scholarly journals Multipoint Approximation of Statistical Descriptors of Local Strain and Stress Fields in Heterogeneous Media Using Integral Equation Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Mikhail Tashkinov
Keyword(s):  
Correlation Functions ◽  
Heterogeneous Media ◽  
Boundary Value ◽  
Local Strain ◽  
Statistical Characteristics ◽  
Stress And Strain ◽  
Strain Fields ◽  
Representative Volume ◽  
Multipoint Approximation ◽  
Analytical Expressions

This paper is devoted to derivation of analytic expressions for statistical descriptors of stress and strain fields in heterogeneous media. Multipoint approximations of solutions of stochastic elastic boundary value problems for representative volume elements are investigated. The stress and strain fields are represented in the form of random coordinate functions, for which analytical expressions for the first- and second-order statistical central moments are obtained. Such moments characterize distribution of fields under prescribed loading of a representative volume element and depend on the geometry features and location of components within a volume. The information of the internal geometrical structure is taken into account by means of multipoint correlation functions. Within the framework of the second approximation of the boundary value problem, the correlation functions up to the fifth order are required to calculate the statistical characteristics. Using the method of Green’s functions, analytical expressions for the moments in distinct phases of the microstructure are obtained explicitly in a form of integral equations. Their analysis and comparison with previously obtained results are performed.

On uniform fields in heterogeneous media

1990 ◽  
Vol 431 (1881) ◽  
pp. 89-110 ◽  
Keyword(s):  
Heterogeneous Media ◽  
Transversely Isotropic ◽  
Stress And Strain ◽  
Influence Functions ◽  
Uniform Field ◽  
Fibrous Media ◽  
Two Phase ◽  
Strain Fields ◽  
Transverse Geometry ◽  
Concentration Factors

Uniform elastic strain fields are found in two-phase fibrous media of arbitrary transverse geometry, and in two-phase media of any phase geometry. In initially stress-free fibrous solids, a single uniform field can be created by certain proportionally changing tractions derived from a uniform overall stress. In the presence of phase eigenstrains, many overall stress states can be superimposed to create uniform strain fields in fibrous media. The existence of such fields is exploited to establish a number of exact results for two-phase fibre systems. These include universal connections between phase and overall moduli, and between components of phase stress and strain fields; expressions for new transformation influence functions and concentration factors in terms of their mechanical counterparts; and also expressions for the overall stresses and strains caused by phase eigenstrains. Examples are presented for macroscopically monoclinic fibrous composites with transversely isotropic phases. In two-phase media of arbitrary phase geometry there is only a single uniform stress and strain field for each non-vanishing eigenstrain state. The existence of this field is utilized in derivation of exact connections between transformation and mechanical influence functions and concentration factors.

scholarly journals Calculation of residual stresses in the state of elastic unloading of a preheated inhomogeneous thermoelastoplastic material under conditions of toroidal symmetry

2021 ◽  
pp. 105-113
Author(s):  
Евгений Павлович Дац ◽  
Евгений Валерьевич Мурашкин ◽  
Алексей Михайлович Буруруев ◽  
Тимофей Константинович Нестеров ◽  
Никита Эдуардович Стадник
Keyword(s):  
Residual Stresses ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Analytical Approximation ◽  
Stress And Strain ◽  
Temperature Stresses ◽  
Strain Fields ◽  
Static Approximation ◽  
Toroidal Coordinates ◽  
Elastic Unloading

Статья посвящена численному моделированию остаточных напряжений в неоднородном торе. Материал тора полагается термоупругопластическим. Расчет температурных напряжений происходит в рамках квазистатического приближения. Рассчитываются поля остаточных напряжений и деформаций. Приводятся численные результаты решения краевой задачи в тороидальных координатах. Рассматриваются случаи длинного тора и возможность аналитического приближения исходной краевой задачи. The article is devoted to the numerical simulation of residual stresses in an inhomogeneous torus. The torus material is assumed to be thermoelastoplastic. The calculation of temperature stresses is carried out within the framework of the quasi-static approximation. Residual stress and strain fields are calculated. Numerical results of solving the boundary value problem in toroidal coordinates are presented. The cases of a long torus and the possibility of an analytical approximation of the original boundary value problem are considered

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

The stress and strain fields in the neighbourhood of a notch in polyethylene

Polymer ◽  
1989 ◽  
Vol 30 (8) ◽  
pp. 1456-1461 ◽  
Author(s):  
Xue-qin Wang ◽  
Norman Brown
Keyword(s):  
Stress And Strain ◽  
Strain Fields
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