Mechanical Engineering Commons^™

Peridynamic Material Correspondence Models: Bond-Associated And Higher-Order Formulations, Wailam Chan

Theses and Dissertations--Mechanical Engineering

Peridynamic material correspondence model is able to incorporate material constitutive models directly from classical continuum mechanics theory. However, conventional correspondence model faces two major technical issues for its application to practical problems. The first is the material instability, which results severe oscillations in the predicted displacement fields. The second issue is the length scale effects of materials mechanical behavior at low length scales. This research journey mainly consists of three stages. The first two stages of this research journey focus on the development of the bond-associated peridynamic material correspondence model to inherently remove the material instability. The last stage focuses …

Novel Peridynamic Models For Material Degradation And Mass Transport, Jiangming Zhao

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Fracture and corrosion are two major causes of structure failure. They can interact with each other, leading to faster material degradation. They are also under the influence of environmental conditions. The corrosion rate highly depends on the transportation rate of involving substances, while the fracture can be accelerated significantly due to fluid flow. These complex mechanisms involved in structure failure have troubled classical models for decades. The peridynamic (PD) theory introduced in 2000 has shown great potential in modeling such problems. In this work, we develop novel PD models for fracture, corrosion, mass transport, and viscous flow, which are building …

Peridynamic Approaches For Damage Prediction In Carbon Fiber And Carbon Nanotube Yarn Reinforced Polymer Composites, Forrest E. Baber

Theses and Dissertations

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 …

Peridynamic Models For Fatigue And Fracture In Isotropic And In Polycrystalline Materials, Guanfeng Zhang

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

To improve design and reliability, extensive efforts has been devoted to understanding damage and failure of materials and structures using numerical simulation, as a complement of theory and experiment. In this thesis, peridynamics is adopted to study fatigue and dynamic failure problems.

Fatigue is a major failure mode in engineering structures. Predicting fracture/failure under cyclic loading is a challenging problem. Classical model cannot directly be applied to problems with discontinuities. A peridynamic model is adopted in this work because of important advantages of peridynamics in allowing autonomous crack initiation and propagation. A recently proposed peridynamic fatigue crack model is considered …

The Formulation And Computation Of The Nonlocal J-Integral In Bond-Based Peridynamics, Wenke Hu, Youn Doh Ha, Florin Bobaru, Stewart A. Silling

Florin Bobaru Ph.D.

This work presents a rigorous derivation for the formulation of the J-integral in bond-based peridynamics using the crack infinitesimal virtual extension approach. We give a detailed description of an algorithm for computing this nonlocal version of the J-integral.We present convergence studies (m-convergence and δ-convergence) for two different geometries: a single edge-notch configuration and a double edge-notch sample.We compare the results with results based on the classical J-integral and obtained from FEM calculations that employ special elements near the crack tip.We identify the size of the nonlocal region for which the peridynamic J-integral value is near the classical FEM solutions.We discuss …

The Meaning, Selection, And Use Of The Peridynamic Horizon And Its Relation To Crack Branching In Brittle Materials, Florin Bobaru, Wenke Hu

Florin Bobaru Ph.D.

This note discusses the peridynamic horizon (the nonlocal region around a material point), its role, and practical use in modeling. The objective is to eliminate some misunderstandings and misconceptions regarding the peridynamic horizon. An example of crack branching in a nominally brittle material (homalite) is addressed and we show that crack branching takes place without wave interaction. We explain under what conditions the crack propagation speed depends on the horizon size and the role of incident stress waves on this speed.

Convergence, Adaptive Refinement, And Scaling In 1d Peridynamics, Florin Bobaru Ph.D., Mijia Yabg Ph.D., Leonardo F. Alves M.S., Stewart A. Silling Ph.D., Ebrahim Askari Ph.D., Jifeng Xu Ph.D.

Florin Bobaru Ph.D.

We introduce here adaptive refinement algorithms for the non-local method peridynamics, which was proposed (in J. Mech. Phys. Solids 2000; 48:175–209) as a reformulation of classical elasticity for discontinuities and long-range forces. We use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected. We discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1D in the limit of the horizon going to zero. Continuous micromoduli lead to optimal rates of …

Influence Of Van Der Waals Forces On Increasing The Strength And Toughness In Dynamic Fracture Of Nanofibre Networks: A Peridynamic Approach, Florin Bobaru Ph.D.

Florin Bobaru Ph.D.

The peridynamic method is used here to analyse the effect of van der Waals forces on the mechanical behaviour and strength and toughness properties of three-dimensional nanofibre networks under imposed stretch deformation. The peridynamic formulation allows for a natural inclusion of long-range forces (such as van der Waals forces) by considering all interactions as ‘long-range’. We use van der Waals interactions only between different fibres and do not need to model individual atoms. Fracture is introduced at the microstructural (peridynamic bond) level for the microelastic type bonds, while van der Waals bonds can reform at any time. We conduct statistical …

Studies Of Dynamic Crack Propagation And Crack Branching With Peridynamics, Youn Doh Ha Ph.D., Florin Bobaru Ph.D.

Florin Bobaru Ph.D.

In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement (m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons.We also analyze the influence of the particular shape of themicro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well …

Peridynamic Models For Dynamic Brittle Fracture, Wenke Hu

Department of Engineering Mechanics: Dissertations, Theses, and Student Research

Damage and failure in composite materials under dynamic loading has been extensively studied in experiments for several decades. Composite materials exhibit various damage and failure patterns under different loading rates, such as splitting and branching. Classical models cannot directly be applied to problems with discontinuous fields. A new nonlocal continuum model, peridynamics, has been proposed with the goal of solving dynamic fracture problems.

The J-integral has the physical significance of energy flow into the crack tip region. We present a rigorous derivation for the formulation of the J-integral in peridynamics using the crack infinitesimal virtual extension approach. We …

Studies Of Dynamic Crack Propagation And Crack Branching With Peridynamics, Youn Doh Ha Ph.D., Florin Bobaru Ph.D.

Department of Engineering Mechanics: Faculty Publications

In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement (m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons.We also analyze the influence of the particular shape of themicro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well …

Convergence, Adaptive Refinement, And Scaling In 1d Peridynamics, Florin Bobaru Ph.D., Mijia Yabg Ph.D., Leonardo F. Alves M.S., Stewart A. Silling Ph.D., Ebrahim Askari Ph.D., Jifeng Xu Ph.D.

Department of Engineering Mechanics: Faculty Publications

We introduce here adaptive refinement algorithms for the non-local method peridynamics, which was proposed (in J. Mech. Phys. Solids 2000; 48:175–209) as a reformulation of classical elasticity for discontinuities and long-range forces. We use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected. We discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1D in the limit of the horizon going to zero. Continuous micromoduli lead to optimal rates of …

Influence Of Van Der Waals Forces On Increasing The Strength And Toughness In Dynamic Fracture Of Nanofibre Networks: A Peridynamic Approach, Florin Bobaru Ph.D.

Department of Engineering Mechanics: Faculty Publications

The peridynamic method is used here to analyse the effect of van der Waals forces on the mechanical behaviour and strength and toughness properties of three-dimensional nanofibre networks under imposed stretch deformation. The peridynamic formulation allows for a natural inclusion of long-range forces (such as van der Waals forces) by considering all interactions as ‘long-range’. We use van der Waals interactions only between different fibres and do not need to model individual atoms. Fracture is introduced at the microstructural (peridynamic bond) level for the microelastic type bonds, while van der Waals bonds can reform at any time. We conduct statistical …