Comparison of Concurrent Multiscale Methods in the Application of Fracture in Nickel

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Vincent Iacobellis ◽  
Kamran Behdinan
Keyword(s):  
Multiscale Modeling ◽  
Multiscale Methods ◽  
Static Case ◽  
Original Formulation ◽  
Simulation Techniques ◽  
Coupling Methods ◽  
Continuum Region ◽  
Dynamic Case ◽  
Common Framework ◽  
Similarities And Differences

This paper presents a study of fracture in nickel using multiscale modeling. A comparison of six concurrent multiscale methods was performed in their application to a common problem using a common framework in order to evaluate each method relative to each other. Each method was compared in both a quasi-static case of crack tip deformation as well as a dynamic case in the study of crack growth. Each method was compared to the fully atomistic model with similarities and differences between the methods noted and reasons for these provided. The results showed a distinct difference between direct and handshake coupling methods. In general, for the quasi-static case, the direct coupling methods took longer to run compared to the handshake coupling methods but had less error with respect to displacement and energy. In the dynamic case, the handshake methods took longer to run, but had reduced error most notably when wave dissipation at the atomistic/continuum region was an issue. Comparing each method under common conditions showed that many similarities exist between each method that may be hidden by their original formulation. The comparison also showed the dependency on the application as well as the simulation techniques used in determining the performance of each method.

Static and Dynamic Response of a Beam on a Winkler Elastic Foundation

2005 ◽  
Author(s):  
Timour M. A. Nusirat ◽  
M. N. Hamdan
Keyword(s):  
Elastic Foundation ◽  
Governing Equation ◽  
Initial Value Problem ◽  
Nonlinear Partial Differential Equation ◽  
Static Case ◽  
Initial Value ◽  
Characteristic Curves ◽  
System Parameters ◽  
Winkler Elastic Foundation ◽  
Dynamic Case

This paper is concerned with analysis of dynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation. The beam is assumed to be subjected to a uniformly distributed lateral static load, have an initial quarter-sine shape deflection. At one end, the beam is assumed to be restrained by a pin, while at the other end, the beam is assumed to be restrained by a torsional and a translational linear spring. The beam is modeled by a nonlinear partial differential equation where the nonlinearity enters the governing equation through the beam axial force. In the static case, because of a unique feature of governing equation, the analysis was carried out using the theory of linear differential equations, but takes into account the effect of actual deflection on the induced axial thrust. In the dynamic case, stability analysis of the beam is carried out by calculating the nonlinear frequencies of free vibration of the beam about its static equilibrium configuration. The assumed mode method is used to discretize and find an equivalent nonlinear initial value problem. Then the harmonic balance is used to obtain an approximate solution to the nonlinear oscillator described by the equivalent initial value problem. The analyses of results were carried out for a selected range of values of the system parameters: foundation elastic stiffness, lateral load, and maximum beam edge deflection. In the static case the results are presented as characteristic curves showing the variation of the beam static deflection and associated bending moment distribution with each of the above system parameters. In the dynamic case, the presented characteristic curves show the variation of the nonlinear natural frequency corresponding to the first and the second modes over a range of each of the above system parameters.

Review of Hierarchical Multiscale Modeling to Describe the Mechanical Behavior of Amorphous Polymers

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
J. L. Bouvard ◽  
D. K. Ward ◽  
D. Hossain ◽  
S. Nouranian ◽  
E. B. Marin ◽  
...  
Keyword(s):  
Mechanical Behavior ◽  
Multiscale Modeling ◽  
Coarse Graining ◽  
Amorphous Polymers ◽  
Multiscale Methods ◽  
Structure Property ◽  
Lightweight Materials ◽  
Structure Property Relationships ◽  
Modeling Strategy ◽  
Hierarchical Multiscale

Modern computational methods have proved invaluable for the design and analysis of structural components using lightweight materials. The challenge of optimizing lightweight materials in the design of industrial components relates to incorporating structure-property relationships within the computational strategy to incur robust designs. One effective methodology of incorporating structure-property relationships within a simulation-based design framework is to employ a hierarchical multiscale modeling strategy. This paper reviews techniques of multiscale modeling to predict the mechanical behavior of amorphous polymers. Hierarchical multiscale methods bridge nanoscale mechanisms to the macroscale/continuum by introducing a set of structure-property relationships. This review discusses the current state of the art and challenges for three distinct scales: quantum, atomistic/coarse graining, and continuum mechanics. For each scale, we review the modeling techniques and tools, as well as discuss important recent contributions. To help focus the review, we have mainly considered research devoted to amorphous polymers.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (04) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (4) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

scholarly journals A Lexical-Functional Analysis of Predicate Topicalization in German

1999 ◽  
Vol 11 (1) ◽  
pp. 1-61 ◽  
Author(s):  
Gert Webelhuth ◽  
Farrell Ackerman
Keyword(s):  
Functional Analysis ◽  
Original Formulation ◽  
Grammatical Function ◽  
Complex Predicates ◽  
Functional Grammar ◽  
Long Distance ◽  
Lexical Functional Grammar ◽  
Lexical Representations ◽  
Idiomatic Expressions ◽  
Similarities And Differences

In this paper we examine the topicalization paradigm for ten different verbal constructions in German. We argue that a uniform explanation for the observed behaviors follows from the interpretation of the relevant expressions as (parts of) lexical representations. To this end we motivate a revision of Functional Uncertainty as proposed in Kaplan and Zaenen 1989 to account for filler/gap relations in long-distance dependencies. We assume with the original formulation of this principle that topicalized elements share values with the (grammatical) function status of an entity an indeterminate distance away. We appeal to the inventory of functions posited within LEXICAL-FUNCTIONAL GRAMMAR (LFG), inclusive of the frequently neglected PREDICATE function, which, we argue, is associated with both simple and complex predicates. In addition we show that topicalization, given this function-based proposal, should not be limited to maximal categories. We argue that the need to posit a PREDICATE function for German topicalization is supported by an independent line of research within LFG concerning the analysis of complex predicates. For this purpose we employ the proposals of T. Mohanan (1990/1994), which argue for the independence of the construct PREDICATE from its categorial realization. We show that this type of proposal extends to provide a uniform account of the German topicalization paradigm. This permits us to explain the similarities and differences in the behaviors of various sorts of predicators as well as certain idiomatic expressions interpreted as complex predicates.

A Generalized Model for Dynamic Contact Angle

2017 ◽  
Author(s):  
Joseph J. Thalakkottor ◽  
Kamran Mohseni
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Force Balance ◽  
Surface Tension Gradient ◽  
Static Case ◽  
Dynamic Case ◽  
Microscopic Dynamic

Contact angle is an important parameter that characterizes the degree of wetting of a material. While for a static case, estimation and measurement of contact angle has been well established, same can not be said for the dynamic case. There is still a lack of understanding and consensus as to the fundamental factors governing the microscopic dynamic contact angle. With the aim of understanding the physics and identifying the parameters that govern the actual or microscopic dynamic contact angle, we derive a model based on first principles, by performing a force balance around the region containing the contact line. It is found that in addition to the surface tension, the microscopic dynamic contact angle is also a function of surface tension gradient and the jump in normal stress across the interface. In addition to having a significant contribution in determining the microscopic dynamic contact angle, surface tension gradient is also a key cause for contact angle hysteresis.

scholarly journals Analytical Comparison of Two Multiscale Coupling Methods for Nonlinear Solid Mechanics

2020 ◽  
Vol 87 (9) ◽  
Author(s):  
Daria Koliesnikova ◽  
Isabelle Ramière ◽  
Frédéric Lebon
Keyword(s):  
Multigrid Method ◽  
Solid Mechanics ◽  
Multiscale Methods ◽  
Local Models ◽  
Numerical Homogenization ◽  
Unified Framework ◽  
Scale Separation ◽  
Coupling Methods ◽  
Locally Adaptive ◽  
Nonlinear Solid Mechanics

Abstract The aim of this work is to compare two existing multilevel computational approaches coming from two different families of multiscale methods in a nonlinear solid mechanics framework. A locally adaptive multigrid method and a numerical homogenization technique are considered. Both classes of methods aim to enrich a global model representing the structure’s behavior with more sophisticated local models depicting fine localized phenomena. It is clearly shown that even being developed with different vocations, such approaches reveal several common features. The main conceptual difference relying on the scale separation condition has finally a limited influence on the algorithmic aspects. Hence, this comparison enables to highlight a unified framework for multiscale coupling methods.

scholarly journals Experimental detection of debonding of piezoelectric sensors with the segmented electrode

2019 ◽  
Author(s):  
Hector Andres Tinoco
Keyword(s):  
Structural Control ◽  
Adhesive Layer ◽  
Static Case ◽  
Linear Behavior ◽  
First Case ◽  
Electrode Voltage ◽  
Dynamic Case ◽  
The Right ◽  
Segmented Electrode ◽  
Left Middle

The piezoelectric transducers (PZT) are bonded to smart structures by means of an intermediate adhesive layer, with the main objectives of applying methodologies of structural health monitoring, nondestructive evaluation, nondestructive inspection and structural control to the structures. However, the application of these methodologies depends on the health of the adhesive joint that couples mechanically the PZT with the structure. This research shows an experimental technique based on the segmentation of electrodes of a PZT patch in sheet form. One electrode is segmented in three equal parts (end left, middle and end right) to obtain three electrical signatures of a PZT. The electrical signatures (voltage) of the end electrodes are related to the middle electrode voltage. Three experiments were carried out in this study: two static cases and one dynamic case. For the static case, the left end (first case) and the right end (first case) were debonded. In the dynamic case, only one side was debonded. The results show that the voltage relations present linear behavior and the changing in the slope of the voltage ratio allows identifying which electrode is debonded. This technique showed to be effective in the three studied cases of debonding and it could be used to identify debonding in real time

Multiscale Modeling of Wave Propagation: FDTD/MD Hybrid Method

2002 ◽  
Vol 731 ◽  
Author(s):  
Krishna Muralidharan ◽  
Pierre A. Deymier ◽  
Joseph H. Simmons
Keyword(s):  
Wave Propagation ◽  
Multiscale Modeling ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Equations Of Motion ◽  
Model System ◽  
Atomic Level ◽  
Simulation Techniques ◽  
Difference Time ◽  
The Continuum

AbstractAtomic level processes often play an important role in the way a material responds to an external field. Thus in order to model the behavior of materials accurately, it is necessary to develop simulation techniques which can effectively couple atomistic effects to the macroscopic properties of the model system and vice-versa. In other words, a multiscale methodology needs to be developed to bridge the different length and time scales. In this work we study the propagation of an elastic wave through a coupled continuum-atomistic medium. The equations of motion for the wave propagation through the continuum are solved using the Finite Difference Time Domain Method (FDTD). Simultaneously we use Molecular Dynamics (MD) to examine the effect of the wave packet on the atomic dynamics and the effect of atomic dynamics on the propagation of the wave. The handshaking between the FDTD region and the MD region is concurrent.

scholarly journals Dynamic Snap-Through of a Shallow Arch Under a Moving Point Load

2004 ◽  
Vol 126 (4) ◽  
pp. 514-519 ◽  
Author(s):  
Jen-San Chen ◽  
Jian-San Lin
Keyword(s):  
Critical Load ◽  
Energy Barrier ◽  
Equations Of Motion ◽  
Critical Energy ◽  
Point Load ◽  
Static Case ◽  
Shallow Arch ◽  
Finite Speed ◽  
Dynamic Case ◽  
Moving Speed

In this paper we study the dynamic behavior of a shallow arch under a point load Q traveling at a constant speed. Emphasis is placed on finding whether snap-through buckling will occur. In the quasi-static case when the moving speed is almost zero, there exists a critical load Qcr in the sense that no static snap-through will occur as long as Q is smaller than Qcr. In the dynamic case when the point load travels with a nonzero speed, the critical load Qcrd is, in general, smaller than the static one. When Q is greater than Qcrd, there exists a finite speed zone within which the arch runs the risk of dynamic snap-through either while the point load is still on the arch or after the point load leaves the arch. The boundary of this dangerous speed zone can be determined by a more conservative criterion, which employs the concept of total energy and critical energy barrier, to guarantee the safe passage of the point load. This criterion requires the numerical integration of the equations of motion only up to the instant when the point load reaches the other end of the arch.

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