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Peridynamic thermal diffusion

This study presents the derivation of ordinary state-based peridynamic heat conduction equation based on the Lagrangian formalism. The peridynamic heat conduction parameters are related to those of the classical theory. An explicit time stepping scheme is adopted for numerical solution of various benchmark problems with known solutions. It paves the way for applying the peridynamic theory to other physical fields such as neutronic diffusion and electrical potential distribution.

Hygro-thermo-mechanical analysis and failure prediction in electronic packages by using peridynamics

This study presents an integrated approach for the simulation of hygro-thermo-vapor-deformation analysis of electronic packages by using peridynamics. This theory is suitable for such analysis because of its mathematical structure. Its governing equation is an integro-differential equation and it is valid regardless of the existence of material and geometric discontinuities in the structure. It permits the specification of distinct properties of interfaces between dissimilar materials in the direct modeling of thermal and moisture diffusion, and deformation. Therefore, it enables progressive damage analysis in materials or layered material systems such as the electronic packages. It describes the validation procedure by considering a particular package for each thermomechanical, hygromechanical deformation as well as vapor pressure predictions. Also, it presents results concerning failure sites and mechanisms due to hygro-thermo-vapor-deformation.

Fully coupled thermomechanical analysis of fiber reinforced composites using peridynamics

The utilization of composite materials in aerospace industry is consistently increasing. One area which requires attention is the modeling of mechanical and/or thermal shock loading on composite structures. Such a phenomenon can be expressed within a fully coupled framework where both the mechanical and thermal fields may have an effect on each other. Furthermore, if damage initiation and propagation predictive capability is also required, the complexity of the analysis increases significantly. Performing such an analysis by using traditional techniques is challenging if not impossible. However, a new continuum mechanics formulation, peridynamics, can overcome such difficulties due to its natural suitability for failure modeling in an intrinsic manner. The peridynamics is a nonlocal continuum theory which allows governing field equations to be applicable at discontinuities. This applicability at discontinuities is achieved by replacing the spatial derivatives, which lose meaning at discontinuities, with integrals that are valid regardless of the existence of a discontinuity. Furthermore, its multi-physics capability makes it a unique approach for fully coupled analysis of different fields. This study presents a fully coupled peridynamic thermomechanical analysis of fiber-reinforced composites.

Simulation of electro-migration through peridynamics

Thin film metallic conductors or interconnects are subjected to increasingly high current densities as the feature sizes decrease that can lead to failure of interconnects in moderately short times. Modelling of failure in micro electronic materials involves several challenges such as electro-migration and stress driven diffusion. These physical phenomena are usually negligible in conventional applications. However, the material within an interconnect is subjected to severe thermal-mechanical and electrical loading. In this study, the peridynamic (PD) framework is applied to model the electro-migration process by coupling physical fields of mechanical deformation, heat transfer, electrical potential distribution, and vacancy diffusion simultaneously.

Crack growth prediction in fully-coupled thermal and deformation fields using peridynamic theory

This study presents a fully coupled peridynamic thermomechanical equations, and their nondimensional form for two-dimensional analysis. Peridynamic solutions to both the thermal and deformation field equations are verified against the known solutions. Subsequently, the coupled thermal and structural response of a plate with a pre-existing crack is investigated. It accurately predicts the temperature rise at the crack tips as the crack propagates.

Peridynamic Direct Concentration Approach by Using ANSYS

Moisture can have damaging effects on electronic packages by inducing hygro-thermo-mechanical stresses and vapor pressure. Commonly accepted wetness approach for indirect calculation of moisture concentration can yield unrealistic results. Therefore, a direct concentration approach becomes unavoidable. This study presents the Peridynamic Direct Concentration Approach (PDCA) and its implementation in ANSYS, a commercial finite element software. Numerical results show that PDCA provides accurate predictions, and removes the anomalies associated with the wetness approach. Moreover, ANSYS allows the utilization of implicit time integration resulting in significant computational advantages.

An Euler-Bernoulli beam formulation in ordinary state-based peridynamic framework

Every object in the world has a three-dimensional geometrical shape and it is usually possible to model structures in a three-dimensional fashion, although this approach can be computationally expensive. In order to reduce computational time, the three-dimensional geometry can be simplified as a beam, plate or shell type of structure depending on the geometry and loading. This simplification should also be accurately reflected in the formulation that is used for the analysis. In this study, such an approach is presented by developing an Euler–Bernoulli beam formulation within ordinary state-based peridynamic framework. The equation of motion is obtained by utilizing Euler–Lagrange equations. The accuracy of the formulation is validated by considering various benchmark problems subjected to different loading and displacement/rotation boundary conditions.

A review of nondestructive examination methods for new-building ships undergoing classification society survey

Classification societies require ship manufacturers to perform nondestructive examination (NDE) of ship weldments to ensure the welding quality of new-building ships. Ships can contain hundreds of kilometers of weld lines and 100% inspection of all welded connections is not feasible. Hence, a limited number of weldments are specified by rules of classification societies to be inspected on a sampling basis. There is a variation between the rules and guidelines used by different classification societies in terms of both philosophy and implementation which results in significant discrepancy in the prescribed checkpoints, numbers, and their locations. In this article, relevant sections of the rules of mainstream International Association of Classification Societies members are studied and potential ways of improving them are discussed. The authors have endeavored to make this study as comprehensive as much as possible. However, given the challenges of covering every single aspect and variable related to NDE in the classification societies’ rules and guidelines reviewed here, the authors can only attempt to cover the key features.

Peridynamic Modeling of Diffusion by Using Finite-Element Analysis

Diffusion modeling is essential in understanding many physical phenomena such as heat transfer, moisture concentration, and electrical conductivity. In the presence of material and geometric discontinuities and nonlocal effects, a nonlocal continuum approach, named peridynamics (PD), can be advantageous over the traditional local approaches. PD is based on integro-differential equations without including any spatial derivatives. In general, these equations are solved numerically by employing meshless discretization techniques. Although fundamentally different, commercial finite-element software can be a suitable platform for PD simulations that may result in several computational benefits. Hence, this paper presents the PD diffusion modeling and implementation procedure in a widely used commercial finite-element analysis software, ANSYS. The accuracy and capability of this approach is demonstrated by considering several benchmark problems.

Peridynamic modeling of thermo-oxidative damage evolution in a composite lamina

Surface oxidation degrades the durability of polymer marix composites operating at high temperatures due to the presence of strong coupling between the thermal oxidation and structural damage evolution. The mechanism of oxidation in polymer matrix composites leads to shrinkage and damage growth. The thermo-oxidative behavior of composites introduces changes in diffusion behavior and mechanical response of the material. This study presents the derivation of peridynamic formulation for the thermo-oxidative behavior of the polymer matrix composites. As a demonstration purposes, isothermal aging of a unidirectional composite lamina is presented by using peridynamics. Oxidation contributed to the damage growth and its propagation.