Related papers: Dislocation in Motion as the Dynamic Distribution …
This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…
Progress toward a first-principles theory of plasticity and work-hardening is currently impeded by an insufficient picture of dislocation kinetics (the dynamic effect of driving forces in a given dislocation theory). This is because present…
We review the continuous theory of dislocations from a mathematical point of view using mathematical tools, which were only partly available when the theory was developed several decades ago. We define a space of dislocation measures, which…
This paper focuses on an elastic dislocation problem that is motivated by applications in the geophysical and seismological communities. In our model, the displacement satisfies the Lam\'e system in a bounded domain with a mixed homogeneous…
We study strain-controlled plastic deformation of crystalline solids via two-dimensional discrete dislocation dynamics simulations. To this end, we characterize the average stress-strain curves as well as the statistical properties of…
Dislocation motion in body centered cubic (bcc) metals displays a number of specific features that result in a strong temperature dependence of the flow stress, and in shear deformation asymmetries relative to the loading direction as well…
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…
Crystal plasticity of sub-micron finite volumes is characterized by the flow of emergent dislocation defects, giving rise to size effects in mechanical properties and avalanche phenomena. In this chapter, we present a minimal model for…
We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity…
Most of crystalline materials develop an hysteresis on their deformation curve when a mechanical loading is applied in alternating directions. This effect, also known as the Bauschinger effect, is intimately related to the reversibile part…
The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various point-like defects such as precipitates or solute atoms. These…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the…
We develop a non-singular theory of three-dimensional dislocation loops in a particular version of Mindlin's anisotropic gradient elasticity with up to six length scale parameters. The theory is systematically developed as a generalization…
Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic…
The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation pro- cesses, including…
We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We…
Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli…
New aspects of a relation between lattice and dislocation structures are examined within a physically transparent theoretical scheme. Predicted features originating from the lattice discreteness include: (i) multiple core dislocation…
The chapter presents the problem of the complexity of plastic flow in alloys, which is manifested by serrated deformation curves and transient plastic strain localizations. This phenomenon uncovers an inherently collective nature of the…