Applications of Higher-Order Continua to Size Effects in Bending: Theory and Recent Experimental Results

2016 ◽  
pp. 237-260 ◽  
Author(s):  
Christian Liebold ◽  
Wolfgang H. Müller
Keyword(s):  
Size Effects ◽  
Higher Order ◽  
Experimental Results

scholarly journals A Method to Determine Material Length Scale Parameters in Elastic Strain Gradient Theory

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Jingru Song ◽  
Yueguang Wei
Keyword(s):  
Strain Gradient ◽  
Size Effects ◽  
Elastic Strain ◽  
Higher Order ◽  
Experimental Results ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Face Centered Cubic ◽  
Scale Parameters

Abstract With specimen size decrease for advanced structural materials, the measured mechanics behaviors display the strong size effects. In order to characterize the size effects, several higher-order theories have been presented in the past several decades, such as the strain gradient theories and the micro-polar theories, etc. However, in each higher-order theory, there are several length scale parameters included, which are usually taken as the material parameters and are determined by using the corresponding theoretical predictions to fit experimental results. Since such kind of experimental approaches needs high techniques, it is very difficult to be performed; therefore, the obtained experimental results are very few until now; in addition, the physical meanings of the parameters still need to be investigated. In the present research, an equivalent linkage method is used to simply determine the elastic length parameters appeared in the elastic strain gradient theory for a series of typical metal materials. We use both the elastic strain gradient theory and the higher-order Cauchy-Born rule to model the materials mechanics behaviors by means of a spherical expanding model and then make a linkage for both kinds of results according to the equivalence of strain energy densities. The values of the materials length parameters are obtained for a series of typical metal systems, such as the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) metals.

Study of the Size Effects and Friction Conditions in Microextrusion—Part II: Size Effect in Dynamic Friction for Brass-Steel Pairs

2007 ◽  
Vol 129 (4) ◽  
pp. 677-689 ◽  
Author(s):  
Lapo F. Mori ◽  
Neil Krishnan ◽  
Jian Cao ◽  
Horacio D. Espinosa
Keyword(s):  
Grain Size ◽  
Friction Coefficient ◽  
Size Effect ◽  
Contact Pressure ◽  
Size Effects ◽  
Numerical Models ◽  
Kolsky Bar ◽  
Experimental Results ◽  
Material Response ◽  
Dynamic Coefficients

In this paper, the results of experiments conducted to investigate the friction coefficient existing at a brass-steel interface are presented. The research discussed here is the second of a two-part study on the size effects in friction conditions that exist during microextrusion. In the regime of dimensions of the order of a few hundred microns, these size effects tend to play a significant role in affecting the characteristics of microforming processes. Experimental results presented in the previous companion paper have already shown that the friction conditions obtained from comparisons of experimental results and numerical models show a size effect related to the overall dimensions of the extruded part, assuming material response is homogeneous. Another interesting observation was made when extrusion experiments were performed to produce submillimeter sized pins. It was noted that pins fabricated from large grain-size material (211μm) showed a tendency to curve, whereas those fabricated from billets having a small grain size (32μm), did not show this tendency. In order to further investigate these phenomena, it was necessary to segregate the individual influences of material response and interfacial behavior on the microextrusion process, and therefore, a series of frictional experiments was conducted using a stored-energy Kolsky bar. The advantage of the Kolsky bar method is that it provides a direct measurement of the existing interfacial conditions and does not depend on material deformation behavior like other methods to measure friction. The method also provides both static and dynamic coefficients of friction, and these values could prove relevant for microextrusion tests performed at high strain rates. Tests were conducted using brass samples of a small grain size (32μm) and a large grain size (211μm) at low contact pressure (22MPa) and high contact pressure (250MPa) to see whether there was any change in the friction conditions due to these parameters. Another parameter that was varied was the area of contact. Static and dynamic coefficients of friction are reported for all the cases. The main conclusion of these experiments was that the friction coefficient did not show any significant dependence on the material grain size, interface pressure, or area of contact.

scholarly journals An evaluation of higher-order plasticity theories for predicting size effects and localisation

2006 ◽  
Vol 43 (7-8) ◽  
pp. 1857-1877 ◽  
Author(s):  
R.A.B. Engelen ◽  
N.A. Fleck ◽  
R.H.J. Peerlings ◽  
M.G.D. Geers
Keyword(s):  
Size Effects ◽  
Higher Order

scholarly journals A General Multi-agent Epistemic Planner Based on Higher-order Belief Change

2017 ◽  
Author(s):  
Xiao Huang ◽  
Biqing Fang ◽  
Hai Wan ◽  
Yongmei Liu
Keyword(s):  
Normal Form ◽  
Belief Change ◽  
Common Knowledge ◽  
Dynamic Logic ◽  
Higher Order ◽  
Experimental Results ◽  
General Representation ◽  
Multi Agent ◽  
Representation Language ◽  
Contingent Planning

In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper, we propose a general representation language for multi-agent epistemic planning where the initial KB and the goal, the preconditions and effects of actions can be arbitrary multi-agent epistemic formulas, and the solution is an action tree branching on sensing results.To support efficient reasoning in the multi-agent KD45 logic, we make use of a normal form called alternative cover disjunctive formula (ACDF). We propose basic revision and update algorithms for ACDF formulas. We also handle static propositional common knowledge, which we call constraints. Based on our reasoning, revision and update algorithms, adapting the PrAO algorithm for contingent planning from the literature, we implemented a multi-agent epistemic planner called MAEP. Our experimental results show the viability of our approach.

Size Effects in the Impact of Carbon Fiber Reinforced Composite Structures

2018 ◽  
Vol 789 ◽  
pp. 155-160
Author(s):  
Yi Ou Shen ◽  
Yan Li
Keyword(s):  
Size Effects ◽  
Composite Structures ◽  
Impact Force ◽  
Flexural Rigidity ◽  
Experimental Results ◽  
Target Size ◽  
Mass Model ◽  
Energy Impact ◽  
Maximum Impact Force ◽  
The Impact

In this study, target size effects in the low energy impact response of plain CFRP plateswere investigated. It was found that increase the target size leads to a reduction in the maximumimpact force recorded during the test. This is due to the reduction on flexural rigidity of the largerpanels. The experimental results indicated that at energies above the first failure threshold, themaximum impact force does not coincidence with the predicting value. Two mathematical modelswere used to predict the maximum impact force including single degree of freedom (SDOF)spring-mass model and Energy-Balance (E-B) model. The predicting results were then comparedwith the experimental results, and both of the two models show good agreement with theexperimental results in elastic deformation region. In addition, the level of agreement between thepredictions and the experimental results indicate that both models are capable of modelling theimpact response of these CFRP panels at elastic regime.

Nitpick: A Counterexample Generator for Isabelle/HOL Based on the Relational Model Finder Kodkod

10.29007/6shf ◽  
2018 ◽  
Author(s):  
Jasmin Christian Blanchette
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Experimental Results ◽  
Relational Model ◽  
Finite Model ◽  
Higher Order Logic ◽  
First Order ◽  
Recursive Functions

Nitpick is a counterexample generator for Isabelle/HOL that builds on Kodkod, a SAT-based first-order relational model finder. Nitpick supports unbounded quantification, (co)inductive predicates and datatypes, and (co)recursive functions. Fundamentally a finite model finder, it approximates infinite types by finite subsets. Our experimental results on Isabelle theories and the TPTP library indicate that Nitpick generates more counterexamples than other model finders for higher-order logic, without restrictions on the form of the formulas to falsify.

scholarly journals Size effects in ductile cellular solids. Part II: experimental results

2001 ◽  
Vol 43 (3) ◽  
pp. 701-713 ◽  
Author(s):  
E.W Andrews ◽  
G Gioux ◽  
P Onck ◽  
L.J Gibson
Keyword(s):  
Size Effects ◽  
Experimental Results ◽  
Cellular Solids
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