It is expressed in a similar way as elasticity problem and it could be divided into three symmetric groups. Based on the work Smith et. al [SmSm63], Tu [Tu68] has presented an additive decomposition of the forth-and second-order exibility and consti-tutive tensors, where the symmetries...
With this purpose, we start with the basic concepts of the linearised theory of elasticity, that is, the stress and strain tensors and how the elastic constants c 11 , c 12 , c 44 of the silicon crystal have to be recalculated when the atomic planes are differently oriented with ...
Conditions are derived that show the integrals exhibit alternative behavior and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay, provided the elasticity tensor is positive definite or satisfies a strong ellipticity condition.doi:...
3.5.2 Conjugage Stress Tensors 3.5.3 Stress Rates References Chapter 4 Elasticity 4.1 Constitutive laws for simple materials 4.1.1 General Remarks on Constitutive Laws 4.1.2 Simple Materials 4.1.3 Material Uniformity and Homogeneity 4.2 Cauchy elastic materials 4.2.1 The Constitutive Equation for a...
In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensorC. The decomposition ofCinto a parti... Y Itin,FW Hehl - 《Journal of Mathematical Physics》 被引量: 26发表: 2013年 Thermomechanical fatigue crack propagation in an anisotropic...
This is possible for the isotropic case and also if the anisotropy is present only in the tensor of elastic constants corresponding to the classical strain tensor. If the material is isotropic with respect to rotational deformations but the (anisotropic) coupling between rotational and classical ...
Non-linear elasticityDamage induced anisotropyRheologyDamage tensorWe extend the isotropic nonlinear damage rheology model with a scalar damage parameter to a more complex formulation that accounts for anisotropic damage growth under true triaxial loading. The model takes account of both the anisotropy of...
The plastic flow potential function has the same form as that of the Yld91 yield function but a different fourth order tensor is adopted to improve its flexibility. The anisotropic plasticity model is applied to describe anisotropy of both yield stresses and R-values for a cold-rolled steel ...
The equilibrium, compatibility and elasticity equations governing the behaviour of that structure may be expressed as [25]:Ds+b-cρu̇-mρu¨=0e=D∗us=keThe vectors s, e and u list the independent components of the stress, strain and displacement fields, respectively. Assuming a ...
Among the common shearing moduli of elasticity new coupled shearing moduli of elasticity are introduced. Some useful invariants of the compliance tensor are derived and expressed in terms of engineering constants. The invariants are linear, quadratic and cubic. They can be used in analyzing ...