[SY-K4] Disclination dipole model of kink deformation in layered solid
Invited
Kink deformation is commonly observed in layered solid for a wide variety of scales from atomistic layers to geological structures, and their structural similarity means possibility of universal application of deformable body mechanics. In our previous works, the deformation mechanism of kink deformation in a layered solid with a single-slip system has been studied and it is shown that the fundamental process of kink deformation is represented by disclination dipole model.
In this study, first, we review the relationship between generalized continuum theories and the disclination dipole dynamics from a multiscale point of view.
Secondly, nucleation of kink deformation under a compressive force in the direction parallel to the layers is studied using configulational force of disclination dipole based on instability theory, in which the deformation mechanism is discussed from the viewpoint of the instability theory with the Maxwell's equal area rule.
Third, we use cellular automaton as a discretized model of disclination dipole theory, in which each layer is divided into segments and the amount of Frank vector of each segment is encoded using integers. In this study, total strain energy is calculated as sum of the local bending strain energy of each layer and inter-layer energy, in which the local strain energy density is evaluated as a linear function of square of curvature and inter-layer energy is assumed to be expressed by a form of Lennard-Jones 12-6 potential. The Metropolis Monte Carlo Method is adopted to evolve the state of the material system. The result of this scheme is verified on the classical problem of buckling of Euler's column with comparing analytical solution. After that, simulation of kinking deformation is examined for various values of the inter-layer strength parameter.
In this study, first, we review the relationship between generalized continuum theories and the disclination dipole dynamics from a multiscale point of view.
Secondly, nucleation of kink deformation under a compressive force in the direction parallel to the layers is studied using configulational force of disclination dipole based on instability theory, in which the deformation mechanism is discussed from the viewpoint of the instability theory with the Maxwell's equal area rule.
Third, we use cellular automaton as a discretized model of disclination dipole theory, in which each layer is divided into segments and the amount of Frank vector of each segment is encoded using integers. In this study, total strain energy is calculated as sum of the local bending strain energy of each layer and inter-layer energy, in which the local strain energy density is evaluated as a linear function of square of curvature and inter-layer energy is assumed to be expressed by a form of Lennard-Jones 12-6 potential. The Metropolis Monte Carlo Method is adopted to evolve the state of the material system. The result of this scheme is verified on the classical problem of buckling of Euler's column with comparing analytical solution. After that, simulation of kinking deformation is examined for various values of the inter-layer strength parameter.