29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES最新文献

Multi-level direct crystal plasticity model of polycrystalline specimen: Grains generation 多晶试样多级直接结晶塑性模型:晶粒生成

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059602

A. A. Tokarev, A. Y. Yants, A. Shveykin, N. S. Kondratiev

引用次数: 1

Modeling of nonlinear effects in the theory of the flow of polymer liquids when superposition periodic oscillations on a stationary shear flow 稳态剪切流叠加周期振荡时聚合物液体流动理论中非线性效应的建模

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0060935

G. O. Rudakov, A. A. Laas, M. A. Makarova, A. S. Malygina, G. V. Pyshnograi

引用次数: 0

Nucleation and evolution of crystals taking into account fluctuations in their growth rates: Test of theory with experiment 考虑到晶体生长速率波动的晶体成核和进化:理论与实验的检验

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059600

E. Makoveeva

{"title":"Nucleation and evolution of crystals taking into account fluctuations in their growth rates: Test of theory with experiment","authors":"E. Makoveeva","doi":"10.1063/5.0059600","DOIUrl":"https://doi.org/10.1063/5.0059600","url":null,"abstract":"This article presents a mathematical model of the crystal growth process in a metastable liquid. The model takes into account the presence of fluctuations in crystal growth rates and “diffusion” of the crystal-size distribution function along the axis of particle radii. For the sake of definiteness, the model equations are reformulated in dimensionless form. An exact analytical solution of the model under consideration is found and compared with experimental data. Namely, the distribution function, liquid supercooling (supersaturation), and nucleation rate are analytically found using the integral Laplace transform method. Two frequently met cases of the Meirs and Weber-Volmer-Frenkel-Zel’dovich nucleation kinetics are considered. In the case of Meirs kinetics, the analytical solution is obtained in an explicit form. The distribution function takes a bell-shaped form, and eventually moves towards larger crystal radii with decreasing the maximal function value. It is shown that the metastability degree (supersaturation of the liquid phase) is in good agreement with experimental data on canavalin crystallization.","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117010775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A molecular dynamics simulation analysis of mixed mode crack growth 混合模式裂纹扩展的分子动力学模拟分析

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059574

L. Stepanova, O. Belova

引用次数: 4

Assessment of the SIF, T-stress and higher-order coefficient values of the cracked specimens with two interacting cracks or notches under mixed mode loadings by digital photoelasticity method 采用数字光弹性法评估双裂纹或缺口相互作用裂纹试件在混合模式荷载作用下的SIF、t应力和高阶系数值

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059578

L. Stepanova, V. Dolgikh

{"title":"Assessment of the SIF, T-stress and higher-order coefficient values of the cracked specimens with two interacting cracks or notches under mixed mode loadings by digital photoelasticity method","authors":"L. Stepanova, V. Dolgikh","doi":"10.1063/5.0059578","DOIUrl":"https://doi.org/10.1063/5.0059578","url":null,"abstract":"The purpose of this work is to determine experimentally and computationally the coefficients of the Williams series expansion in the vicinity of two interacting cracks or notches. In this study, the multi-parameter description of the crack-tip fields for digital processing of the experimental data obtained from photoelastic experiments is complied. The special programming tool for digital processing of the experimental data is elaborated. The Williams expansion is introduced for approximation of the stress/displacement distribution. The over-deterministic method is used for calculation of the coefficients of the power series terms because it requires only a conventional FE analysis. Results determined via finite element analysis are compared to those calculated by means of the stress distribution expressed via the Williams expansion under consideration of various numbers of initial terms of the series. It is shown that the higher-order terms of the Williams expansion can be significant when the extent of the isochromatic fringe is far enough in comparison to the crack length. It is shown that the use of higher order terms leads to increase of the domain where the Williams series expansion can be used.","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115488485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Method for analyzing the kinetics of damage accumulation in the structure of polymer materials under tensile stresses 拉伸应力作用下高分子材料结构损伤积累动力学分析方法

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059899

T. Nizina, D. Nizin, N. Kanaeva, D. Artamonov

{"title":"Method for analyzing the kinetics of damage accumulation in the structure of polymer materials under tensile stresses","authors":"T. Nizina, D. Nizin, N. Kanaeva, D. Artamonov","doi":"10.1063/5.0059899","DOIUrl":"https://doi.org/10.1063/5.0059899","url":null,"abstract":"The paper states main provisions of the method for assessing the accumulation of damage in the structure of polymer materials under tensile stresses. The proposed method involves fractal analyses of deformation curves recorded with a high frequency. The minimum coverage method was used to determine the coordinates of critical points identified by the minimum levels of the fractality index. To determine the change in the fractality index depending on the relative elongation, we used a sequence of nested partitions. The amplitude variation was calculated for each of them as a sum of the differences between the maximum and minimum increase in tensile stresses in each analyzed time interval. The fractality index values were determined in the previous time interval of 0.16 sec. with a step of 0.01 sec. The paper provides the results of implementing the proposed method, which makes it possible to determine critical levels of stresses and relative deformations of polymer samples under tensile loads. We used ten samples of epoxy polymer based on modified Etal-247 resin cured by Etal-1472 hardener, including one sample with initial structural defects, as objects of study. We have identified the \"critical\" levels of tensile stresses and relative elongations, at which the failure rate grows, assessed by the minimum levels of fractality indices of the deformation curves.","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114438810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Strain measurement in concrete sample under static loading using embedded fiber-optic sensors 用嵌入式光纤传感器测量静载下混凝土试样的应变

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059550

G. Serovaev, N. Kosheleva, G. Gusev

引用次数: 1

Stress concentration factors in a plain woven ceramic textile composite with the flexible graphite matrix 柔性石墨基平纹编织陶瓷纺织复合材料的应力集中系数

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059560

D. Dedkov, A. Zaitsev, Vitaliy Koksharov, A. Tashkinov

{"title":"Stress concentration factors in a plain woven ceramic textile composite with the flexible graphite matrix","authors":"D. Dedkov, A. Zaitsev, Vitaliy Koksharov, A. Tashkinov","doi":"10.1063/5.0059560","DOIUrl":"https://doi.org/10.1063/5.0059560","url":null,"abstract":"The paper aims at solving a problem of determining the stress concentration factor in the plain square (1/1 twill, i.e. equal warp and weft orders) woven composite layer caused by the texture complex geometry and local technological defects (internal pores and local fiber breakages). Also, the paper examines the mechanisms that predetermine the main damage scenario based on the earlier developed two-level model of the woven textile composite with reinforcement coefficients equal to 0.14, curved ceramic fibers and FG matrix. Plain weaves provide such benefits as the shortest overlaps, maximum strength, density and increased stiffness of a homogeneous textile surface (geometrically identical both from the front and back sides), but cause internal technological pores. Modeling macrohomogeneous deformations of a woven composite layer in its plane was carried out on the basis of numerical solutions of the boundary-value problems by FEM using an open integrable platform SALOME-MECA. Ceramic fibers and FG matrix were assumed to be isotropic, linearly elastic, not changing their geometry, relative position and type of elastic symmetry under loading. Under the macroscopically homogeneous pure shape change of the woven composite layer, we determined values of the stress concentration factors caused by local technological defects in the presence of a guaranteed FG matrix interlayer around the ceramic fiber of the reinforcing frame, as well as in the presence of a friction contact between them. So, to increase of a woven composite capability to oppose the external action (when closed internal pores are revealed), we need to carry out operations that provide the FG matrix penetration into the local technological caverns. Otherwise, the FG matrix can be damaged by shear and breaking mechanisms.","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124602275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Mathematical modeling of some aerohydroelastic systems 气动水弹性系统的数学建模

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059960

P. A. Velmisov, A. Ankilov

引用次数: 1

Mathematical modeling of damage accumulation near grain boundaries in titanium alloys 钛合金晶界附近损伤积累的数学模型

29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES Pub Date : 2021-07-13 DOI: 10.1063/5.0059536

N. A. Knyazev, P. Volegov

引用次数: 1