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Tom Ziegler - One of the best experts on this subject based on the ideXlab platform.
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calculation of excitation energies of open shell molecules with spatially degenerate ground states ii transformed reference via Intermediate Configuration kohn sham time dependent density functional theory oscillator strengths and magnetic circular dichroism c terms
Journal of Chemical Physics, 2006Co-Authors: Michael Seth, Tom ZieglerAbstract:An extension of the transformed reference via an Intermediate Configuration Kohn-Sham time dependent density functional theory (TRICKS-TDDFT) method for calculating the transition energies of molecules with spatially degenerate ground states is proposed that enables oscillator strengths to also be evaluated. The oscillator strengths are calculated starting from a description of the degenerate ground state and the excited states of interest in terms of linear combinations of Slater determinants based upon the F-vectors obtained in the TRICKS-TDDFT calculation. This approach for calculating oscillator strengths can also be applied to several other properties that involve excited states. An example of such a property, the C term of magnetic circular dichroism (MCD), is presented. The new method is illustrated through example calculations of the absorbance and MCD spectra of several octahedral and C(4v) d(5) transition metal complexes. The calculated transition energies and oscillator strengths are somewhat too low and too high, respectively, but these errors are within the range that would normally be expected for TDDFT calculations of this type. The calculations help to resolve some previously unexplained problems with the MCD spectra of the C(4v) complexes.
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calculation of excitation energies of open shell molecules with spatially degenerate ground states ii transformed reference via Intermediate Configuration kohn sham time dependent density functional theory oscillator strengths and magnetic circular dichroism c terms
Journal of Chemical Physics, 2006Co-Authors: Michael Seth, Tom ZieglerAbstract:An extension of the transformed reference via an Intermediate Configuration Kohn-Sham time dependent density functional theory (TRICKS-TDDFT) method for calculating the transition energies of molecules with spatially degenerate ground states is proposed that enables oscillator strengths to also be evaluated. The oscillator strengths are calculated starting from a description of the degenerate ground state and the excited states of interest in terms of linear combinations of Slater determinants based upon the F-vectors obtained in the TRICKS-TDDFT calculation. This approach for calculating oscillator strengths can also be applied to several other properties that involve excited states. An example of such a property, the C term of magnetic circular dichroism (MCD), is presented. The new method is illustrated through example calculations of the absorbance and MCD spectra of several octahedral and C4v d5 transition metal complexes. The calculated transition energies and oscillator strengths are somewhat too l...
Michael Seth - One of the best experts on this subject based on the ideXlab platform.
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calculation of excitation energies of open shell molecules with spatially degenerate ground states ii transformed reference via Intermediate Configuration kohn sham time dependent density functional theory oscillator strengths and magnetic circular dichroism c terms
Journal of Chemical Physics, 2006Co-Authors: Michael Seth, Tom ZieglerAbstract:An extension of the transformed reference via an Intermediate Configuration Kohn-Sham time dependent density functional theory (TRICKS-TDDFT) method for calculating the transition energies of molecules with spatially degenerate ground states is proposed that enables oscillator strengths to also be evaluated. The oscillator strengths are calculated starting from a description of the degenerate ground state and the excited states of interest in terms of linear combinations of Slater determinants based upon the F-vectors obtained in the TRICKS-TDDFT calculation. This approach for calculating oscillator strengths can also be applied to several other properties that involve excited states. An example of such a property, the C term of magnetic circular dichroism (MCD), is presented. The new method is illustrated through example calculations of the absorbance and MCD spectra of several octahedral and C(4v) d(5) transition metal complexes. The calculated transition energies and oscillator strengths are somewhat too low and too high, respectively, but these errors are within the range that would normally be expected for TDDFT calculations of this type. The calculations help to resolve some previously unexplained problems with the MCD spectra of the C(4v) complexes.
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calculation of excitation energies of open shell molecules with spatially degenerate ground states ii transformed reference via Intermediate Configuration kohn sham time dependent density functional theory oscillator strengths and magnetic circular dichroism c terms
Journal of Chemical Physics, 2006Co-Authors: Michael Seth, Tom ZieglerAbstract:An extension of the transformed reference via an Intermediate Configuration Kohn-Sham time dependent density functional theory (TRICKS-TDDFT) method for calculating the transition energies of molecules with spatially degenerate ground states is proposed that enables oscillator strengths to also be evaluated. The oscillator strengths are calculated starting from a description of the degenerate ground state and the excited states of interest in terms of linear combinations of Slater determinants based upon the F-vectors obtained in the TRICKS-TDDFT calculation. This approach for calculating oscillator strengths can also be applied to several other properties that involve excited states. An example of such a property, the C term of magnetic circular dichroism (MCD), is presented. The new method is illustrated through example calculations of the absorbance and MCD spectra of several octahedral and C4v d5 transition metal complexes. The calculated transition energies and oscillator strengths are somewhat too l...
Ch Tsakmakis - One of the best experts on this subject based on the ideXlab platform.
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isoclinic versus arbitrary rotated Intermediate Configuration for gradient plasticity applications
Composites Part B-engineering, 2012Co-Authors: C Broese, D Sfyris, Ch TsakmakisAbstract:Abstract Every multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts is related to a local unloading process, which determines a so-called plastic Intermediate Configuration. Two kinds of such Configurations are commonly used, at least in metal plasticity. The first one is connected with some fixed directions and is known as isoclinic Configuration. The second may be chosen to be arbitrarily rotated and is called here arbitrary rotated Intermediate Configuration. We call formulation of plasticity from the point of view of these Configurations respectively the isoclinic Intermediate Configuration approach (IIC-approach) and the arbitrary rotated Intermediate Configuration approach (ARIC-approach). It is known that in classical (local) plasticity, the IIC- and the ARIC-approaches may be viewed as alternative but equivalent. Under the assumptions made in the present paper, we show that this is generally no longer true, whenever gradient effects are involved.
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plastic Intermediate Configuration and related spatial differential operators in micromorphic plasticity
Mathematics and Mechanics of Solids, 2010Co-Authors: P Grammenoudis, Ch TsakmakisAbstract:The finite deformation kinematics of micromorphic plasticity is discussed in the framework of multiplicative decomposition of the macro- and microdeformation gradient tensor, suggesting the introduction of a so-called plastic Intermediate Configuration for the micromorphic continuum. The geometrical structure of the plastic Intermediate Configuration and the micromorphic curvature tensors are elucidated by invoking the differential operator of the relative covariant derivative with respect to the plastic Intermediate Configuration. Micromorphic curvature tensors arise in a natural way by considering scalar-valued differences. The latter measure the deformation process and are required to be form-invariant with respect to the chosen Configuration.
Kane C Bennett - One of the best experts on this subject based on the ideXlab platform.
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anisotropic finite hyper elastoplasticity of geomaterials with drucker prager cap type constitutive model formulation
International Journal of Plasticity, 2019Co-Authors: Kane C Bennett, Richard A Regueiro, Darby J LuscherAbstract:Abstract The formulation of large strain anisotropic hyper-elastoplasticity of geomaterials is examined. Attention is given to the role of structure tensors (also called fabric tensors), especially in context of the Eshelby–Mandel stress and large inelastic volume changes attributable to porosity. Both (hyper-)elastic and inelastic orthotropic symmetry, reducing to the particular case of transverse isotropy, are considered. Specific material assumptions and constitutive choices are identified for the development of a novel Anisotropic Drucker–Prager/Cap (ADPC) model formulated within the Intermediate Configuration consistent with multiplicative split of the deformation gradient. The model is calibrated to existing experimental measurements, including high pressure large strain triaxial compression of lithographic (Solnhofen) limestone and triaxial compression measurements on Tournemire shale assessing elastoplastic anisotropy. Manifest implications of constitutive theory are investigated, including consequences of recognizing (or not) the Eshelby–Mandel stress as energy conjugate to the plastic velocity gradient and including (or not) contribution from the skew-symmetric parts of the Mandel stress to the plastic anisotropy. Numerical simple shear experiments and large deformation simulated indentation experiments are provided in order to investigate model predictions and demonstrate the overall robustness in finite element modeling.
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finite strain elastoplasticity considering the eshelby stress for materials undergoing plastic volume change
International Journal of Plasticity, 2016Co-Authors: Kane C Bennett, Richard A Regueiro, Ronaldo I BorjaAbstract:Abstract In consideration of materials capable of undergoing significant plastic changes in volume, an alternative finite strain hyper-elastoplastic constitutive framework is proposed in terms of the Eshelby stress. Taking a phenomenological point of view, a thermodynamically-consistent approach to developing the constitutive equations is presented and discussed. Various Eshelby-like stresses are defined and shown to be energy-conjugate to the plastic velocity gradient, and a general framework is formulated in the stress-free/plastically-deformed Intermediate Configuration associated with the multiplicative split of the deformation gradient, as well as the current Configuration. A novel Eshelby-like stress measure is proposed, which is scaled by the elastic Jacobian, and is shown to be energy-conjugate to the plastic velocity gradient in the spatial representation. Modified Cam–Clay and Drucker–Prager cap plasticity constitutive equations are introduced, and large strain isotropic compression simulations are performed and compared with experimental measurements. The model results are compared with standard approaches formulated in terms of the Mandel and Kirchhoff stresses, which are shown to require the assumption of isochoric plasticity to satisfy the Clausius Planck inequality (Mandel) and preserve that the Intermediate Configuration remains stress-free (Kirchhoff). The simulations show that both the material and spatial Eshelby-like stress measures presented here produce the same mean Cauchy stress results; whereas, standard formulations, which make use of isochoric plasticity assumptions, diverge from each other at significant plastic volume strains. Standard formulations are further shown to violate the second law of thermodynamics under certain loading conditions. Calibration of model parameters to high pressure isotropic compression of Boulder clay is used to compare the various models.
Jerome L Sackman - One of the best experts on this subject based on the ideXlab platform.
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elastic plastic multiplicative decomposition with a stressed Intermediate Configuration
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Shmuel L Weissman, Jerome L SackmanAbstract:Abstract This paper presents an extension to the elastic–plastic multiplicative decomposition to permit the origin, in stress space, to reside outside the closure of the elastic domain. In this work the classical assumption of a stress-free Intermediate Configuration is abandoned in favor of a new one where the Intermediate Configuration could be stressed. This stress is identified as the maximal unloading point in stress space, and denoted the plastic stress. To motivate the discussion, the infinitesimal plasticity model is considered first. A remarkable result is obtained, where, for the case of linear elastic response, the classical infinitesimal model is, after some reinterpretation, recovered. The fully nonlinear model is developed, and is shown to reduce to the classical one when the Intermediate Configuration is stress-free. The new framework is then applied to the case of J 2 -plasticity, where it is shown that when coupled with neo-Hookean elasticity, as in the infinitesimal case, after some reinterpretation, the classical model is recovered ( i.e. , the total stress is independent of the plastic stress). Numerical simulations are used to illustrate the importance of properly modeling the hardening behavior even during (external) loading in cases where load redistribution may take place.