Plane-Stress Deformation in Strain Gradient Plasticity

1999 ◽  
Vol 67 (1) ◽  
pp. 105-111 ◽  
Author(s):  
J. Y. Chen ◽  
Y. Huang ◽  
K. C. Hwang ◽  
Z. C. Xia
Keyword(s):  
Boundary Conditions ◽  
Plane Stress ◽  
Strain Gradient ◽  
Three Dimensional ◽  
Strain Gradient Plasticity ◽  
Plane Boundary ◽  
Gradient Plasticity ◽  
Governing Equations ◽  
Stress Deformation ◽  
Out Of Plane

A systematic approach is proposed to derive the governing equations and boundary conditions for strain gradient plasticity in plane-stress deformation. The displacements, strains, stresses, strain gradients and higher-order stresses in three-dimensional strain gradient plasticity are expanded into a power series of the thickness h in the out-of-plane direction. The governing equations and boundary conditions for plane stress are obtained by taking the limit h→0. It is shown that, unlike in classical plasticity theories, the in-plane boundary conditions and even the order of governing equations for plane stress are quite different from those for plane strain. The kinematic relations, constitutive laws, equilibrium equation, and boundary conditions for plane-stress strain gradient plasticity are summarized in the paper. [S0021-8936(00)02301-1]

FEM solutions for plane stress mode-I and mode-II cracks in strain gradient plasticity

2000 ◽  
Vol 43 (9) ◽  
pp. 969-979
Author(s):  
Xinming Qiu ◽  
Tianfu Guo ◽  
Kezhi Huang ◽  
Kehchih Hwang
Keyword(s):  
Plane Stress ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Mode I ◽  
Mode Ii ◽  
Gradient Plasticity ◽  
Stress Mode

Analysis of particle induced dislocation structures using three-dimensional dislocation dynamics and strain gradient plasticity

2012 ◽  
Vol 52 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Hyung-Jun Chang ◽  
Anaïs Gaubert ◽  
Marc Fivel ◽  
Stéphane Berbenni ◽  
Olivier Bouaziz ◽  
...  
Keyword(s):  
Strain Gradient ◽  
Three Dimensional ◽  
Strain Gradient Plasticity ◽  
Dislocation Dynamics ◽  
Gradient Plasticity ◽  
Induced Dislocation

Guidelines for Constructing Strain Gradient Plasticity Theories

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
N. A. Fleck ◽  
J. W. Hutchinson ◽  
J. R. Willis
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Analytical Methods ◽  
Flow Theory ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Initial Yield ◽  
Energetic Stress ◽  
Elastic Loading ◽  
Continuum Theories

Issues related to the construction of continuum theories of strain gradient plasticity which have emerged in recent years are reviewed and brought to bear on the formulation of the most basic theories. Elastic loading gaps which can arise at initial yield or under imposition of nonproportional incremental boundary conditions are documented and analytical methods for dealing with them are illustrated. The distinction between unrecoverable (dissipative) and recoverable (energetic) stress quantities is highlighted with respect to elastic loading gaps, and guidelines for eliminating the gaps are presented. An attractive gap-free formulation that generalizes the classical J2 flow theory is identified and illustrated.

Stress analysis in transverse loading of soft core sandwich plates with various boundary conditions

2018 ◽  
Vol 22 (8) ◽  
pp. 2692-2734 ◽  
Author(s):  
Isa Ahmadi
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Sandwich Plates ◽  
Local Concentration ◽  
Governing Equations ◽  
Transverse Loading ◽  
Weak Formulation ◽  
Various Boundary Conditions ◽  
Out Of Plane

In this paper, the transverse loading of sandwich plate is formulated to study the three-dimensional stress field in the sandwich plates for various edge conditions. The formulation is based on the weak formulation approach. A complete three-dimensional displacement field is considered and the weak formulation approach is employed to obtain the governing equations of the plate using the three dimensional equilibrium equations of elasticity. An analytical solution is presented for governing equations when two opposite edges of plate are simply supported. A one-step stress recovery scheme is used to compute the out-of-plane stresses in the sandwich plates. A comparison is made with the predictions of exact elasticity solutions in the open literature and very good agreements are achieved. The distribution of stresses is investigated for various boundary conditions and the log-linear procedure is employed to study the order of stress singularity at free and clamped edge of the plate. It is seen that the present approach accurately predicts the distribution of out-of-plane stresses and local concentration of stresses in the vicinity of free and clamped edges of sandwich structures.

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