxation modulus with only one non-linear material parameter, the dilution modulus.
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a hierarchical multimode molecular Stress Function model for linear polymer melts in extensional flows
Journal of Rheology, 2016Co-Authors: Esmaeil Narimissa, Manfred H WagnerAbstract:A novel hierarchical multimode molecular Stress Function (HMMSF) model for linear polymer melts is proposed, which implements the basic ideas of (i) hierarchical relaxation, (ii) dynamic dilution, and (iii) interchain tube pressure. The capability of this approach is demonstrated in modeling the extensional viscosity data of monodisperse, bidisperse, and polydisperse linear polymer melts. Predictions of the HMMSF model, which are solely based on the linear-viscoelastic relaxation modulus and a single free model parameter, the segmental equilibration time, are compared to elongational viscosity data of monodisperse polystyrene melts and solutions as well as to the elongational viscosity data of a bidisperse blend of two monodisperse polystyrenes, and good agreement between model and experimental data is observed. By using a simplified relation between the Rouse stretch-relaxation times and the relaxation times of the melts, the modeling is extended to the uniaxial, equibiaxial, and planar extensional viscosity data of a high-density polyethylene, the uniaxial and equibiaxial extensional viscosity data of a polydisperse polystyrene, the elongational viscosity data of three high-density polyethylenes, and a linear low-density polyethylene. For polydisperse melts, the modeling is again based exclusively on the linear-viscoelastic relaxation modulus with only one material parameter, the dilution modulus, which quantifies the onset of dynamic dilution.
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a modification of the convective constraint release mechanism in the molecular Stress Function model giving enhanced vortex growth
Journal of Non-newtonian Fluid Mechanics, 2006Co-Authors: P Olley, Manfred H WagnerAbstract:Abstract The molecular Stress Function model with convective constraint release (MSF with CCR) constitutive model [M.H. Wagner, P. Rubio, H. Bastian, The molecular Stress Function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported “steady-state” elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J.L. White, A. Kondo, Flow patterns in polyethylene and polystyrene melts during extrusion through a die entry region: measurement and interpretation, J. Non-Newtonian Fluid Mech. 3 (1977) 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative Function and the large stretch levels caused by the contraction flow. A modified combination of dissipative Functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.
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quantitative assessment of strain hardening of low density polyethylene melts by the molecular Stress Function model
Journal of Rheology, 2003Co-Authors: Manfred H Wagner, Masayuki Yamaguchi, M TakahashiAbstract:The elongational viscosity of three tubular and five autoclave low-density polyethylene (LDPE) melts is analyzed, and quantitative comparison of the strain-hardening characteristics is made by using the molecular Stress Function model. This is based on a new strain-energy Function, which assumes that the total strain energy of a branched section of a macromolecule is given by the addition of the strain energies of the individual chain segments contained in this section. The model employs only two nonlinear material parameters: one parameter describes the average number of crosslinked chain segments, which occupy the same tube section, and determines the slope of the elongational viscosity after inception of strain hardening. The second parameter indicates the maximum relative stretch of the chain segments and determines the steady-state (plateau) value of the elongational viscosity. Both parameters depend on the complex branching topology of LDPE melts. While quantitative relationships between branching structure and the two nonlinear parameters are not yet available, the results of this comparison seem to indicate that the more tree-like structure of autoclave LDPE leads to a higher density of crosslinked chain segments in the same tube section than in the case of LDPE polymerized in tubular reactors.
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the molecular Stress Function model for polydisperse polymer melts with dissipative convective constraint release
Journal of Rheology, 2001Co-Authors: Manfred H Wagner, P Rubio, H BastianAbstract:The molecular Stress Function theory for polymer melts is extended to include a new, dissipative convective constraint release process. First the Helmholtz free energy of tube segments with strain-dependent tube diameter is established neglecting constraint release, and it is demonstrated that the molecular Stress is a Function of the average logarithmic stretch under these conditions. Then convective constraint release is introduced as a dissipative process in the energy balance of tube deformation, which leads to a strain-dependent evolution equation for the molecular Stress Function. Constraint release is considered to be the consequence of different convection mechanisms for tube orientation and tube cross section. Our new, dissipative constraint release model emphasizes that tube kinematics are fundamentally different for rotational and nonrotational flows, and therefore distinguishes explicitly between simple shear and pure shear (planar extension). For the startup of simple shear and extensional flows, the predictions of our set of constitutive equations consisting of a history integral for the Stress tensor and a differential evolution equation for the molecular Stress Function with only two nonlinear material parameters are in excellent agreement with experimental data of a polydisperse high-density polyethylene (HDPE) and a polydisperse low-density polyethylene (LDPE) melt. Also, Stress relaxation after step-shear strain is described for both the HDPE and the LDPE melt.
Esmaeil Narimissa - One of the best experts on this subject based on the ideXlab platform.
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from linear viscoelasticity to elongational flow of polydisperse linear and branched polymer melts the hierarchical multi mode molecular Stress Function model
Polymer, 2016Co-Authors: Esmaeil Narimissa, Manfred H WagnerAbstract:Abstract We developed a novel Hierarchical Multi-mode Molecular Stress Function (HMMSF) model for polydisperse polymer melts, which implements the basic ideas of (i) hierarchical relaxation, (ii) dynamic dilution, and (iii) interchain tube pressure. Here, the capability of this approach is demonstrated by comparison of predictions of the HMMSF model with uniaxial extensional viscosity data of sixteen different grades of high and low density polyethylene melts, as well as two different polystyrene melts with defined topology. The modelling is solely based on the linear-viscoelastic relaxation modulus with only one non-linear material parameter, the dilution modulus.
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a hierarchical multimode molecular Stress Function model for linear polymer melts in extensional flows
Journal of Rheology, 2016Co-Authors: Esmaeil Narimissa, Manfred H WagnerAbstract:A novel hierarchical multimode molecular Stress Function (HMMSF) model for linear polymer melts is proposed, which implements the basic ideas of (i) hierarchical relaxation, (ii) dynamic dilution, and (iii) interchain tube pressure. The capability of this approach is demonstrated in modeling the extensional viscosity data of monodisperse, bidisperse, and polydisperse linear polymer melts. Predictions of the HMMSF model, which are solely based on the linear-viscoelastic relaxation modulus and a single free model parameter, the segmental equilibration time, are compared to elongational viscosity data of monodisperse polystyrene melts and solutions as well as to the elongational viscosity data of a bidisperse blend of two monodisperse polystyrenes, and good agreement between model and experimental data is observed. By using a simplified relation between the Rouse stretch-relaxation times and the relaxation times of the melts, the modeling is extended to the uniaxial, equibiaxial, and planar extensional viscosity data of a high-density polyethylene, the uniaxial and equibiaxial extensional viscosity data of a polydisperse polystyrene, the elongational viscosity data of three high-density polyethylenes, and a linear low-density polyethylene. For polydisperse melts, the modeling is again based exclusively on the linear-viscoelastic relaxation modulus with only one material parameter, the dilution modulus, which quantifies the onset of dynamic dilution.
Yi Bao - One of the best experts on this subject based on the ideXlab platform.
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a quasi static crack propagation simulation based on shape free hybrid Stress Function finite elements with simple remeshing
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Mingjue Zhou, Song Cen, Yi BaoAbstract:In this paper, a new shape-free multi-node singular hybrid Stress-Function (HSF) element and a shape-free 8-node plane HSF element proposed recently are employed to simulate the quasi-static 2D crack propagation problem. Compared with other well-known methods, such new scheme exhibits four advantages: (i) for the singular element, the shape and the number of nodes can be flexibly adjusted as required; (ii) high precision for Stress intensity factors (SIF) can be obtained due to the advantages of the HSF method; (iii) only simple remeshing with a very coarse mesh is needed for each simulation step; (iv) unstructured mesh containing extremely distorted elements can be used without losing precision. It demonstrates that the proposed scheme is an effective technique for dealing with crack propagation problems. 2014 Elsevier B.V. All rights reserved.
