Modeling and Simulation of cracks and fractures with peridynamics in brittle materials

Today, ceramic materials are an essential component of batteries for electric cars. One key feature of this kind of battery is the safety of the ceramic core. Here, the precise approximation of the evolution of damage after the impact and the wave propagation is important to analyze the safety of the battery. The initiation of cracks is especially essential, because the core is normally not damaged. This thesis studies bond-based peridynamics (PD), a non-local generalization of continuum mechanics, with a focus on discontinuous displacements as they arise in fracture mechanics. With respect to the modeling, the initiation and growth of cracks, two bond-based peridynamic material models for linear isotropic elastic materials are considered. One important feature here is to relate the PD energy to the classical theory energy. The PD is a model, discretized here with the EMU nodal discretization. The neighbor search in node clouds is an essential part of the computational costs. Therefore, an efficient sorting-based library for the neighbor search in generic node clouds is presented. To achieve the full utilization of modern super computers, a combination of processors and acceleration cards is essential. The asynchronous integration of CUDA into the High Performance ParallelX framework is presented. For the comparison with experimental data, two post processing techniques for the extraction of fragments and stress waves are shown. Finally, three numerical results for the initiation and evolution of cracks are considered. First, the evolution of damage and wave propagation according to the Edge-On impact experiment. Second, the critical traction prescribed value for the critical traction for Mode I crack opening by Linear Fracture Mechanics (LEFM) is compared with the ones obtained in the simulation for a wide range of materials. Third, the Poisson ratio and the Young modulus obtained by a tensile test for PMMA are compared with the computed values

On the treatment of boundary conditions for bond-based peridynamic models

In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the simulation of structural mechanics problems as an alternative approach to classical local continuum models. However, a major issue, which is often disregarded when dealing with this class of models, is concerned with the manner by which boundary conditions should be prescribed. Our point of view here is that classical boundary conditions, since applied on surfaces of solid bodies, are naturally associated with local models. The paper describes two methods to incorporate classical Dirichlet and Neumann boundary conditions into bond-based peridynamics. The first method consists in artificially extending the domain with a thin boundary layer over which the displacement field is required to behave as an odd function with respect to the boundary points. The second method resorts to the idea that peridynamic models and local models should be compatible in the limit that the so-called horizon vanishes. The approach consists then in decreasing the horizon from a constant value in the interior of the domain to zero at the boundary so that one can directly apply the classical boundary conditions. We present the continuous and discrete formulations of the two methods and assess their performance on several numerical experiments dealing with the simulation of a one-dimensional bar

Shared memory parallelism in Modern C++ and HPX

Parallel programming remains a daunting challenge, from the struggle to express a parallel algorithm without cluttering the underlying synchronous logic, to describing which devices to employ in a calculation, to correctness. Over the years, numerous solutions have arisen, many of them requiring new programming languages, extensions to programming languages, or the addition of pragmas. Support for these various tools and extensions is available to a varying degree. In recent years, the C++ standards committee has worked to refine the language features and libraries needed to support parallel programming on a single computational node. Eventually, all major vendors and compilers will provide robust and performant implementations of these standards. Until then, the HPX library and runtime provides cutting edge implementations of the standards, as well as proposed standards and extensions. Because of these advances, it is now possible to write high performance parallel code without custom extensions to C++. We provide an overview of modern parallel programming in C++, describing the language and library features, and providing brief examples of how to use them

Stellar Mergers with HPX-Kokkos and SYCL: Methods of using an Asynchronous Many-Task Runtime System with SYCL

Ranging from NVIDIA GPUs to AMD GPUs and Intel GPUs: Given the heterogeneity of available accelerator cards within current supercomputers, portability is a key aspect for modern HPC applications. In Octo-Tiger, we rely on Kokkos and its various execution spaces for portable compute kernels. In turn, we use HPX to coordinate kernel launches, CPU tasks, and communication. This combination allows us to have a fine interleaving between portable CPU/GPU computations and communication, enabling scalability on various supercomputers. However, for HPX and Kokkos to work together optimally, we need to be able to treat Kokkos kernels as HPX tasks. Otherwise, instead of integrating asynchronous Kokkos kernel launches into HPX's task graph, we would have to actively wait for them with fence commands, which wastes CPU time better spent otherwise. Using an integration layer called HPX-Kokkos, treating Kokkos kernels as tasks already works for some Kokkos execution spaces (like the CUDA one), but not for others (like the SYCL one). In this work, we started making Octo-Tiger and HPX itself compatible with SYCL. To do so, we introduce numerous software changes, most notably an HPX-SYCL integration. This integration allows us to treat SYCL events as HPX tasks, which in turn allows us to better integrate Kokkos by extending the support of HPX-Kokkos to also fully support Kokkos' SYCL execution space. We show two ways to implement this HPX-SYCL integration and test them using Octo-Tiger and its Kokkos kernels, on both an NVIDIA A100 and an AMD MI100. We find modest, yet noticeable, speedups by enabling this integration, even when just running simple single-node scenarios with Octo-Tiger where communication and CPU utilization are not yet an issue

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. © 2022, The Author(s)

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized

A Fracture Multiscale Model for Peridynamic enrichment within the Partition of Unity Method

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of linear elasticity and zones where fractures occur. Here, the peridynamic (PD) model is used in regions of fracture and smooth PUM is used in the surrounding linear elastic media. The method is a so-called global-local enrichment strategy. The elastic fields of the undamaged media provide appropriate boundary data for the localized PD simulations. The first steps for a combined PD/PUM simulator are presented. In part I of this series, we show that the local PD approximation can be utilized to enrich the global PUM approximation to capture the true material response with high accuracy efficiently. Test problems are provided demonstrating the validity and potential of this numerical approach