A closed-form solution for the stress field in a rigid-perfectly plastic material under plane-strain conditions

1989 ◽  
Vol 77 (3-4) ◽  
pp. 307-313 ◽  
Author(s):  
D. E. Panayotounakos ◽  
N. P. Andrianopoulos
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Plane Strain ◽  
Plastic Material ◽  
Closed Form Solution ◽  
Form Solution ◽  
Perfectly Plastic

scholarly journals A closed-form solution for the stress field in a rigidperfectly plastic material under plane-strain conditions

1994 ◽  
Vol 104 (1-2) ◽  
pp. 121-123
Author(s):  
D. E. Panayotounakos ◽  
N. P. Andrianopoulos
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Plane Strain ◽  
Plastic Material ◽  
Closed Form Solution ◽  
Form Solution

Finite Deformations of a Rigid Perfectly Plastic Arch

1962 ◽  
Vol 29 (3) ◽  
pp. 549-553 ◽  
Author(s):  
E. T. Onat ◽  
L. S. Shu
Keyword(s):  
Closed Form ◽  
Yield Point ◽  
Finite Deformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Deformations ◽  
Deformation History ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
History Of

The quasi-static postyield deformation of a rigid-plastic arch in the presence of geometry changes is considered. The problem is formulated in terms of a series of boundary-value problems concerned with rates of stress and velocities. In the present simple case, the consideration of the rate problem associated with the yield-point state of the structure enables one to construct a closed-form solution which describes the entire deformation history of the arch. However, the principal aim of the present study is to stress the central role played by the rate problem in the investigation of the finite deformation of structures.

On the Application of Stress Triaxiality Formula for Plane Strain Fracture Testing

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Yuanli Bai ◽  
Xiaoqing Teng ◽  
Tomasz Wierzbicki
Keyword(s):  
Closed Form ◽  
Plane Strain ◽  
Fracture Strain ◽  
Closed Form Solution ◽  
Stress Triaxiality ◽  
Form Solution ◽  
Fracture Locus ◽  
Strain Fracture ◽  
Lode Angle ◽  
Angle Parameter

Theoretical and experimental studies have shown that stress triaxiality is the key parameter controlling the magnitude of the fracture strain. Smooth and notched round bar specimens are mostly often used to quantify the effect of stress triaxiality on ductile fracture strain. There is a mounting evidence (Bai and Wierzbicki, 2008, “A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence,” Int. J. Plast., 24(6), pp. 1071–1096) that, in addition to the stress triaxiality, the normalized third deviatoric stress invariant (equivalent to the Lode angle parameter) should also be included in characterization of ductile fracture. The calibration using round notched bars covers only a small range of possible stress states. Plane strain fracture tests provide additional important data. Following Bridgman’s stress analysis inside the necking of a plane strain specimen, a closed-form solution is derived for the stress triaxiality inside the notch of a flat-grooved plane strain specimen. The newly derived formula is verified by finite element simulations. The range of stress triaxiality in round notched bars and flat-grooved specimens is similar, but the values of the Lode angle parameter are different. These two groups of tests are therefore very useful in constructing a general 3D fracture locus. The results of experiments and numerical simulations on 1045 and DH36 steels have proved the applicability of the closed-form solution and have demonstrated the effect of the Lode angle parameter on the fracture locus.

Closed-form solution of Cattaneo equation including volumetric source in relation to laser short-pulse heating

2011 ◽  
Vol 89 (7) ◽  
pp. 761-767 ◽  
Author(s):  
H. Al-Qahtani ◽  
B.S. Yilbas
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Short Pulse ◽  
Closed Form Solution ◽  
Transformation Method ◽  
Substrate Material ◽  
Form Solution ◽  
Cooling Period ◽  
Wave Nature ◽  
Heating Model

The wave nature of the heating model is considered, incorporating the Cattaneo equation with the presence of a volumetric heat source. The volumetric heat generation resembles the step input laser short-pulse intensity. The governing of the heat equation is solved analytically using the Laplace transformation method. The stress field generated due to thermal contraction and expansion of the substrate material is formulated and the closed-form solution is presented. It is found that the wave nature of the heating is dominant during the period of the irradiated short-pulse; however, in the late cooling period, the wave nature of heating is replaced by diffusional heat conduction, governed by Fourier’s law. The stress field during the heating cycle is compressive and becomes tensile in the cooling cycle.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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