A higher-order stress point method for non-ordinary state-based peridynamics

2020 ◽  
Vol 117 ◽  
pp. 104-118
Author(s):  
Hao Cui ◽  
Chunguang Li ◽  
Hong Zheng
Keyword(s):  
Higher Order ◽  
Point Method ◽  
Stress Point ◽  
Order Stress

Equivalence Between Higher-Order Stress Power and Heat Flux in Energy Equation Based on Lattice Dynamics

1999 ◽  
Vol 121 (2) ◽  
pp. 240-246 ◽  
Author(s):  
Y. Yasui ◽  
K. Shizawa ◽  
K. Takahashi
Keyword(s):  
Heat Flux ◽  
Lattice Dynamics ◽  
Energy Equation ◽  
Solid Mechanics ◽  
Higher Order ◽  
First Law Of Thermodynamics ◽  
Internal Forces ◽  
Order Stress ◽  
As Stress

The essence of macroscopic quantities in solid mechanics can be grasped by expressing these quantities in terms of kinematic and mechanical quantities of atoms. In this paper, a method is proposed for obtaining the microscopic definitions of internal forces of continua such as stress, higher-order stresses and heat flux. Moreover, the relation between higher-order stress power and heat flux is discussed expressing the first law of thermodynamics with microscopic quantities in the mesodomain. Comparing heat flux with higher-order stress power, it is clarified that the divergence of heat flux is equivalent to the total of each order power due to higher-order stresses.

Analytical Solutions for Crack-Tip Higher Order Stress Fields in Thermal Barrier Coating

2008 ◽  
Vol 47-50 ◽  
pp. 1023-1026
Author(s):  
Yao Dai ◽  
Chang Qing Sun ◽  
Sun Qi ◽  
Wei Tan
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Stress Fields ◽  
Thermal Barrier ◽  
Barrier Coating ◽  
Graded Material ◽  
Stress Functions ◽  
Order Stress ◽  
Analytical Expressions

Analytical expressions for crack-tip higher order stress functions for a plane crack in a special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously. Furthermore, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for non-homogeneity effects on the crack- tip stress fields. These results provide the basis for fracture analysis and engineering applications of this FGM.

Localized Deformation Using Higher Order Stress/Strain Theory

1990 ◽  
Vol 112 (1) ◽  
pp. 51-53 ◽  
Author(s):  
M. A. Koenders
Keyword(s):  
Slip Band ◽  
Failure Modes ◽  
Tangential Force ◽  
Higher Order ◽  
Strain Theory ◽  
Granular Soils ◽  
Localized Deformation ◽  
Contact Points ◽  
Force Ratio ◽  
Order Stress

A material is considered which consists of rough interacting blocks. The interaction, which is expressed in terms of the ratio of the normal and tangential force at the contact points of the blocks, is pure frictional if a certain maximal force ratio is reached, and elastic otherwise. The shape of the blocks is determined by the double shearing geometry. Failure modes for this material depend on the thickness of the slip band. The investigation is relevant to granular soils and rocks.

A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis

2016 ◽  
Vol 304 ◽  
pp. 584-604 ◽  
Author(s):  
Tran Quoc Thai ◽  
Timon Rabczuk ◽  
Yuri Bazilevs ◽  
Günther Meschke
Keyword(s):  
Isogeometric Analysis ◽  
Damage Model ◽  
Higher Order ◽  
Model Based ◽  
Order Stress

Higher-Order Stress due to Self Energy of Geometrically Necessary Dislocations

2007 ◽  
Vol 340-341 ◽  
pp. 173-178
Author(s):  
Nobutada Ohno ◽  
Dai Okumura
Keyword(s):  
Size Dependence ◽  
Dislocation Cell ◽  
Higher Order ◽  
The Self ◽  
Initial Yield Stress ◽  
Self Energy ◽  
Dependent Term ◽  
Stress Changes ◽  
Order Stress ◽  
2D And 3D

The self energy of geometrically necessary dislocations (GNDs) in single crystals is considered to inevitably introduce a higher-order stress as the work conjugate to slip gradient. It is pointed out that this higher-order stress changes stepwise in response to in-plane slip gradient and thus explicitly influences the initial yielding of polycrystals. The self energy of GNDs is then incorporated into the strain gradient plasticity theory of Gurtin (2002). The resulting theory is applied to 2D and 3D model crystal grains of diameter D, leading to a D-1-dependent term with a coefficient determined by grain shape. This size effect term is verified using published experimental data of several polycrystalline metals. It is thus found that the D-1-dependent term is successful for predicting not only the grain size dependence of initial yield stress but also the dislocation cell size dependence of flow stress in the submicron to several micron range of D.

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