Engineering Commons^™

The Essential Work Of Fracture In Peridynamics, Christer Stenström, Kjell Eriksson, Florin Bobaru, Stefan Golling, Pär Jonsén

Department of Mechanical and Materials Engineering: Faculty Publications

In this work, the essential work of fracture (EWF) method is introduced for a peridynamic (PD) material model to characterize fracture toughness of ductile materials. First, an analytical derivation for the path-independence of the PD J -integral is provided. Thereafter, the classical J -integral and PD J-integral are computed on a number of analytical crack problems, for subsequent investigation on how it performs under large scale yielding of thin sheets. To represent a highly nonlinear elastic behavior, a new adaptive bond stiffness calibration and a modified bonddamage model with gradual softening are proposed. The model is employed for two …

Interfaces In Dynamic Brittle Fracture Of Pmma: A Peridynamic Analysis, Longzhen Wang, Javad Mehrmashhadi, Florin Bobaru

Department of Mechanical and Materials Engineering: Faculty Publications

Recent experiments in bonded PMMA layers have shown dramatic changes in dynamic crack growth characteristics depending on the interface location and toughness. In this paper we present a peridynamic (PD) analysis of this phenomenon and determine three elements that are essential in a model reproducing the observed fracture behavior: (1) softening near the crack tip to account for changes in PMMA due to heat-generation induced by the high strain rates reached around the crack tip in dynamic fracture; (2) independent extension (mode I) and shear (mode II) modes of fracture; (3) a two-parameter fracture model, which matches both strength and …

Peridynamic Simulation Of Elastic Wave Propagation By Applying The Boundary Conditions With The Surface Node Method, Francesco Scabbia, Mirco Zaccariotto, Ugo Galvanetto, Florin Bobaru

Department of Mechanical and Materials Engineering: Faculty Publications

Peridynamics is a novel nonlocal theory able to deal with discontinuities, such as crack initiation and propagation. Near the boundaries, due to the incomplete nonlocal region, the peridynamic surface effect is present, and its reduction relies on using a very small horizon, which ends up being expensive computationally. Furthermore, the imposition of nonlocal boundary conditions in a local way is often required. The surface node method has been proposed to solve both the aforementioned issues, providing enhanced accuracy near the boundaries of the body. This method has been verified in the cases of quasi-static elastic problems and diffusion problems evolving …

Construction Of A Peridynamic Model For Viscous Flow, Jiangming Zhao, Adam Larios, Florin Bobaru Ph.D.

Department of Mechanical and Materials Engineering: Faculty Publications

We derive the Eulerian formulation for a peridynamic (PD) model of Newtonian viscous flow starting from fundamental principles: conservation of mass and momentum. This formulation is different from models for viscous flow that utilize the so-called “peridynamic differential operator” with the classical Navier- Stokes equations. We show that the classical continuity equation is a limiting case of the PD one, assuming certain smoothness conditions. The PD model for viscous flow is calibrated to the classical Navier-Stokes equations by enforcing linear consistency for the viscous stress term. Couette and Poiseuille flows, and incompressible fluid flow past a regular lattice of cylinders …

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 …

Novel And Fast Peridynamic Models For Material Degradation And Failure, Siavash Jafarzadeh

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

Fracture is one of the main mechanisms of structural failure. Corroded surfaces with chemically-induced damage are, notably, potential sites for crack initiation and propagation in metals, which can lead to catastrophic failure of structures. Despite some progress in simulating fracture and damage using classical models, realistic prediction of complex damage progression and failure has been out of reach for many decades. Peridynamics (PD), a nonlocal theory introduced in 2000, opened up new avenues in modeling material degradation and failure. Existing numerical methods used to discretize PD equations, however, are quite expensive as the PD nonlocal interactions make them unaffordable for …

Predictive Peridynamic 3d Models Of Pitting Corrosion In Stainless Steel With Formation Of Lacy Covers, Siavash Jafarzadeh, Florin Bobaru, Ziguang Chen

Department of Mechanical and Materials Engineering: Faculty Publications

In this work, the peridynamic corrosion model is used for 3D simulation of pitting corrosion in stainless steel. Models for passivation and salt layer formation are employed to predict detailed characteristics of pit growth kinetic in stainless steels, such as lacy cover formation on top of the pit, and the diffusion-controlled regime at the pit bottom. The model is validated against an experimentally grown pit on 316L stainless steel in NaCl solution. Lacy covers in this model are formed autonomously during the simulation process. They are remarkably similar to the covers observed on top of the real pits.

Predictive Peridynamic 3d Models Of Pitting Corrosion In Stainless Steel With Formation Of Lacy Covers, Siavash Jafarzadeh, Florin Bobaru, Ziguang Chen

Department of Mechanical and Materials Engineering: Faculty Publications

In this work, the peridynamic corrosion model is used for 3D simulation of pitting corrosion in stainless steel. Models for passivation and salt layer formation are employed to predict detailed characteristics of pit growth kinetic in stainless steels, such as lacy cover formation on top of the pit, and the diffusion-controlled regime at the pit bottom. The model is validated against an experimentally grown pit on 316L stainless steel in NaCl solution. Lacy covers in this model are formed autonomously during the simulation process. They are remarkably similar to the covers observed on top of the real pits.

Peridynamic Modeling Of Dynamic Fracture In Bio-Inspired Structures For High Velocity Impacts, Sneha Akula

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

Bio-inspired damage resistant models have distinct patterns like brick-mortar, Voronoi, helicoidal etc., which show exceptional damage mitigation against high-velocity impacts. These unique patterns increase damage resistance (in some cases up to 3000 times more than the constituent materials) by effectively dispersing the stress waves produced by the impact. Ability to mimic these structures on a larger scale can be ground-breaking and could be used in numerous applications. Advancements in 3D printing have now made possible fabrication of these patterns with ease and at a low cost. Research on dynamic fracture in bio-inspired structures is very limited but it is …

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 …

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 …

Numerical Simulation Of Thermo-Elasticity, Inelasticity And Rupture Inmembrane Theory, Michael Taylor

Mechanical Engineering

Two distinct two-dimensional theories for the modeling of thin elastic bodies are developed. These are demonstrated through numerical simulation of various types of membrane deformation. The work includes a continuum thermomechanics-based theory for wrinkled thin films. The theory takes into account single-layer sheets as well as composite membranes made of multiple lamina. The resulting model is applied to the study of entropic elastic elastomers as well as Mylar/aluminum composite films. The latter has direct application in the area of solar sails. Several equilibrium deformations are illustrated numerically by applying the theory of dynamic relaxation to a finite difference discretization based …

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 …