Related papers: Numerical simulation of model problems in plastici…
Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
The present paper extends the thermodynamic dislocation theory initiated by Langer, Bouchbinder and Lookman [2010] to non-uniform finite plastic deformations. The equations of motion are derived from the variational equation involving the…
The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective behavior of dislocation dynamics at the mesoscale leads to…
In this article we present the numerical simulation of a dislocation incorporated into a Cosserat plate. The simulation is based on the mathematical model for bending of Cosserat elastic plates recently developed by the authors. The…
The present paper extends the thermodynamic dislocation theory developed by Langer, Bouchbinder, and Lookmann to non-uniform plastic deformations. The free energy density as well as the positive definite dissipation function are proposed.…
Grain structure plays a key role in the mechanical properties of alloy materials. Engineering the grain structure requires a comprehensive understanding of the evolution of grain boundaries (GBs) when a material is subjected to various…
We present a continuum model to determine the dislocation structure and energy of low angle grain boundaries in three dimensions. The equilibrium dislocation structure is obtained by minimizing the grain boundary energy that is associated…
This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation lines. The model is geometrically and elastically nonlinear,…
We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium.…
A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in Ref. [48]. The model is based on the motion and reaction of the constituent…
According to recent experimental and numerical investigations if the characteristic size of a specimen is in the submicron size regime several new interesting phenomena emerge during the deformation of the samples. Since in such a systems…
This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to…
In this study, we use discrete dislocation dynamics (DDD) simulation to investigate the effect of heterogeneous dislocation density on the transition between quasi-elastic deformation and plastic flow in face-centered cubic single crystals.…
When the deformations of a solid body are sufficiently large, parts of the body undergo a permanent deformation commonly refereed to as plastic deformation. Several plasticity models describing such phenomenon have been proposed, e.g. von…
A numerical strategy to simulate plastic deformation in Mg alloys including dislocation slip and twin propagation is presented. Dislocation slip is included through a crystal plasticity model which is solved using the finite element method…
Discrete dislocation dynamics (DDD) simulations offer valuable insights into the plastic deformation and work-hardening behavior of metals by explicitly modeling the evolution of dislocation lines under stress. However, the computational…
The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial…