Youn Doh Ha

The formulation and computation of the nonlocal J-integral in bond-based peridynamics

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 how the boundary conditions and the peridynamic “skin effect” may influence the peridynamic J-integral value. We also observe, computationally, the path-independence of the peridynamic J-integral.

Damage progression from impact in layered glass modeled with peridynamics

Dynamic fracture in brittle materials has been difficult to model and predict. Interfaces, such as those present in multi-layered glass systems, further complicate this problem. In this paper we use a simplified peridynamic model of a multi-layer glass system to simulate damage evolution under impact with a high-velocity projectile. The simulation results are compared with results from recently published experiments. Many of the damage morphologies reported in the experiments are captured by the peridynamic results. Some finer details seen in experiments and not replicated by the computational model due to limitations in available computational resources that limited the spatial resolution of the model, and to the simple contact conditions between the layers instead of the polyurethane bonding used in the experiments. The peridynamic model uncovers a fascinating time-evolution of damage and the dynamic interaction between the stress waves, propagating cracks, interfaces, and bending deformations, in three-dimensions.

Crack coalescence morphology in rock-like material under compression

This paper uses peridynamic simulations to determine the extent of coalescing damage and identify the underlying causes. The basic crack types and crack coalescence patterns in specimens with a flaw pair under uniaxial compression are systematically investigated. Various crack types including horsetail cracks, anti-wing cracks, and tensile wing cracks are successfully observed and the coalescence sequences are identified. By varying angles, six crack coalescence categories with respect to the overlapping ratios provide insightful information of different crack growths and indicate various cracking modes underlying various coalescence patterns. The arrangement of the flaw pair strongly influences the crack initiation position and trajectories, allowing for different coalescence morphologies. Coalescence formed by two internal tensile wing cracks, or transfixion, shows unbroken crack segments with a further loading, along with growing shear cracks until failure. In contrast, after the coalescence is formed through two horsetail cracks, the interior of the rhombic shape gets deformed with further loading. The peridynamic code adopted in this research can provide realistic simulation results and help researchers to conduct expanded tests as well as to enhance understanding the fracture of rock-like material.

Dynamic Brittle Fracture Captured With Peridynamics

The bond-based peridynamic model is able to capture many of the essential characteristics of dynamic brittle fracture observed in experiments: crack branching, crack-path instability, asymmetries of crack paths, successive branching, secondary cracking at right angles from existing crack surfaces, etc. In this paper we investigate the influence of the stress waves on the crack branching angle and the velocity profile. We observe that crack branching in peridynamics evolves as the phenomenology proposed by the experimental evidence [1]: when a crack reaches a critical stage (macroscopically identified by its stress intensity factor) it splits into two or more branches, each propagating with the same speed as the parent crack, but with a much reduced process zone.Copyright

Nonlocal Peridynamic Models for Dynamic Brittle Fracture in Fiber-Reinforced Composites: Study on Asymmetrically Loading State

In this paper a computational method for a homogenized peridynamics description of unidirectional fiber-reinforced composites is presented. For these materials, dynamic brittle fracture and damage are simulated with the proposed peridynamic model. Compared with observations from dynamic experiments by Coker et al.(2001), the peridynamic computational model can reproduce various characteristics of dynamic fracture and supersonic or intersonic crack growth in asymmetrically loaded unidirectional fiber-reinforced composite plates. Also we analyze the same model in the symmetric loading condition and figure out that the asymmetric loading leads to a much higher propagation speed. Consistent results have been reported in the experiments.

Dynamic Fracture Analysis with State-based Peridynamic Model: Crack Patterns on Stress Waves for Plane Stress Elastic Solid

Abstract A state-based peridynamic model is able to describe a general constitutive model from the standard continuum theory. The response of a material at a point is dependent on the deformation of all bonds connected to the point within the nonlocal horizon region. Therefore, the state-based peridynamic model permits both the volume and shear changes of the material which is promising to reproduce the complicated dynamic brittle fracture phenomena, such as crack branching, secondary cracks, cascade cracks, crack coalescence, etc. In this paper, the two-dimensional state-based peridynamic model for a linear elastic plane stress solid is employed. The damage model incorporates the energy release rate and the peridynamic energy potential. For brittle glass materials, the impact of the crack-parallel compressive stress waves on the crack branching pattern is investigated. The peridynamic solution for this problem captures the main features, observed experimentally, of dynamic crack propagation and branching. Cascade cracks under strong tensile loading and secondary cracks are also well reproduced with the state-based peridynamic simulations.

Force-based Coupling of Peridynamics and Classical Elasticity Models

In solid mechanics, the peridynamics theory has provided a suitable framework for material failure and damage propagation simulation. Peridynamics is computationally expensive since it is required to solve enormous nonlocal interactions based upon integro-differential equations. Thus, multiscale coupling methods with other local models are of interest for efficient and accurate implementations of peridynamics. In this study, peridynamic models are restricted to regions where discontinuities or stress concentrations are present. In the domains characterized by smooth displacements, classical local models can be employed. We introduce a recently developed blending scheme to concurrently couple bond-based peridynamic models and the Navier equation of classical elasticity. We demonstrate numerically that the proposed blended model is suitable for point loads and static fracture, suggesting an alternative framework for cases where peridynamic models are too expensive, while classical local models are not accurate enough.

Isogeometric Shape Design Sensitivity Analysis Using Mixed Transformation Method for Kronecker Delta Property

The isogeometric method is very effective in shape design optimization due to its effectiveness through the easy design parameterization and accurate sensitivities considering the higher order geometric terms. Due to non-interpolatory property of the NUBRS basis functions, however, the treatment of essential boundary condition is not as straightforward in the isogeometric analysis as in the finite element analysis. Taking advantages of the transformation method developed in meshfree methods, we investigate the isogeometric shape sensitivity analysis with the treatment of essential boundary conditions. Using the property that isogeometric basis functions do not depend on design changes, the transformed shape sensitivity equation is developed and verified for the problem having the essential boundary conditions. Numerical costs to construct the transformed basis function are not as much as the meshfree methods due to the NURBS property that only boundary nodes have their supports on the boundary. Through demonstrative numerical examples having the essential boundary conditions, the effectiveness of proposed design sensitivity analysis is verified.Copyright