Discrete convolution and FFT modified with double influence-coefficient superpositions (DCSS–FFT) for contact of nominally flat heterogeneous materials involving elastoplasticity

2021 ◽  
Vol 67 (3) ◽  
pp. 989-1007
Author(s):  
Linlin Sun ◽  
Q. Jane Wang ◽  
Ning Zhao ◽  
Mengqi Zhang
Keyword(s):  
Heterogeneous Materials ◽  
Influence Coefficient ◽  
Discrete Convolution

Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm

2001 ◽  
Vol 124 (1) ◽  
pp. 36-45 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Frequency Response ◽  
High Efficiency ◽  
Contact Stresses ◽  
Influence Coefficient ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Discrete Convolution ◽  
Influence Coefficients

The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green’s function for the cases with known Green’s functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC-FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.

Probabilistic multiscale modeling of fracture in heterogeneous materials and structures

2020 ◽  
Vol 86 (7) ◽  
pp. 45-54
Author(s):  
A. M. Lepikhin ◽  
N. A. Makhutov ◽  
Yu. I. Shokin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fracture Mechanics ◽  
Multiscale Modeling ◽  
Virtual Work ◽  
Numerical Models ◽  
Heterogeneous Materials ◽  
Heterogeneous Structure ◽  
Generalized Coordinates ◽  
Heterogeneous Structures

The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

Consideration of the temperature factor of atmospheric air when determining standard consumption of fuel and energy resources for train traction

2018 ◽  
Vol 77 (6) ◽  
pp. 375-381
Author(s):  
K. M. Popov
Keyword(s):  
Statistical Processing ◽  
Specific Consumption ◽  
Energy Resources ◽  
Effect Of Temperature ◽  
Influence Coefficient ◽  
Specific Work ◽  
Specific Flow ◽  
Temperature Changes ◽  
Work Area ◽  
Physical Laws

Abstract. Influence of air temperature on the consumption of fuel and energy resources (FER) on train traction is due to a number of physical laws. The extent of this effect is specified in the Rules for Traction Settlement (RTS). At the same time, when rationing FER consumption for train traction, a specialized methodical base is used, which involves a different approach to accounting for the effect of temperature on FER consumption for train traction. At the same time in different documents of this base, the effects of low temperature on the absolute and specific consumption of fuel and energy resources on train traction are taken into account in a different way, which is due to the lack of consensus among specialists on the way this factor is taken into account. Specialists of JSC “VNIIZhT” carried out an analysis of a significant amount of driver’s routes data, results of which showed that the dependence of the specific flow rate on temperature, on the basis of which the corresponding influence coefficient is determined, needs to be periodically updated. In addition, when technically standardizing the consumption of fuel and energy resources (for the locomotive crew work site), the temperature effect coefficients need to be calculated for a specific work area and direction of motion on it, while using the average network coefficient values will lead to errors. When calculating additional flow of fuel and energy from the effect of temperature for electric multiple units (EMU), the equations of regression dependencies should be used, obtained by statistical processing of data on temperature changes and specific consumption of fuel and energy resources for EMU and determined for each series of EMU when working on a particular suburban area.

scholarly journals Microstructure and Mechanical Properties of Al-Mg-Si Similar Alloy Laminates Produced by Accumulative Roll Bonding

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4200
Author(s):  
Zhigang Li ◽  
Hao Jiang ◽  
Minghui Wang ◽  
Hongjie Jia ◽  
Hongjiang Han ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Accumulative Roll Bonding ◽  
Thin Sheet ◽  
Heterogeneous Materials ◽  
Thick Sheet ◽  
Subsequent Aging ◽  
Roll Bonding ◽  
Roll Casting ◽  
Promotive Effect ◽  
Similar Materials

As the applications of heterogeneous materials expand, aluminum laminates of similar materials have attracted much attention due to their greater bonding strength and easier recycling. In this work, an alloy design strategy was developed based on accumulative roll bonding (ARB) to produce laminates from similar materials. Twin roll casting (TRC) sheets of the same composition but different cooling rates were used as the starting materials, and they were roll bonded up to three cycles at varying temperatures. EBSD showed that the two TRC sheets deformed in distinct ways during ARB processes at 300°C. Major recrystallizations were significant after the first cycle on the thin sheet and after the third cycle on the thick sheet. The sheets were subject to subsequent aging for better mechanical properties. TEM observations showed that the size and distribution of nano-precipitations were different between the two sheet sides. These nano-precipitations were found to significantly promote precipitation strengthening, and such a promotive effect was referred to as hetero-deformation induced (HDI) strengthening. Our work provides a new promising method to prepare laminated heterogeneous materials with similar alloy TRC sheets.

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