Elastoplastic Modified STILLINGER-WEBER Potential-based Discretized Virtual Internal Bond Model And Its Application

The failure of material usually involves with the elasto-plastic deformation and fracturing process.For the plastic deformation,the continuum mechanics can well deal with the plastic deformation through a yield function and the flow rule while it has some limitations in dealing with the fracture problem since it is a theory based on the continuous field hypothesis.The lattice model can simulate the fracture problem very well,but it is inadequate in dealing with the plastic deformation.To combine the plasticity and the fracture in lattice system,the present thesis develops a new lattice model that can account for the plasticity based on the discretized virtual internal bond model(DVIB).DVIB is a kind of lattice method.It considers material to comprise of bond cells.Each bond cell may have any geometry with finite number of bonds.The strain energy of a bond cell can be characterized by the two-body potential or the multi-body potential.Different potential reflects different fracturing mechanisms.The two-body potential leads to the fixed Poisson ratio while the multi-body potential can overcome the limitation of the fixed Poisson ratio.In the present thesis,the modified Stillinger-Weber(SW)potential,a kind of multi-body potential,is employed to characterize the bond cell energy.The SW potential is composed of two parts.One part is the two-body potential that describes the interatomic interactions between particles.Another is the three-body potential that describes the bond angle interactions between particles.Because the SW interaction can represent the bond stretch and bond angle contribution,the SW potential-based DVIB(SW-DVIB)can represent the various Poisson ratio.To embed the plasticity in the SW-DVIB,the plasticity is considered in the two-body part of the SW-potential.It is done by reducing the bond stiffness to a lower level once the bond reaches the yielding point.While before the bond reaches the yielding point,the bond is elastic.When the bond deformation exceeds the yielding point,the bond stiffness is softened to a lower value.When unloaded,the irreversible deformation occurs.With the bond length increasing further to a critical value,termed as the failure bond length,the bond fails.The critical failure bond length is related to the cell size and the macro fracture energy.By this means,the fracture energy is conserved so that the cell size sensitivity problem is relieved to great extent.In addition,the plasticity and the fracture are also unified on the bond level.To make the DVIB able to simulate different Poisson ratios,the three-body part of the SW potential is kept elasto-brittle.Before the bond angle increment is smaller than a critical value,the bond angle can bear the moment.The moment is linear with the bond angle increment.However,once the bond angle increment exceeds this critical value,the bond angle fails.That means the bond angle will no longer bear the moment.By this method,the SW-DVIB can simulate the plastic deformation and the fracturing process of material with various Poisson ratio.The elasto-plastic SW-DVIB is used to simulate the plastic deformation of material,the plastic fracturing process and the tunnel plastic deformation.It is verified that the present elasto-plastic SW-DVIB is an effective method to simulate the elasto-plastic deformation and the plastic fracture.It provides a new lattice approach to the analysis of the elasto-plastic failure behaviors of material.