On the coupling of peridynamics with the classical theory of continuum mechanics in a meshless framework

The classical theory of solid mechanics employs partial derivatives in the equation of motion and hence requires the differentiability of the displacement field. Such an assumption breaks down when simulation of problems containing discontinuities, such as cracks, comes into the picture. peridynamics is considered to be an alternative and promising nonlocal theory of solid mechanics that is formulated suitably for discontinuous problems. Peridynamics is well designed to cope with failure analysis as the theory deals with integral equations rather than partial differential equations. Indeed, peridynamics defines the equation of motion by substituting the divergence of the stress tensor, involved in the formulation of the classical theory, with an integral operator. One of the most common techniques to discretize and implement the theory is based on a meshless approach. However, the method is computationally more expensive than some meshless methods based on the classical theory. This originates from the fact that in peridynamics, similar to other nonlocal theories, each computational node interacts with many neighbors over a finite region. To this end, performing realistic numerical simulations with peridynamics entails a vast amount of computational resources. Moreover, the application of boundary conditions in peridynamics is nonlocal and hence it is more challenging than the application of boundary conditions adopted by methods based on the classical continuum theory. This issue is well-known to scientists working on peridynamics. Therefore, it is reasonable to couple computational methods based on classical continuum mechanics with others based on peridynamics to develop an approach that applies different computational techniques where they are most suited for. The main purpose of this dissertation is to develop an effective coupled nonlocal/local meshless technique for the solution of two-dimensional elastodynamic problems involving brittle crack propagation. This method is based on a coupling between the peridynamic meshless method, and other meshless methods based on the classical continuum theory. In this study, two different meshless methods, the Meshless Local Exponential Basis Functions and the Finite Point Method are chosen as both are classified within the category of strong form meshless methods, which are simple and computationally cheap. The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only peridynamics is applied, one in which only the meshless method is applied and a transition zone where a transition between the two approaches takes place. The coupling adopts a local/nonlocal framework that benefits from the full advantages of both methods while overcoming their limitations. The parts of the domain where cracks either exist or are likely to propagate are described by peridynamics; the remaining part of the domain is described by the meshless method that requires less computational effort. We shall show that the proposed approach is suited for adaptive coupling of the strategies in the solution of crack propagation problems. Several static and dynamic examples are performed to demonstrate the capabilities of the proposed approach

Modelling of dynamic friction across solid material interfaces using molecular dynamics techniques

The topic of this PhD is to investigate materials interfaces under the application of com-pressive forces and dynamic friction. Friction studies are important in applications for high-speed machining and ballistic penetration modelling, two areas where it is important to understand the behaviour of rapidly moving interfaces. Gaining insight into the velocity dependence of the effective tangential force, and its time-evolution, under various external loads is also of particular interest. It is important to understand on an atomic and/or molec-ular level the fundamentals of tribological processes. Some of the processes investigated in this thesis include plastic deformation due to high compression, the response of materials when sliding occurs in terms of temperature variation across the interface and its relation-ship with atomic diffusion. Moreover, the materials dependence on operating conditions of temperature, loading and dynamic friction are factors that ultimately determine the design of tribological systems. In the last few years it has been shown that materials properties depend on the size, as smaller specimens are relatively stronger than larger ones. This thesis is aiming to em-ploy state of the art numerical and theoretical methods, which are vital to give a significant insight and understanding of the fundamental issues concerning dynamic friction of tribo-logical processes at the atomic scale. The mechanical behaviour is investigated in detail to reveal an accurate theoretical description of the frictional force at metallic surfaces. Special consideration is taken into account for the mechanism that causes dissipation in the form of heat. The strong deformation when materials undergo dynamic friction causes energy to dissipate away from the interface at a high rate. Additionally, investigation of the plastic deformation and its variation under conditions prevalent at high speed sliding is carried out. Knowledge of the yield point under these conditions is important to obtain accurate constitutive models for the shear stresses. In-vestigating how the material strength varies under sliding friction and obtaining accurate evaluation of the stresses involved has proved difficult and time consuming. This is primar¬ily attributed to the fact that experiments are difficult to conduct and expensive facilities are required. This thesis focuses on aspects of this complex process with the aid of molecular dynamic simulations.EThOS - Electronic Theses Online ServiceGBUnited Kingdo