The present paper focuses on the consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm. A general and modular algorithmic setting, suited for ...
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The present paper focuses on the consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm. A general and modular algorithmic setting, suited for almost any rate constitutive equations, is presented where the finite deformation consistent tangent modulus is obtained as a by-product of the integration algorithm. Numerical examples illustrate the good performance of the proposed formulation, especially for large deformation increments with noteworthy superimposed rotation, where the consistent formulation converges quadratically in a reasonable number of iterations. Copyright (C) 2008 John Wiley & Sons, Ltd.
The reference wave phase was modulated with a sinusoidal vibrating mirror attached to a Piezoelectric Transducer(PZT), the integration was performed by a CCD,and the charge storage period of the CCD image sensor was o...
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The reference wave phase was modulated with a sinusoidal vibrating mirror attached to a Piezoelectric Transducer(PZT), the integration was performed by a CCD,and the charge storage period of the CCD image sensor was one-quarter period of the sinusoidal phase *** the frequency- synchronous detection technique,four images(four frames of interference pattern)were recorded during one period of the phase *** order to obtain the optimum modulation parameter,the values of amplitude and phase of the sinusoidal phase modulation were determined by considering the measurement error caused by the additive noise contained in the detected *** PZT oscillation was controlled by a closed loop control system based on PID *** ideal discrete digital sine function at 50Hz with adjustable amplitude was used to adjust the vibrating of PZT,and a digital phase shift techniques was used to adjust vibrating phase of PZT so that the phase of the modulation could reach their optimum *** CCD detector was triggered with software at *** on work above,a small coherent signal masked by the preponderant incoherent background with a CCD detector was obtained.
An integration algorithm is presented for approximate closed-form expressions for the spectrum of constant-amplitude Polynomial-phase signals (PPS) with a given degree. The algorithm introduces a slowly varying functi...
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An integration algorithm is presented for approximate closed-form expressions for the spectrum of constant-amplitude Polynomial-phase signals (PPS) with a given degree. The algorithm introduces a slowly varying function as the amplitude of PPS. The slowly varying function is then approximated by Hermite polynomial expansion and the Fourier transform of PPS with the slowly varying amplitude, i.e., the expression of spectrum is thus expressed as a sum of constituent integrals with integrands containing a Hermite polynomial multiplied by polynomial phase factors. The expression for spectrum of the constant-amplitude PPS is just the first term of the constituent integrals which are approximately expressed by means of obtaining the inverse of a banded coefficients matrix in a system of linear equations. Simulation results are provided to indicate that the expressions derived by using the integration algorithm have high precision.
This paper describes a new. integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inela...
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ISBN:
(纸本)3908451264;9783908451266
This paper describes a new. integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inelastic strain rate in HSCE so that the inelastic strain rate can be solved indirectly from the Lambda. The proposed integration algorithm is based on the stress update concept and the effect of normal stress updating on the material compression is also discussed thoroughly in this paper. The investigation results show that the new algorithm can integrate the HSCE efficiently and the normal stress should keep constant as the deviatoric stress updating. An example of semi-solid extruding was given in the paper at last to illustrate the implementation of new algorithm and effect of normal stress updating on the compression of material.
This paper describes a new. integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inela...
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This paper describes a new. integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inelastic strain rate in HSCE so that the inelastic strain rate can be solved indirectly from the Lambda. The proposed integration algorithm is based on the stress update concept and the effect of normal stress updating on the material compression is also discussed thoroughly in this paper. The investigation results show that the new algorithm can integrate the HSCE efficiently and the normal stress should keep constant as the deviatoric stress updating. An example of semi-solid extruding was given in the paper at last to illustrate the implementation of new algorithm and effect of normal stress updating on the compression of material.
The problem of planar reflected-shock/spiral-vortex interactions near an open-ended duct is considered. The reflected shock is formed after exiting the duct and impinging on a vertical wall that is located downstream ...
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The problem of planar reflected-shock/spiral-vortex interactions near an open-ended duct is considered. The reflected shock is formed after exiting the duct and impinging on a vertical wall that is located downstream or the duct. Two cases associated with the shock diffraction around the duct exit are investigated for understanding the detailed flow structure and acoustic waves due to the reflected shock/spiral-vortex interaction. One is a 90-deg diffraction;the other is a 180-deg diffraction. An Euler solver with a high-resolution scheme of weighted essential nonoscillation is used to study these complicated flow problems. The Euler solver is validated to be reasonably accurate by comparing the computed solution with experimental data. For the study of reflected-shock/spiral-vortex interactions, the techniques of computational shadowgraph, computational schlieren image, and computational interferometry are used. Detailed flow structures of reflected shock/vortex interactions are reported for different incident shock Mach numbers. An interesting result of stagnant reflected shock waves downstream of the duct is found for an incident shock Mach number equal to or greater than 1.4. For the incident shock Mach number below this critical value, the reflected shock RE will eventually enter the duct. The mechanism for the formation of acoustic waves generated by reflected-shock/vortex interactions is analyzed.
Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable fi...
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Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright (C) 2004 John Wiley Sons, Ltd.
A model is proposed for hereditary elasticity and viscoplasticity of salt rocks. The features of rock sample deformation to be connected with loosening and original damaged state are considered in construction of nucl...
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A model is proposed for hereditary elasticity and viscoplasticity of salt rocks. The features of rock sample deformation to be connected with loosening and original damaged state are considered in construction of nuclei of shear and volume creep.
A stress integration algorithm for granular materials based on fully implicit integration with explicit updating is presented. In the implicit method the solution makes use of the gradient to the potential surface at ...
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A stress integration algorithm for granular materials based on fully implicit integration with explicit updating is presented. In the implicit method the solution makes use of the gradient to the potential surface at the final stress state which is unknown. The final stress and hardening parameters are determined solving the non-linear equations iteratively so that the stress increment fulfills the consistency condition. The integration algorithm is applicable for models depending on all the three stress invariants and it is applied to a characteristic state model for granular material. Since tensile stresses are not supported the functions and their derivatives are not representative outside the compressive octant of the principal stress space. The elastic predictor is therefore preconditioned in order to ensure that the first predictor is within the valid region. Capability and robustness of the integration algorithm are illustrated by simulating both drained and undrained triaxial tests on sand. The algorithm is developed in a standard format which can be implemented in several general purpose finite element codes. It has been implemented as an ABAQUS subroutine, and a traditional geotechnical problem of a flexible strip footing resting on a surface of sand is investigated in order to demonstrate the global accuracy and stability of the numerical solution. (C) 2003 Elsevier B.V. All rights reserved.
The development of a new constitutive model would normally require a new procedure to be established for derivation of the incremental response. However, for models generated within the framework of hyperplasticity (u...
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The development of a new constitutive model would normally require a new procedure to be established for derivation of the incremental response. However, for models generated within the framework of hyperplasticity (using single, multiple or continuous yield surfaces), this derivation can be carried out using standard procedures. In this paper we present first the unified incremental response for a model using a single internal variable for general loading conditions. Next, we develop and explore three different numerical techniques for implementation of this procedure. One of the approaches, which seems superior, is extended to the multi-surface hyperplastic formulation. Finally, to allow integration of continuous hyperplastic models within the same multi-surface hyperplastic setting, the issue of discretization of the continuous field of yield surfaces is addressed. Copyright (C) 2003 John Wiley Sons, Ltd.
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