The Experts below are selected from a list of 18273 Experts worldwide ranked by ideXlab platform
Mikhail Itskov - One of the best experts on this subject based on the ideXlab platform.
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Computation of the exponential and other Isotropic Tensor functions and their derivatives
Computer Methods in Applied Mechanics and Engineering, 2003Co-Authors: Mikhail ItskovAbstract:Abstract In the present paper we focus on numerical aspects of the computation of Isotropic Tensor functions and their derivative. In the general case of non-symmetric Tensor arguments only two numerical algorithms appear to be appropriate. The first one represents a recurrent procedure resulting from the Taylor power series expansion of an Isotropic Tensor function. The second algorithm is based on a recently proposed closed-form representation which can be obtained from the definition of an Isotropic Tensor function either by the Tensor power series or by the Dunford–Taylor integral. To improve the accuracy in the case of nearly equal eigenvalues a series expansion of this closed formula is proposed. Both algorithms are finally illustrated by an example of the exponential Tensor function where emphasis is placed on the precision issue.
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Application of the Dunford-Taylor integral to Isotropic Tensor functions and their derivatives
Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 2003Co-Authors: Mikhail ItskovAbstract:In this paper we obtain closedform representations for Isotropic Tensor functions and their derivative using the DunfordTaylor integral. These representations are given in terms of eigenvalues of t...
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A generalized orthotropic hyperelastic material model with application to incompressible shells
International Journal for Numerical Methods in Engineering, 2001Co-Authors: Mikhail ItskovAbstract:In the present paper a new orthotropic hyperelastic constitutive model is proposed which can be applied to the numerical simulation of a wide range of anIsotropic materials and particularly biological soft tissues. The model represents a non-linear extension of the orthotropic St. Venant–Kirchhoff material and is described in each principal material direction by an arbitrary Isotropic Tensor function coupled with the corresponding structural Tensor. In the special case of isotropy this constitutive formulation reduces to the Valanis–Landel hypothesis and may therefore be considered as its generalization to the case of orthotropy. Constitutive relations and tangent moduli of the model are expressed in terms of eigenvalue bases of the right Cauchy–Green Tensor C and obtained for the case of distinct and coinciding eigenvalues as well. For the analysis of shells the model is then coupled with a six (five in incompressible case) parametric shell kinematics able to deal with large strains as well as finite rotations. The application of the developed finite shell element is finally illustrated by a number of numerical examples. Copyright © 2001 John Wiley & Sons, Ltd.
B A Younis - One of the best experts on this subject based on the ideXlab platform.
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Isotropic Tensor valued polynomial functions of fourth order Tensors
arXiv: Representation Theory, 2018Co-Authors: B A Younis, Gerald F SmithAbstract:Fourth-order Tensor-valued functions appear in numerous fields of study. The formulation of practical models for these complex functions often requires their representation in terms of Tensors of order two. In this paper, we develop an appropriate representation formula by assuming that the Isotropic fourth--order Tensor--valued function is a polynomial function in the components of two symmetric second-order Tensors of degree $\leq$ 2. We illustrate the utility of the result by applying it to obtain a representation of the fluctuating velocity, pressure-gradient correlations of turbulence.
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Isotropic Tensor valued polynomial function of second and third order Tensors
International Journal of Engineering Science, 2005Co-Authors: Gerald F Smith, B A YounisAbstract:Third-order Tensor-valued functions appear in the theory of turbulence as the stropholysis Tensor that parametrizes the breaking of reflectional symmetry in the spectrum of turbulence and as the correlations of triple fluctuating velocity components whose spatial gradients represent the rate of transport of turbulence by random fluctuations. The formulation of rational models for these quantities involves, in the first instance, the correct representation of a third-order Tensor-valued Isotropic function as a function of Tensors of order two and three. In this paper, we present the derivation of an appropriate representation formula and discuss its potential applications.
Gerald F Smith - One of the best experts on this subject based on the ideXlab platform.
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Isotropic Tensor valued polynomial functions of fourth order Tensors
arXiv: Representation Theory, 2018Co-Authors: B A Younis, Gerald F SmithAbstract:Fourth-order Tensor-valued functions appear in numerous fields of study. The formulation of practical models for these complex functions often requires their representation in terms of Tensors of order two. In this paper, we develop an appropriate representation formula by assuming that the Isotropic fourth--order Tensor--valued function is a polynomial function in the components of two symmetric second-order Tensors of degree $\leq$ 2. We illustrate the utility of the result by applying it to obtain a representation of the fluctuating velocity, pressure-gradient correlations of turbulence.
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Isotropic Tensor valued polynomial function of second and third order Tensors
International Journal of Engineering Science, 2005Co-Authors: Gerald F Smith, B A YounisAbstract:Third-order Tensor-valued functions appear in the theory of turbulence as the stropholysis Tensor that parametrizes the breaking of reflectional symmetry in the spectrum of turbulence and as the correlations of triple fluctuating velocity components whose spatial gradients represent the rate of transport of turbulence by random fluctuations. The formulation of rational models for these quantities involves, in the first instance, the correct representation of a third-order Tensor-valued Isotropic function as a function of Tensors of order two and three. In this paper, we present the derivation of an appropriate representation formula and discuss its potential applications.
Christian Miehe - One of the best experts on this subject based on the ideXlab platform.
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Comparison of two algorithms for the computation of fourth-order Isotropic Tensor functions
Computers & Structures, 1998Co-Authors: Christian MieheAbstract:Abstract This paper compares two possible representations of a certain class of fourth-order Isotropic Tensor functions. It focusses on the derivatives of symmetric second-order Isotropic Tensor functions by a symmetric second-order Tensor argument. This Tensor argument is assumed to be given in spectral form. The first representation explicitly needs the eigenvectors of the argument Tensor and is well-known in the literature. The second representation proposed here is based on the knowledge of second-order eigenvalue bases and avoids the computation of eigenvectors. The evaluation of a typical model problem shows that the second representation needs less computer time than the first one. The representations discussed here are of high importance for numerical solvers of nonlinear initial-boundary-value problems in large-strain elasticity and elastoplasticity.
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Computation of Isotropic Tensor functions
Communications in Numerical Methods in Engineering, 1993Co-Authors: Christian MieheAbstract:An explicit formulation and a procedure for the computation of Isotropic Tensor-valued Tensor functions is discussed. The formulation is based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors. As an important result a compact structure of the fourth-order derivatives of general second-order Isotropic Tensor functions is presented.
Guansuo Dui - One of the best experts on this subject based on the ideXlab platform.
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On the derivatives of a subclass of Isotropic Tensor functions of a nonsymmetric Tensor
International Journal of Solids and Structures, 2007Co-Authors: Zhi-qiao Wang, Guansuo DuiAbstract:This paper studies a subclass of Isotropic Tensor-valued functions of a nonsymmetric Tensor, which satisfy the commutative condition, and their derivatives. This subclass of Tensor functions includes Tensor power series, exponential Tensor function, etc., and is more general than those investigated before. In the case of three distinct eigenvalues, the derivatives of these Tensor functions are constructed by solving a Tensor equation, which is acquired by differentiating the commutative condition. By taking limits, the results are extended to the cases of repeated eigenvalues.
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Derivatives on the Isotropic Tensor functions
Science in China Series G, 2006Co-Authors: Guansuo Dui, Wang Zhengdao, Ming JinAbstract:The derivative of the Isotropic Tensor function plays an important part in continuum mechanics and computational mechanics, and also it is still an opening problem. By means of a scalar response function f (Λ i I 1 , I 2 ) and solving a Tensor equation, this problem is well studied. A compact explicit expression for the derivative of the Isotropic Tensor function is presented, which is valid for both distinct and repeated eigenvalue cases. Throughout the analysis, the formulation holds for general Isotropic Tensor functions without need to solve eigenvector problems or determine coefficients. On the theoretical side, a very simple solution of a Tensor equation is obtained. As an application to continuum mechanics, a base-free expression for the Hill’s strain rate is given, which is more compact than the existent results. Finally, with an example we compute the derivative of an exponent Tensor function. And the efficiency of the present formulations is demonstrated.
