Anisotropic Continuum-Molecular Models: A Unified Framework Based on Pair Potentials for Elasticity, Fracture and Diffusion-Type Problems

This paper presents a unified framework for continuum-molecular modeling of anisotropic elasticity, fracture and diffusion-based problems within a generalized two-dimensional peridynamic theory. A variational procedure is proposed to derive the governing equations of the model, that postulates oriented material points interacting through pair potentials from which pairwise generalized actions are computed as energy conjugates to properly defined pairwise measures of primary field variables. While mass is considered as continuous function of volume, we define constitutive laws for long-range interactions such that the overall anisotropic behavior of the material is the result of the assigned elastic, conductive and failure micro-interaction properties. The non-central force assumption in elasticity, together with the definition of specific orientation-dependent micromoduli functions respecting material symmetries, allow to obtain a fully anisotropic non-local continuum using a purely pairwise description of deformation and constitutive properties. A general and consistent micro-macro moduli correspondence principle is also established, based on the formal analogy with the classic elastic and conductivity tensors. The main concepts presented in this work can be used for further developments of anisotropic continuum-molecular formulations to include other mechanical behaviors and coupled phenomena involving different physics

The numerical simulation of standard concrete tests and steel reinforcement using force flux peridynamics

Peridynamics is a numerical particle-based solid mechanics method that enables the simulation of brittle and quasi-brittle materials, as well as ductile materials. It allows cracking to appear spontaneously in the arms joining the particles and can therefore be used to simulate progressive fracture. In this article, we apply our version of peridynamics, which we call force flux peridynamics, to the simulation of concrete where the appearance of cracks plays an important role in the global mechanical properties. It is not difficult to modify the material parameters in peridynamics to achieve a given tensile strength or a given compressive strength. However, it is much more difficult to choose parameters which will model all the strength parameters of a material within the same model. When concrete fails in compression it may split or spall showing a complex relationship between compressive and tensile failure. We therefore set ourselves the simple task of producing a single peridynamics model which can predict the stiffness and strength behavior of concrete in standard compression and tension tests for which we chose the American Society for Testing and Materials standards for the cylinder compression test, the split cylinder test, and the modulus of rupture test. A parameter sensitivity study was performed based on the cylinder compression test to tune the key peridynamics parameters that determine the global material behavior. The compressive and tensile strengths were then determined from the combined simulation data. While the fracture modes, crack branching pattern and also the stress–strain curve show promising results, the maximum tensile strength was found to be significantly larger than physical experiments suggest. This is probably due to imperfections within real concrete at the interface between aggregate particles and cement paste and it shows that the detailed numerical modeling of the failure of concrete is highly complex with a large number of unknown material parameters

Master of Science

thesisTight shale reservoirs have recently emerged as potential game changers in oil and gas and energy sectors worldwide. Consequently, exploration and exploitation of unconventional reservoirs has significantly increased over the last decade. Currently used stimulation designs are based on conventional planar fracture models that cannot realistically simulate the geometry and the extent of hydraulically induced fractures. For that reason, developing models that can thoroughly and accurately describe fracture network initiation and propagation plays a significant role in evaluating well production. The main goal of this work is to evaluate the utility of the peridynamic theory (PD) in modeling the process of hydraulic fracturing. Peridynamics is a nonlocal theory of continuum media that can facilitate a direct coupling between classical continuum mechanics and molecular dynamics. A linear-viscoelastic PD model was applied to a three-dimensional domain that was discretized with cubic lattices of particles. Damage in the model is represented by the bond breakage; as the stretch between two lattices reaches its critical limit, s_0, the bond breaks. The validity of the peridynamic simulation was tested by comparing results obtained in this project against the results obtained in a study performed by Zhou et al. Therefore, six sets of experimental tests were conducted to simulate hydraulic fracturing based on the peridynamic method. Five sets of the simulation results produced in this work were in good agreement with the experimental results. The investigation examined the influences of the differential horizontal stress and preexisting fracture, along with different approach angles, on the geometry of the hydraulic fracture. Different injection rates were applied to the model in order to compare the fractured area that resulted from different injection rates. The simulation showed that the maximum dilatation and fractured zone occurred at the injection rate of 0.61 m3?min. The 0.61 m3/min injection rate caused the highest complete damage (0.9-1) with 5.24 % of the total number of atoms. As a result, the peridynamic approach presents promising results in predicting fracture propagation and damage area

Peridynamic Approaches for Damage Prediction in Carbon Fiber and Carbon Nanotube Yarn Reinforced Polymer Composites

Aerospace structures are increasingly utilizing advanced composites because of their high specific modulus and specific strength. While the introduction of these material systems can dramatically decrease weight, they pose unique certification challenges, often requiring extensive experimental testing in each stage of the design cycle. The expensive and time-consuming nature of experimental testing necessitates the advancement of simulation methodologies to both aid in the certification process and assist in the exploration of the microstructure design space. Peridynamic (PD) theory, originating from Sandia National Lab’s in the early 2000’s, is a nonlocal continuum-based method that reformulates the equation of motion into an integral equivalent form. The integral form, on which the theory is based, is well suited to explore discontinuity rich phenomena such as damage and material failure. This dissertation develops PD-based simulation approaches to investigate two polymer based composite material systems of different maturity: carbon fiber and carbon nanotube (CNT) yarn. For carbon fiber reinforced composites, simulation approaches were developed to predict damage resulting from low-velocity impact, an important part of the certification process because often damage associated with this loading goes undetected leading to premature structural failure. In contrast to the more established carbon fiber, CNT yarn is a promising constituent material still very much in the developmental process. With this in mind, PD simulation approaches were developed with a different objective, which was to systematically explore microstructure property relationships, providing early feedback in the material design process

Peridynamics modelling of weibull distributions for nuclear fuel fracture

Peridynamics is a non-local continuum mechanics modelling method, with fundamental equations built upon integrals as opposed to partial differentials, which gives benefits when modelling brittle fracture relative to other continuum mechanics modelling techniques. Notably absent from peridynamics literature is an investigation of the effect of fracture strength distributions (an important element of brittle fracture) in peridynamics. This thesis outlines a method for appropriately including fracture strength distributions in peridynamics, and presents a model of a UO2 fuel pellet fracturing in service using this method. It was shown that using a Weibull distribution in peridynamics without adjusting the distribution of strengths to account for the difference in size between bonds and the part to be modelled produces inaccurate results. Using Weibull scaling to account for this did not alone solve this problem, as there was still a disconnect between the stress at which the first bond fails (stage 1 failure) and the stress at which the overall part modelled fails (stage 2 failure). Bond strengths were localised by linking bond strength to the material points they are connected to. Combining this localisation with using the most extreme strengths, the shape of the Weibull curve was accurately recreated in 1D peridynamics. The method was applied in two dimensions, and it was shown that the method which had worked in one dimension is no longer adequate. It was found that edge length is the most appropriate size-scaling criteria, as opposed to total area of the two-dimensional model. The model was able to recreate Weibull distributions of fracture strain in a two dimensional tensile test using a Weibull modulus of 10, but was less accurate with lower Weibull moduli. The effect of Weibull distributions on radial crack numbers in in-service UO2 nuclear fuel pellets was investigated. It was found that using a Weibull distribution of fracture strains in a peridynamics model of fuel pellets allows the model to more accurately predict the number of cracks expected at a given power. The model was compared to low-burnup post irradiation examination data.Open Acces

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

Virtual spring damper method for nonholonomic robotic swarm self-organization and leader following

In this paper, we demonstrate a method for self-organization and leader following of nonholonomic robotic swarm based on spring damper mesh. By self-organization of swarm robots we mean the emergence of order in a swarm as the result of interactions among the single robots. In other words the self-organization of swarm robots mimics some natural behavior of social animals like ants among others. The dynamics of two-wheel robot is derived, and a relation between virtual forces and robot control inputs is defined in order to establish stable swarm formation. Two cases of swarm control are analyzed. In the first case the swarm cohesion is achieved by virtual spring damper mesh connecting nearest neighboring robots without designated leader. In the second case we introduce a swarm leader interacting with nearest and second neighbors allowing the swarm to follow the leader. The paper ends with numeric simulation for performance evaluation of the proposed control method

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)

Peridynamic Galerkin methods for nonlinear solid mechanics

Simulation-driven product development is nowadays an essential part in the industrial digitalization. Notably, there is an increasing interest in realistic high-fidelity simulation methods in the fast-growing field of additive and ablative manufacturing processes. Thanks to their flexibility, meshfree solution methods are particularly suitable for simulating the stated processes, often accompanied by large deformations, variable discontinuities, or phase changes. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. Over the years, several meshfree schemes have been developed. Nevertheless, along with their flexibility in discretization, meshfree methods often endure a decrease in accuracy, efficiency and stability or suffer from a significantly increased computation time. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a non-local integro-differential form. The combination of the so-called peridynamic correspondence formulation with a particle discretization yields a flexible meshfree simulation method, though does not lead to reliable results without further treatment.\newline In order to develop a reliable, robust and still flexible meshfree simulation method, the classical correspondence formulation is generalized into the Peridynamic Galerkin (PG) methods in this work. On this basis, conditions on the meshfree shape functions of virtual and actual displacement are presented, which allow an accurate imposition of force and displacement boundary conditions and lead to stability and optimal convergence rates. Based on Taylor expansions moving with the evaluation point, special shape functions are introduced that satisfy all the previously mentioned requirements employing correction schemes. In addition to displacement-based formulations, a variety of stabilized, mixed and enriched variants are developed, which are tailored in their application to the nearly incompressible and elasto-plastic finite deformation of solids, highlighting the broad design scope within the PG methods. Extensive numerical validations and benchmark simulations are performed to show the impact of violating different shape function requirements as well as demonstrating the properties of the different PG formulations. Compared to related Finite Element formulations, the PG methods exhibit similar convergence properties. Furthermore, an increased computation time due to non-locality is counterbalanced by a considerably improved robustness against poorly meshed discretizations