Source code for OpenCL Peridynamics solver

Source code for an OpenCL Peridynamics solver described in the paper "OpenCL implementation of a high performance 3D Peridynamic model on graphics accelerators" by F. Mossaiby, A. Shojei, M. Zaccariotto and U. Galvanetto<br

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

Discontinuous mechanical problems studied with a Peridynamics-based approach

The classical theory of solid mechanics is rooted in the assumption of a continuous distribution of mass within a body. It employs partial differential equations (PDEs) with significant smoothness to obtain displacements and internal forces of the body. Although classical theory has been applied to wide range of engineering problems, PDEs of the classical theory cannot be applied directly on a discontinuity such as cracks. Peridynamics is considered to be an alternative and promising nonlocal theory of solid mechanics that, by replacing PDEs of classical theory with integral or integro-differential equations, attempts to unite the mathematical modelling of continuous media, cracks and particles within a single framework. Indeed, the equations of peridynamic are based on the direct interaction of material points over finite distances. Another concept, derived from the peridynamic approach to cope with engineering problems with discontinuities, is that of the peridynamic differential operator (PDDO). The PDDO uses the non-local interaction of the material points in a way similar to that of peridynamics. PDDO is capable to recast partial derivatives of a function through a nonlocal integral operator whose kernel is free of using any correction function. In this dissertation, application of peridaynamics and PDDO, to three different important engineering problems including fatigue fracture, thermo-mechanics and sloshing phenomena, is examined comprehensively. To cope with fatigue fracture problems, an algorithm has been developed in such a way that the increment of damage due to fatigue is added to that due to the static increment of the opening displacement. A one degree of freedom cylinder model has been used to carry out an efficient comparison of the computational performance of three fatigue degradation strategies. The three laws have been implemented in a code using bond based peridynamics (BBPD) to simulate fatigue crack propagation. Both the cylinder model and the bond base peridynamics code provide the same assessment of the three fatigue degradation strategies. To deal with thermo-mechanical problems, an effective way is proposed to use a variable grid size in a weakly coupled thermal shock peridynamic model. The proposed numerical method is equipped with stretch control criterion to transform the grid discretization adaptively in time. Hence, finer grid spacing is only applied in limited zones where it is required. This method is capable of predicting complex crack patterns in the model. By introducing fine grid discretization over the boundaries of the model the surface (softening) effect can be reduced. The accuracy and performance of the model are examined through problems such as thermo-elastic and thermal-shock induced fracture in ceramics. Finally to investigate sloshing phenomena, the PDDO has been applied to the solution of problems of liquid sloshing in 2D and 3D tanks with potential flow theory and Lagrangian description. Moreover, liquid sloshing in rectangular tanks containing horizontal and vertical baffles are investigated to examine the robustness and accuracy of PDDO. With respect to other approaches such as meshless local Petrov-Galerkin (MLPG), volume of fluid (VOF) and and local polynomial collocation methods the examples are solved with a coarser grid of nodes. Using this new approach, one is able to obtain results with a high accuracy and low computational cost

Peridynamic and Finite Element Coupling Strategies for the Simulation of Brittle Fracture

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe Peridynamic theory is a nonlocal approach, based on an integral formulation that avoids the use of spatial derivatives. This attribute is very desirable in fracture simulations, making Peridynamics a versatile tool for failure analyses. A major disadvantage however is the high computational cost associated with its numerical implementation. The aim of this study is to propose coupling strategies between standard Finite Element methodologies and Peridynamic grids in order to simultaneously exploit the inherent ability of the latter to simulate crack initiation and propagation with the computational efficiency of the former. Initially a coupling technique, where the thermal field is approximated using Finite Elements and the mechanical field using Peridynamics, is applied to a thermal shock problem for refractory ceramics. The results, although very accurate, verify the increased computational cost of Peridynamic simulations. To remedy this, a methodology to couple Peridynamics with finite element solvers for classical continuum theories, restricting the use of particles at the vicinity of the crack tip, is developed. The coupling method introduces fictitious particles inside the finite elements near the coupling interface. This method is selected after comparing three different methodologies with respect to spurious reflections observed during pulse propagation in a 1D bar. A crack tip tracking algorithm and an adaptive expansion/contraction methodology are developed for the dynamic relocation of the Peridynamic patch around the emerging crack fronts. This methodology also employs enrichment of the Finite Elements with Heaviside functions (Extended Finite Element Method) to limit the use of Peridynamics only near the crack tip. The proposed method is used for the simulation of several fracture problems, including the complex case of dynamic crack branching. The results are in close agreement with those obtained using a Peridynamic only approach while featuring significant computational savings.Brunel University Londo