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P Areias - One of the best experts on this subject based on the ideXlab platform.
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An objective and path-independent 3D Finite-Strain beam with least-squares assumed-Strain formulation
Computational Mechanics, 2019Co-Authors: P Areias, M. Pires, N. Vu Bac, Timon RabczukAbstract:An all-encompassing Finite-Strain representation of rods, shells and continuum can share a common kinematic/constitutive framework where specific conditions for Strain, stress and constitutive updating are applied. In this work, Finite Strain beams are under examination, with several classical requirements met by cooperative techniques judiciously applied. Specifically: the use of a continuum constitutive law is possible due to the relative Strain formulation previously introduced, the rotation singularity problem is absent due to the use of a consistent (quadratic) updated Lagrangian technique. Objectiveness and path-independence of director interpolation are satisfied due to the use of a Löwdin frame. These properties are proved in this work. Moreover, high coarse-mesh accuracy is introduced by the least-squares assumed-Strain technique, here specialized for a beam. Examples show the accuracy and robustness of the formulation.
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phase field analysis of Finite Strain plates and shells including element subdivision
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: P Areias, Timon Rabczuk, Mohammed A MsekhAbstract:With the theme of fracture of Finite-Strain plates and shells based on a phase-field model of crack regularization, we introduce a new staggered algorithm for elastic and elasto-plastic materials. To account for correct fracture behavior in bending, two independent phase-fields are used, corresponding to the lower and upper faces of the shell. This is shown to provide a realistic behavior in bending-dominated problems, here illustrated in classical beam and plate problems. Finite Strain behavior for both elastic and elasto-plastic constitutive laws is made compatible with the phase-field model by use of a consistent updated-Lagrangian algorithm. To guarantee sufficient resolution in the definition of the crack paths, a local remeshing algorithm based on the phase-field values at the lower and upper shell faces is introduced. In this local remeshing algorithm, two stages are used: edge-based element subdivision and node repositioning. Five representative numerical examples are shown, consisting of a bi-clamped beam, two versions of a square plate, the Keesecker pressurized cylinder problem, the Hexcan problem and the Muscat-Fenech and Atkins plate. All problems were successfully solved and the proposed solution was found to be robust and efficient.
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Finite Strain laminates bending enhanced hexahedron and delamination
Composite Structures, 2016Co-Authors: P Areias, Timon Rabczuk, P P CamanhoAbstract:Abstract With a new Finite Strain anisotropic framework, we introduce a unified approach for constitutive modeling and delamination of composites. We describe a Finite-Strain semi-implicit integration algorithm and the application to assumed-Strain hexahedra. In a laminate composite, the laminae are modeled by an anisotropic Kirchhoff/Saint-Venant material and the interfaces are modeled by the exponential cohesive law with intrinsic characteristic length and the criterion by Benzeggagh and Kenane for the equivalent fracture toughness. For the element formulation, a weighted least-squares algorithm is used to calculate the mixed Strain. Lowdin frames are used to model orthotropic materials without the added task of performing a polar decomposition or empirical frames. To assess the validity of our proposals and inspect step and mesh size dependence, a least-squares based hexahedral element is implemented and tested in depth in both deformation and delamination examples.
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Finite Strain quadrilateral shell using least squares fit of relative lagrangian in plane Strains
Finite Elements in Analysis and Design, 2015Co-Authors: P Areias, Timon Rabczuk, J GarcaoAbstract:This work presents a Finite Strain quadrilateral element with least-squares assumed in-plane shear Strains (in covariant/contravariant coordinates) and classical transverse shear assumed Strains. It is an alternative to enhanced-assumed-Strain (EAS) formulation and, in contrast to this, produces an element satisfying ab initio the Patch-test. No additional degrees-of-freedom are present, unlike EAS. Least-squares fit allows the derivation of invariant Finite Strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. With that goal, we use automatically generated code produced by AceGen and Mathematica to obtain novel Finite element formulations. The corresponding exact linearization of the internal forces was, until recently, a insurmountable task. We use the tangent modulus in the least-squares fit to ensure that stress modes are obtained from a five-parameter Strain fitting. This reproduces exactly the in-plane bending modes. The discrete equations are obtained by establishing a four-field variational principle (a direct extension of the Hu-Washizu variational principle). The main achieved goal is coarse-mesh accuracy for distorted meshes, which is adequate for being used in crack propagation problems. In addition, as an alternative to spherical interpolation, a consistent director normalization is performed. Metric components are fully deduced and exact linearization of the shell element is performed. Full linear and nonlinear assessment of the element is performed, showing similar performance to more costly approaches, often on-par with the best available shell elements. HighlightsSimplified Finite Strain element formulation satisfying a priori the Patch test.Least-squares determination of in-plane assumed Strains, compatible with the three-field variational principle.Absence of additional degrees-of-freedom (as is the case of EAS).Elastic and inelastic benchmark tests solved without hourglass or locking.
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Finite Strain plasticity the stress condition and a complete shell model
Computational Mechanics, 2010Co-Authors: P Areias, Manuel Rittocorrea, J A C MartinsAbstract:The null stress (s 33 = 0) and incompressibility (J = 1) conditions in Finite Strain elasto-plastic shell analysis are studied in closed-form and implemented with a variant of the combined control by Ritto-Correa and Camotim. Coupling between constitutive laws and shell kinematics results from the satisfaction of either of the conditions; nonlocality results from the coupling. We prove that the conditions are, in general, incompatible. A new thickness-deformable is studied in terms of kinematics and strong-ellipticity. The affected continuum laws are derived and, in the discrete form, it is shown that thickness degrees-of-freedom and enhanced Strains are avoided: a mixed displacement-shear Strain shell element is used. Both hyperelastic and elasto-plastic constitutive laws are tested. Elasto-plasticity follows Lee’s decomposition and direct smoothing of the complementarity condition. A smooth root finder is employed to solve the resulting algebraic problem. Besides closed-form examples, numerical examples consisting of classical and newly proposed benchmarks are solved.
Timon Rabczuk - One of the best experts on this subject based on the ideXlab platform.
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An objective and path-independent 3D Finite-Strain beam with least-squares assumed-Strain formulation
Computational Mechanics, 2019Co-Authors: P Areias, M. Pires, N. Vu Bac, Timon RabczukAbstract:An all-encompassing Finite-Strain representation of rods, shells and continuum can share a common kinematic/constitutive framework where specific conditions for Strain, stress and constitutive updating are applied. In this work, Finite Strain beams are under examination, with several classical requirements met by cooperative techniques judiciously applied. Specifically: the use of a continuum constitutive law is possible due to the relative Strain formulation previously introduced, the rotation singularity problem is absent due to the use of a consistent (quadratic) updated Lagrangian technique. Objectiveness and path-independence of director interpolation are satisfied due to the use of a Löwdin frame. These properties are proved in this work. Moreover, high coarse-mesh accuracy is introduced by the least-squares assumed-Strain technique, here specialized for a beam. Examples show the accuracy and robustness of the formulation.
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phase field analysis of Finite Strain plates and shells including element subdivision
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: P Areias, Timon Rabczuk, Mohammed A MsekhAbstract:With the theme of fracture of Finite-Strain plates and shells based on a phase-field model of crack regularization, we introduce a new staggered algorithm for elastic and elasto-plastic materials. To account for correct fracture behavior in bending, two independent phase-fields are used, corresponding to the lower and upper faces of the shell. This is shown to provide a realistic behavior in bending-dominated problems, here illustrated in classical beam and plate problems. Finite Strain behavior for both elastic and elasto-plastic constitutive laws is made compatible with the phase-field model by use of a consistent updated-Lagrangian algorithm. To guarantee sufficient resolution in the definition of the crack paths, a local remeshing algorithm based on the phase-field values at the lower and upper shell faces is introduced. In this local remeshing algorithm, two stages are used: edge-based element subdivision and node repositioning. Five representative numerical examples are shown, consisting of a bi-clamped beam, two versions of a square plate, the Keesecker pressurized cylinder problem, the Hexcan problem and the Muscat-Fenech and Atkins plate. All problems were successfully solved and the proposed solution was found to be robust and efficient.
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Finite Strain laminates bending enhanced hexahedron and delamination
Composite Structures, 2016Co-Authors: P Areias, Timon Rabczuk, P P CamanhoAbstract:Abstract With a new Finite Strain anisotropic framework, we introduce a unified approach for constitutive modeling and delamination of composites. We describe a Finite-Strain semi-implicit integration algorithm and the application to assumed-Strain hexahedra. In a laminate composite, the laminae are modeled by an anisotropic Kirchhoff/Saint-Venant material and the interfaces are modeled by the exponential cohesive law with intrinsic characteristic length and the criterion by Benzeggagh and Kenane for the equivalent fracture toughness. For the element formulation, a weighted least-squares algorithm is used to calculate the mixed Strain. Lowdin frames are used to model orthotropic materials without the added task of performing a polar decomposition or empirical frames. To assess the validity of our proposals and inspect step and mesh size dependence, a least-squares based hexahedral element is implemented and tested in depth in both deformation and delamination examples.
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Finite Strain quadrilateral shell using least squares fit of relative lagrangian in plane Strains
Finite Elements in Analysis and Design, 2015Co-Authors: P Areias, Timon Rabczuk, J GarcaoAbstract:This work presents a Finite Strain quadrilateral element with least-squares assumed in-plane shear Strains (in covariant/contravariant coordinates) and classical transverse shear assumed Strains. It is an alternative to enhanced-assumed-Strain (EAS) formulation and, in contrast to this, produces an element satisfying ab initio the Patch-test. No additional degrees-of-freedom are present, unlike EAS. Least-squares fit allows the derivation of invariant Finite Strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. With that goal, we use automatically generated code produced by AceGen and Mathematica to obtain novel Finite element formulations. The corresponding exact linearization of the internal forces was, until recently, a insurmountable task. We use the tangent modulus in the least-squares fit to ensure that stress modes are obtained from a five-parameter Strain fitting. This reproduces exactly the in-plane bending modes. The discrete equations are obtained by establishing a four-field variational principle (a direct extension of the Hu-Washizu variational principle). The main achieved goal is coarse-mesh accuracy for distorted meshes, which is adequate for being used in crack propagation problems. In addition, as an alternative to spherical interpolation, a consistent director normalization is performed. Metric components are fully deduced and exact linearization of the shell element is performed. Full linear and nonlinear assessment of the element is performed, showing similar performance to more costly approaches, often on-par with the best available shell elements. HighlightsSimplified Finite Strain element formulation satisfying a priori the Patch test.Least-squares determination of in-plane assumed Strains, compatible with the three-field variational principle.Absence of additional degrees-of-freedom (as is the case of EAS).Elastic and inelastic benchmark tests solved without hourglass or locking.
Zilian Andreas - One of the best experts on this subject based on the ideXlab platform.
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ANN-aided incremental multiscale-remodelling-based Finite Strain poroelasticity
2021Co-Authors: Dehghani Hamidreza, Zilian AndreasAbstract:Mechanical modelling of poroelastic media under Finite Strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming inFinitesimal Strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for Finite Strain and large deformation problems while it ensures inFinitesimal Strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy's law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under uniaxial cyclic test is simulated and studied
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ANN-aided incremental multiscale-remodelling-based Finite Strain poroelasticity
'Springer Science and Business Media LLC', 2021Co-Authors: Dehghani Hamidreza, Zilian AndreasAbstract:Mechanical modelling of poroelastic media under Finite Strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming inFinitesimal Strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for Finite Strain and large deformation problems while it ensures inFinitesimal Strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing a more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy’s law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under the uniaxial cyclic test is simulated and studied
Dai Hui-hui - One of the best experts on this subject based on the ideXlab platform.
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A refined dynamic Finite-Strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle
'The Royal Society', 2020Co-Authors: Yu Xiang, Fu Yibin, Dai Hui-huiAbstract:Based on previous work for the static problem, in this paper we first derive one form of dynamic Finite-Strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic Finite-Strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) Strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional (2D) shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-Strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.Comment: 26 pages, 1 figure. The subscripts of the nominal stress were correcte
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A refined dynamic Finite-Strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle
'The Royal Society', 2020Co-Authors: Yu Xiang, Fu Yibin, Dai Hui-huiAbstract:Based on previous work for the static problem, in this paper we first derive one form of dynamic Finite-Strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic Finite-Strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) Strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional (2D) shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-Strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.Comment: 26 pages, 1 figure. Some errors in Section 4 were fixe
S Stupkiewicz - One of the best experts on this subject based on the ideXlab platform.
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Finite Strain formulation and fe implementation of a constitutive model for powder compaction
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: S Stupkiewicz, A Piccolroaz, D BigoniAbstract:Abstract A Finite-Strain formulation is developed, implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder. This constitutive model (as well as many others employed for geomaterials) embodies a number of features, such as pressure-sensitive yielding, complex hardening rules and elastoplastic coupling, posing considerable problems in a Finite-Strain formulation and numerical implementation. A number of strategies are proposed to overcome the related problems, in particular, a neo-Hookean type of modification to the elastic potential and the adoption of the second Piola–Kirchhoff stress referred to the intermediate configuration to describe yielding. An incremental scheme compatible with the formulation for elastoplastic coupling at Finite Strain is also developed, and the corresponding constitutive update problem is solved by applying a return mapping algorithm.
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closed form matrix exponential and its application in Finite Strain plasticity
International Journal for Numerical Methods in Engineering, 2014Co-Authors: Jože Korelc, S StupkiewiczAbstract:SUMMARY A new method to compute numerically efficient closed-form representation of matrix exponential and its derivative is developed for 3 × 3 matrices with real eigenvalues. The matrix exponential is obtained by automatic differentiation of an appropriate scalar generating function in a general case, and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits ill-conditioning, for instance, for almost equal eigenvalues. Accuracy and numerical efficiency of the closed-form matrix exponential as compared with the truncated series approximation are studied. The application of the closed-form matrix exponential in the Finite-Strain elastoplasticity is also presented. To this end, several time-discrete evolution laws employing the exponential map are discussed for J2 plasticity with isotropic hardening and nonlinear kinematic hardening of Armstrong–Frederick type. The discussion is restricted to the case of elastic isotropy and implicit time integration schemes. In this part, the focus is on a general automatic differentiation-based formulation of Finite-Strain plasticity models. Numerical efficiency of the corresponding incremental schemes is studied in the context of the FEM. Copyright © 2014 John Wiley & Sons, Ltd.