Drop-Shock Failure Prediction in Electronic Packages by Using Peridynamic Theory

Agwai, Abigail; Guven, Ibrahim; Madenci, Erdogan

doi:10.1109/tcpmt.2011.2175924

Cited by 13 publications

(6 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the FEA method, the element stiffness matrix is obtained by equation (16), and in a discretized body, the weak form formulation for the conservation of linear momentum (equation 10) takes the form of equation (17), where K g = e K e is the general stiffness matrix assembled from the element stiffness matrices, and U g and F g ex are the nodal displacement vector and external force vector (including body and surface forces), respectively.…”

Section: Femmentioning

confidence: 99%

See 1 more Smart Citation

Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis

Yaghoobi

Chorzepa

2017

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Peridynamics is an effective method in computational solid mechanics for dealing with discontinuities. However, its computational cost limits its applications, especially when used in the most general form, non-ordinary state-based peridynamics. This paper considers two approaches which decrease the computational cost. The first approach accounts for symmetry boundary conditions in a peridynamic body. In nonlocal peridynamics, boundary conditions are applied to an area. Therefore, when modeling the symmetry boundary condition, assuming fixed particles around the symmetry axis yields incorrect results. The present formulation introduces constraints which allow modeling of local symmetry conditions. Second, the finite-element–peridynamic coupling method is adopted for non-ordinary state-based peridynamics. The coupling method enables the use of peridynamics around discontinuities like cracks, and the faster finite element for the surrounding body. These two methods effectively reduce the solution time with an acceptable accuracy. The validity of these approaches is studied through various examples. Also, ductile crack growth in a compact tension specimen is studied, applying the presented methods. Good agreement is found when comparing experimental results with corresponding numerical results obtained using either fully peridynamic or coupled models.

show abstract

Section: Femmentioning

confidence: 99%

“…They all share the main idea that the region with a discontinuity is analyzed using peridynamic particles while the FEM is utilized for the remaining region. The subregion modeling approach was utilized by Oterkus et al [15] and Agwai et al [16]. In their approach, the global system is first analyzed using the FEM.…”

Section: Introductionmentioning

confidence: 99%

Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis

Yaghoobi

Chorzepa

2017

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…These methods can broadly be classified as kinematic-based, force-based or energy-based coupling methods. In the kinematic-based methods [78][79][80][81], coupling is achieved by implementing a contact algorithm over the interface region that requires the satisfaction of a series of kinematical constraints. The force-based approaches [82][83][84][85][86][87][88] rely on the balance of force in the interface region to achieve coupling of the models.…”

Section: Introductionmentioning

confidence: 99%

A computational homogenization framework for non-ordinary state-based peridynamics

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

View full text Add to dashboard Cite

Peridynamic theory has been shown to possess the capabilities of describing phenomena that theories based on partial differential equations are not capable of describing. These phenomena include nonlocal interactions and presence of singularities in system responses. To exploit the capabilities offered by peridynamics in the homogenization of heterogenous media, a nonlocal computational homogenization theory based on peridynamic correspondence model (non-ordinary state-based peridynamics) is proposed. To set the development of the theory on a rigorous mathematical framework and to ensure consistency with the nonlocal nature of the peridynamic theory, a nonlocal vector calculus was used in the analysis of the nonlocal homogenization theory. The proposed theory is a two-scale micro–macro-homogenization strategy in which the constitutive relation at the macroscale is derived from explicit solution of a nonlocal volume constraint problem at the microscale. To justify the coupling between the two scales, nonlocal analogues of the stress and strain average theorems as well as the Hill–Mandel macrohomogeneity condition were derived. Validation of the proposed theory is achieved via numerical solution of Representative Volume Elements (RVE) from composite materials and comparing the results with those obtained by means of established methodologies.

show abstract

“…The goal is to take advantage of the benefits that each of the connected models has to offer. Multibody concurrent techniques can be characterized as kinematic-based [45][46][47][48], force-based [49][50][51][52][53][54][55], or energy-based [56][57][58][59][60][61][62] methods depending on the coupling mechanism utilized.…”

Section: Introductionmentioning

confidence: 99%

Peridynamic computational homogenization theory for materials with evolving microstructure and damage

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

View full text Add to dashboard Cite

This study aims to establish a framework for multiscale assessment of damage for materials with evolving microstructure based on a recently proposed peridynamic computational homogenization theory. The framework starts with replacing a material with complex microstructure with a constitutively equivalent material that is microstructurally homogenous. Constitutive equivalence between the original and the substitute materials is achieved through enforcing strain energy equivalence via the so-called nonlocal Hill’s lemma. The damage law is obtained by numerically solving boundary volume constraint problem of an RVE. The result from the analysis of the RVE problem was compared with the previously published result to establish the validity of the proposed framework. The comparison shows good agreement between result obtained using the proposed framework and those reported in the literature.

show abstract

Drop-Shock Failure Prediction in Electronic Packages by Using Peridynamic Theory

Cited by 13 publications

References 19 publications

Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis

Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis

A computational homogenization framework for non-ordinary state-based peridynamics

Peridynamic computational homogenization theory for materials with evolving microstructure and damage

Contact Info

Product

Resources

About