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

Every object in the world has a 3-Dimensional geometrical shape and it is usually possible to model structures in a 3-Dimensional fashion although this approach can be computationally expensive. In order to reduce computational time, the 3-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 which 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

Peridynamic modeling of diffusion by using finite element analysis

Diffusion modeling is essential in understanding many physical phenomena such as heat transfer, moisture concentration, electrical conductivity, etc. In the presence of material and geometric discontinuities, and non-local effects, a non-local continuum approach, named as peridynamics, can be advantageous over the traditional local approaches. Peridynamics 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 peridynamic simulations which may result in several computational benefits. Hence, this study presents the peridynamic 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

Dynamic propagation of a macrocrack interacting with parallel small cracks

In this study, the effect of small cracks on the dynamic propagation of a macrocrack is investigated by using a new continuum mechanics formulation, peridynamics. Various combinations of small cracks with different number, location and density are considered. Depending on the location, density and number of small cracks, the propagation speed of macrocrack differs. Some combinations of small cracks slows down the propagation of a macrocrack by 34%. Presented results show that this analysis can be useful for the design of new microstructurally toughened materials

Family member search algorithms for peridynamic analysis

Peridynamic equation of motion is usually solved numerically by using meshless approaches, Family search process is one of the most time consuming parts of a peridynamic analysis. Especially for problems which require continuous update of family members inside the hurizoli of a material point, the time spent to search for family members becomes crucial. Hence, efficient algorithms are required to reduce the computational time. In this study, various family member search algorithms suitable for peridynamic simulations are presented including brute-force search, region partitioning and tree data structures. By considering problem cases for different number of material points, computational time between different algorithms is compared and the most efficient algorithm is determined

Equivalent acceleration assessment of JEDEC moisture sensitivity levels using peridynamics

The moisture inside the IC packages induces the several deformation failures, such as popcorn crack and swelling during the solder reflowing process. In semiconductor industry, over the past few years, the equivalent acceleration time for JEDEC moisture sensitivity level has been updated based on the weight gain measurements when the package structure and materials were modified. It costs long test times which may induce the significant delay of new product development and reliability evaluation. Additionally, the weight gain equivalency may not be sufficient to determine the equivalent accelerated time. In this paper, the new approach for evaluating the equivalent acceleration test time for preconditioning is proposed using the numerical calculation by peridynamics (PD) theory. The essential of proposed method is analyzing a moisture concentration and a vapor pressure which can cause the moisture induced failure in IC packages without facing the discontinuity problems of moisture concentration along the interfaces

Peridynamics for marine structures applications

Peridynamic theory was first introduced by Dr. S. A. Silling at Sandia National Laboratories, USA, in the year of 2000. It is a state-of-the-art technique which is relatively new and promising tool [1]. It is basically re-formulation of classical continuum mechanics theory introduced by A. L. Cauchy more than 200 years ago. The volumetric integral, which does not include spatial derivatives, is used in its formulations

Peridynamics and its applications in marine structures

Prediction of fracture and failure is a challenging research area. There are various methods available in the literature for this purpose including well-known finite element (FE) method. FE method is a powerful technique for deformation and stress analysis of structures. However, it has various disadvantages in predicting failure due to its mathematical structure since it is based on classical continuum mechanics (CCM). CCM has governing equations in the form of partial differential equations. These equat ions are not valid if the displacement field is discontinuous as a result of crack occurrence. In order to overcome this problem, a new continuum mechanics formulation was introduced and named as Peridynamics [1] . Peridynamics uses integrals equations as opposed to partial different equations of CCM. Moreover, it does not contain any spatial derivatives. Hence, its equations are always valid regardless of discontinuities. In this presentation, the applications of Peridynamics for marine structures will be demonstrated. Particularly, the Peridynamic equations are rederived for simplified structures commonly used in marine structures including beams and plates. Furthermore, underwater shock response of marine composites is investigated. Finally, the peridynamic formulation for contact analysis which can be used for collision and grounding of ship structures will be demonstrated. In order to reduce the computational time, several solution strategies will be explained including parallel programming applications

Moisture diffusion modelling by using peridynamics

The moisture concentration in electronic packages can be determined based on the “wetness” approach. The wetness parameter representing the ratio of the moisture concentration with respect to the saturated concentration value of the material is continuous along dissimilar material interfaces. If the saturated concentration value is not dependent on temperature or time, the wetness equation is analogous to the standard diffusion equation whose solution can be constructed by using any commercial finite element analysis software. However, the time dependency of saturated concentration requires special treatment under temperature dependent environmental conditions such as reflow process. The saturated concentration values of most polymer materials in electronic packages are mostly dependent on temperature. As a result, the wetness equation is not directly analogous to the standard diffusion equation. This study presents peridynamic solution of the wetness equation with time dependent saturated concentration. The approach is computationally efficient as well as easy to implement without any iterations in each time step. The implementation is achieved by using the traditional elements and solvers available in a commercial finite element software

A Kirchhoff plate formulation in a state-based peridynamic framework

In recent years, there has been rapid progress on peridynamics. It has been applied to many different material systems, used for coupled field analysis and is suitable for multi-scale analysis. This study mainly focuses on peridynamic analysis for plate-type structures. For this purpose, a new peridynamic Kirchhoff plate is developed. The new formulation is computationally efficient by having only one degree of freedom for each material point. Moreover, it is based on the state-based peridynamic formulation, which does not impose any limitation on material constants. After presenting how to impose simply supported and clamped boundary conditions in this new formulation, several numerical studies are considered to demonstrate the accuracy and capability of the proposed formulation

Full range fragmentation simulation of nanoflake filler-matrix composite coatings on a polymer substrate

This paper presents a comprehensive experimental and computational study to explore the damage evolution mechanisms of polymer matrix nanocomposite films consisting of rigid ceramic fillers coated on a polymer substrate. The weight ratio of montmorillonite (MMT) fillers in the polyvinyl alcohol (PVA) matrix ranges from 30 % to 70 %, and these are applied onto a polyethylene terephthalate (PET) substrate. Through experiments, apart from damage behaviors, the water vapor transmission rates are also measured to gain insight into moisture diffusion characteristics with varying weight ratios of fillers. The optimal weight ratio of nanocomposite films consisting of a PVA matrix with MMT fillers can vary depending on the purpose of damage resistance and moisture barrier characteristics. A peridynamic theory is employed to simulate various damage scenarios of bi-layer nanocomposite films. The solution strategy presented incorporates the use of the cut-boundary and finite element methods to reduce substrate thickness and make initial predictions of crack onset strains, respectively, under quasi-static loading conditions. Several damage scenarios are considered for thin and thick PVA films on the PET substrate, as well as weak to strong interfaces between the PET-PVA and PVA-MMT layers. Additionally, different distributions of MMT fillers are also considered by varying the distances between them and inserting inclusions. The peridynamic damage analyses encompass crack initiation, propagation, and final failure stages across a wide range of strains, including various damage modes such as matrix cracking, cracking at the filler-matrix, or matrix-substrate interfaces, leading to the cohesive film cracking and delamination