On Finite Plastic Flow of Crystalline Solids and Geomaterials

1983 ◽  
Vol 50 (4b) ◽  
pp. 1114-1126 ◽  
Author(s):  
S. Nemat-Nasser
Keyword(s):  
Granular Materials ◽  
Finite Deformation ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Close Relation ◽  
Crystalline Solids ◽  
Hardening Model ◽  
First Case ◽  
Physically Based ◽  
Points Of View

Certain fundamentals of finite-deformation elastoplastic flow of crystalline solids and geomaterials are discussed from microscopic and macroscopic phenomenological points of view. In the first case, physically based constitutive relations for microelements are formulated on the basis of slip-induced plastic deformation with due account of possible frictional or pressure dependencies and inelastic volumetric changes. The close relation between the double-slip theory of single crystals and that of granular materials is discussed. The calculation of overall instantaneous moduli in terms of the local quantities for arbitrary strains and rotations is examined, and some recent results for polycrystals and granular materials are reviewed. Then, attention is focused on phenomenological constitutive relations which apply to both metals and geomaterials. Specific results are given for an isotropic-kinematic hardening model, including frictional and plastic dilatancy effects. Finally, certain fundamental thermodynamic aspects of finite-deformation inelasticity are reviewed, emphasizing conditions under which flow potentials exist.

scholarly journals Influences of Material Variations of Functionally Graded Pipe on the Bree Diagram

2020 ◽  
Vol 10 (8) ◽  
pp. 2936 ◽  
Author(s):  
Aref Mehditabar ◽  
Saeid Ansari Sadrabadi ◽  
Raffaele Sepe ◽  
Enrico Armentani ◽  
Jason Walker ◽  
...  
Keyword(s):  
Internal Pressure ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Bending Moment ◽  
Yield Function ◽  
Functionally Graded ◽  
Loading Conditions ◽  
Mapping Algorithm ◽  
First Case ◽  
Backward Euler

The present research is concerned with the elastic–plastic responses of functionally graded material (FGM) pipe, undergoing two types of loading conditions. For the first case, the FGM is subjected to sustained internal pressure combined with a cyclic bending moment whereas, in the second case, sustained internal pressure is applied simultaneously with a cyclic through-thickness temperature gradient. The properties of the studied FGM are considered to be variable through shell thickness according to a power-law function. Two different designs of the FGM pipe are adopted in the present research, where the inner surface in one case and the outer surface in the other are made from pure 1026 carbon steel. The constitutive relations are developed based on the Chaboche nonlinear kinematic hardening model, classical normality rule and von Mises yield function. The backward Euler alongside the return mapping algorithm (RMA) is employed to perform the numerical simulation. The results of the proposed integration procedure were implemented in ABAQUS using a UMAT user subroutine and validated by a comparison between experiments and finite element (FE) simulation. Various cyclic responses of the two prescribed models of FGM pipe for the two considered loading conditions are classified and brought together in one diagram known as Bree’s diagram.

Errata

1993 ◽  
Vol 443 (1919) ◽  
pp. 625-627
Keyword(s):  
Granular Materials ◽  
Constitutive Relations

Proc. R. Soc. Lond . A 441, 433-463 (1993) Incremental constitutive relations for granular materials based on micromechanics By M. M. Mehra Badi, B. Loret and S. Nemat - Nasser Figures 6 and 10 in this paper were originally printed with an incorrect layout. They are printed below, with their correct layout, complete with captions, which remain unchanged.

Modeling Dislocation-Mediated Hydrogen Transport and Trapping in Fcc Metals

2021 ◽  
pp. 1-54
Author(s):  
Theodore Zirkle ◽  
Luke Costello ◽  
Ting Zhu ◽  
David L. McDowell
Keyword(s):  
Transport Model ◽  
Constitutive Relations ◽  
Crack Tip ◽  
Lattice Diffusion ◽  
Hydrogen Transport ◽  
Crack Tip Field ◽  
Coupled Diffusion ◽  
Crystal Plasticity Model ◽  
Physically Based ◽  
Material Ductility

Abstract The diffusion of hydrogen in metals is of interest due to the deleterious influence of hydrogen on material ductility and fracture resistance. It is becoming increasingly clear that hydrogen transport couples significantly with dislocation activity. In this work, we employ a coupled diffusion-crystal plasticity model to incorporate hydrogen transport associated with dislocation sweeping and pipe diffusion in addition to standard lattice diffusion. Moreover, we consider generation of vacancies via plastic deformation and stabilization of vacancies via trapping of hydrogen. The proposed hydrogen transport model is implemented in a physically-based crystal viscoplasticity framework to model the interaction of dislocation substructure and hydrogen migration. In this study, focus is placed on hydrogen transport and trapping within the intense deformation field of a crack tip plastic zone. We discuss the implications of the model results in terms of constitutive relations that incorporate hydrogen effects on crack tip field behavior and enable exploration of hydrogen embrittlement mechanisms.

scholarly journals Analysis of Undrained Seismic Behavior of Shallow Tunnels in Soft Clay Using Nonlinear Kinematic Hardening Model

2020 ◽  
Vol 10 (8) ◽  
pp. 2834
Author(s):  
Mohsen Saleh Asheghabadi ◽  
Xiaohui Cheng
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Soft Clay ◽  
Hysteresis Loops ◽  
Stiffness Degradation ◽  
Triaxial Tests ◽  
Embedment Depth ◽  
Ground Acceleration ◽  
Cyclic Shear ◽  
Hardening Model

In this study, a soil–tunnel model for clay under earthquake loading is analyzed, using finite element methods and a kinematic hardening model with the Von Mises failure criterion. The results are compared with those from the linear elastic–perfectly plastic Mohr–Coulomb model. The latter model does not consider the stiffness degradation caused by imposing cyclic loading and unloading to the soil, whereas the kinematic hardening model can simulate this stiffness degradation. The parameters of the kinematic hardening model are calibrated based on the results of experimental cyclic tests and finite element simulation. Here, two methods—one using data from cyclic shear tests, and the other a new method using undrained cyclic triaxial tests—are used to calibrate the parameters. The parameters investigated are the peak ground acceleration (PGA), tunnel lining thickness, tunnel shape, and tunnel embedment depth, all of which have an effect on the resistance of the shallow tunnel to the stresses and deformations caused by the surrounding clay soils. The results show that unlike traditional models, the nonlinear kinematic hardening model can predict the response reasonably well, and it is able to create the hysteresis loops and consider the soil stiffness degradation under the seismic loads.

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