The present paper generalizes the method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen （2004） to a subclass of nonsymmetric tensor functions satisfying the commu...The present paper generalizes the method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen （2004） to a subclass of nonsymmetric tensor functions satisfying the commutative condition. This subclass of tensor functions is more general than those investigated by the existing methods. In the case of three distinct eigenvalues, the commutativity makes it possible to introduce two scalar functions, which will be used to construct the general nonsymmetric tensor functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.展开更多
In the paper the elasticity tensor and the relation between stress and strain of transverse isotropic material and isotropic material are deduced by tensor derivate. From the derivation the reason why there are two in...In the paper the elasticity tensor and the relation between stress and strain of transverse isotropic material and isotropic material are deduced by tensor derivate. From the derivation the reason why there are two independent elasticity coefficients for isotropic elastic material and five for transverse isotropic elastic material can be seen more clearly.展开更多
In order to formulate a general expression of elastic tensor for anisotropic materials, a method of tensor derivative is used for determining relationship between fourth-order elastic tensor and second-order structure...In order to formulate a general expression of elastic tensor for anisotropic materials, a method of tensor derivative is used for determining relationship between fourth-order elastic tensor and second-order structure tensor that has satisfied material symmetrical conditions. From this general expression of elastic tensor, specific expressions of elastic tensor for different anisotropic materials, such as isotropic materials, transverse isotropic materials and orthogonal-anisotropic materials, can be deduced. This expression underlies the scalar description of anisotropic factors, which are used for classifying and analyzing anisotropic materials. Cubic crystals are analyzed macroscopically by means of the general expression and anisotropic factor.展开更多
I have already reported “Property of Tensor Satisfying Binary Law”. This article is the article that I revise the contents of “Property of Tensor Satisfying Binary Law”, and increase the report about new character...I have already reported “Property of Tensor Satisfying Binary Law”. This article is the article that I revise the contents of “Property of Tensor Satisfying Binary Law”, and increase the report about new characteristics. We may arrive at the deeper understanding in this about “Property of Tensor Satisfying Binary Law”.展开更多
基金the National Natural Science Foundation of China(No.50539030)
文摘The present paper generalizes the method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen （2004） to a subclass of nonsymmetric tensor functions satisfying the commutative condition. This subclass of tensor functions is more general than those investigated by the existing methods. In the case of three distinct eigenvalues, the commutativity makes it possible to introduce two scalar functions, which will be used to construct the general nonsymmetric tensor functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.
文摘In the paper the elasticity tensor and the relation between stress and strain of transverse isotropic material and isotropic material are deduced by tensor derivate. From the derivation the reason why there are two independent elasticity coefficients for isotropic elastic material and five for transverse isotropic elastic material can be seen more clearly.
文摘In order to formulate a general expression of elastic tensor for anisotropic materials, a method of tensor derivative is used for determining relationship between fourth-order elastic tensor and second-order structure tensor that has satisfied material symmetrical conditions. From this general expression of elastic tensor, specific expressions of elastic tensor for different anisotropic materials, such as isotropic materials, transverse isotropic materials and orthogonal-anisotropic materials, can be deduced. This expression underlies the scalar description of anisotropic factors, which are used for classifying and analyzing anisotropic materials. Cubic crystals are analyzed macroscopically by means of the general expression and anisotropic factor.
文摘I have already reported “Property of Tensor Satisfying Binary Law”. This article is the article that I revise the contents of “Property of Tensor Satisfying Binary Law”, and increase the report about new characteristics. We may arrive at the deeper understanding in this about “Property of Tensor Satisfying Binary Law”.
