Driving forces on dislocations: finite element analysis in the context of the non-singular dislocation theory

This work presents a regularized eigenstrain formulation around the slip plane of dislocations and the resultant non-singular solutions for various dislocation configurations. Moreover, we derive the generalized Eshelby stress tensor of the configurational force theory in the context of the proposed dislocation model. Based on the non-singular finite element solutions and the generalized configurational force formulation, we calculate the driving force on dislocations of various configurations, including single edge/screw dislocation, dislocation loop, interaction between a vacancy dislocation loop and an edge dislocation, as well as a dislocation cluster. The non-singular solutions and the driving force results are well benchmarked for different cases. The proposed formulation and the numerical scheme can be applied to any general dislocation configuration with complex geometry and loading conditions.

On a modeling stress-controlled surface growth of solids

Various processes are associated with the surface growth of solids, such as biological growth, formation of surfaces, processes accompanying additive technologies. Experiments show that the growth process of living and non-living matter can be controlled by external influences, including mechanical ones. This paper presents a surface growth model based on the expression for the configurational force obtained from the fundamental balances of mass, momentum and energy, and the second law of thermodynamics in the form of the Clausius-Duhem inequality. It is shown that the configurational force is the normal component of the tensor, called the surface growth tensor, which controls the processes of growth and adaptation to external mechanical loads. A kinetic equation in the form of the dependence of the growth rate on the growth tensor is formulated. A solid body is considered, in which a volumetric supply and subsequent diffusion of matter to the growth boundary occur. On the surface of the body, the transformation of one substance into another occurs, resulting in surface growth or resorption of the body. The surface growth process depends on the stress-strain state of the body and the concentration of the diffusing matter. In the process of growth, stresses and deformations change, affecting the configurational force and the rate of the matter supply, which also affects the configurational force. In addition, the model takes into account the growth strains that can occur in new layers of the material and affect the growth velocity. Thus, there is a coupled problem including the description of the supply, diffusion and growth processes and determination of the stress-strain state. The model was used for the problems of surface growth of various bodies under various loading conditions.

The force on a defect

This chapter is based on Eshelby’s static energy-momentum tensor which results in an integral expression for the configurational force on a defect. After elucidating the concepts of a configurational force and an elastic singularity the mechanical pressure on an interface, such as a twin boundary or a martensitic interface, is derived. Eshelby’s force on a defect is derived using both physical arguments and more formally using classical field theory. It is equivalent to the J-integral in fracture mechanics. The Peach–Koehler force on a dislocation is rederived using the static energy-momentum tensor. An expression for an image force is derived, where a defect interacts with a free surface.