scholarly journals Analysis of the fracture toughness parameters at the free edge in layered composites

2020 ◽  
pp. 49-59
Author(s):  
D. A Bondarchuk ◽  
B. N Fedulov ◽  
A. N Fedorenko ◽  
E. V Lomakin
Keyword(s):  
Contact Interaction ◽  
Continuum Mechanics ◽  
Constitutive Relations ◽  
External Pressure ◽  
Isotropic Hardening ◽  
Winkler Foundation ◽  
Shells Of Revolution ◽  
Plastic Properties ◽  
Elastic Core ◽  
Wide Range

The problem of deformation and elastoplastic buckling of shells of revolution with a thick-walled elastic core under combined static and dynamic loading is formulated in a two-dimensional planar formulation based on two approaches: full-scale modeling within the framework of continuum mechanics and a simplified formulation based on the hypotheses of the theory of shells of the Timoshenko type and the Winkler foundation. Both approaches allow solving the problems of deformation and stability of non-shallow shells on the basis of Timoshenko's hypotheses, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian coordinate system as a reference one. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the work. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. The nonpenetration conditions are satisfied only in the active phase of the contact interaction; if the contact is broken, they are replaced by conditions on the free surface. In the second approach, the contact interaction of the elastic core with the shell is modeled by the Winkler foundation. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic core, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. Using both approaches, a numerical simulation of contact interaction problem of an elastoplastic cylindrical shell with a thick-walled elastic core at a quasi-static uniform external pressure is carried out. The study of the influence of the thickness and initial deflection of the shell, as well as the stiffness and thickness of the core, on the value of the critical pressure and the form of buckling has been carried out. Based on these calculations, a conclusion was made about a wide range of applicability of the Winkler foundation model.

scholarly journals Investigation of the Winkler foundation model applicability for describing the contact interaction of elastoplastic shells with a core under external pressure

2020 ◽  
pp. 36-48
Author(s):  
V. G Bazhenov ◽  
E. V Nagornykh ◽  
D. A Samsonova
Keyword(s):  
Contact Interaction ◽  
Continuum Mechanics ◽  
Constitutive Relations ◽  
External Pressure ◽  
Isotropic Hardening ◽  
Winkler Foundation ◽  
Shells Of Revolution ◽  
Elastic Core ◽  
Wide Range ◽  
Foundation Model

The problem of deformation and elastoplastic buckling of shells of revolution with a thick-walled elastic core under combined static and dynamic loading is formulated in a two-dimensional planar formulation based on two approaches: full-scale modeling within continuum mechanics and a simplified formulation based on the hypotheses of the theory of shells of the Timoshenko type and the Winkler foundation. Both approaches allow solving the problems of deformation and stability of non-shallow shells on the basis of Timoshenko's hypotheses, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian coordinate system as a reference one. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the work. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. The nonpenetration conditions are satisfied only in the active phase of the contact interaction; if the contact is broken, they are replaced by conditions on the free surface. In the second approach, the contact interaction of the elastic core with the shell is modeled by the Winkler foundation. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic core, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. Using both approaches, a numerical simulation of epy contact interaction problem of an elastoplastic cylindrical shell with a thick-walled elastic core at a quasi-static uniform external pressure is carried out. The study of the influence of the thickness and initial deflection of the shell, as well as the stiffness and thickness of the core, on the value of the critical pressure and the form of buckling has been carried out. Based on these calculations, a conclusion was made about a wide range of applicability of the Winkler foundation model.

scholarly journals About applicability of the winkler model for contact interaction of cylindrical elastoplastic shells with an elastic filler at external pressure

2020 ◽  
pp. 3-8
Author(s):  
Валентин Георгиевич Баженов ◽  
Елена Владимировна Нагорных ◽  
Дарья Анатольевна Самсонова
Keyword(s):  
Contact Interaction ◽  
Continuum Mechanics ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
External Pressure ◽  
Isotropic Hardening ◽  
Shells Of Revolution ◽  
Plastic Properties ◽  
Wide Range ◽  
Elastic Filler

Представлено сравнение результатов расчетов контактного взаимодействия и потери устойчивости упругопластических цилиндрических оболочек с упругим толстостенным заполнителем, выполненных на основе двух подходов: с позиций механики сплошных сред и теории оболочек типа Тимошенко с основанием Винклера. Оба подхода позволяют решать задачи деформирования и устойчивости непологих оболочек с учетом геометрических нелинейностей. Постановка с позиций механики сплошных сред позволяет аппроксимировать оболочку по толщине рядом слоев конечных элементов. Определяющие соотношения формулируются в переменных Лагранжа с использованием в качестве отсчетной неподвижной декартовой или цилиндрической системы координат. Кинематические соотношения записываются в метрике текущего состояния. Упругопластические свойства оболочек описываются теорией пластического течения с изотропным упрочнением. Уравнения движения следуют из баланса виртуальных мощностей работ. В первом подходе контактное взаимодействие оболочки и упругого тела моделируется условиями непроникания по нормали и свободного проскальзывания вдоль касательной. Во втором подходе контактное взаимодействие упругого заполнителя с оболочкой моделируется основанием Винклера. Оба подхода позволяют описать нелинейное докритическое деформирование оболочек вращения с упругим заполнителем, определить предельные (критические) нагрузки в широком диапазоне скоростей нагружения с учетом геометрических несовершенств формы. Оценивается область применимости гипотезы Винклера при контактном взаимодействии оболочки с упругой средой в зависимости от жесткости и толщины основания. Comparison of the results of calculations of contact interaction and loss of stability of elastoplastic cylindrical shells with an elastic thick-walled filler, performed on the basis of two approaches: from the standpoint of continuum mechanics and the theory of Timoshenko-type shells with a Winkler base is presented. Both approaches allow solving the problems of deformation and stability of non-sloping shells, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian or cylindrical coordinate system as a reference. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the jobs. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. In the second approach, the contact interaction of the elastic filler with the shell is modeled by the Winkler base. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. The area of applicability of the Winkler hypothesis is estimated for the contact interaction of a shell with an elastic medium, depending on the stiffness and thickness of the base.

Buckling Analysis of an Orthotropic Elliptical Toroidal Shell

2009 ◽  
Author(s):  
D. Redekop
Keyword(s):  
Differential Quadrature Method ◽  
External Pressure ◽  
Buckling Analysis ◽  
Toroidal Shell ◽  
Shells Of Revolution ◽  
Good Correspondence ◽  
Elliptical Cross ◽  
Wide Range ◽  
Orthotropic Shells ◽  
Toroidal Shells

A theoretical solution is given for the linearized buckling problem of an orthotropic toroidal shell with an elliptical cross-section under external pressure loading. The solution is based on the Sanders-Budiansky shell theory, and makes use of the harmonic differential quadrature method. Theory developed earlier for the buckling of orthotropic shells of revolution, and the vibration of orthotropic elliptical toroidal shells, is incorporated in the present work. Numerical results obtained from the solution are compared with results given in the literature, and good correspondence is generally observed. A parametric study is then conducted, covering a wide range of material and geometric parameters. Regression formulas are derived, indicating the variation of the buckling pressure with the degree of orthotropy of the material. Overall, the study introduces a new tool for the buckling analysis of elliptical toroidal shells, and extends the information available for orthotropic toroidal shells.

Atomistic Aspects of Fracture Modelling in the Framework of Continuum Mechanics

1998 ◽  
Vol 538 ◽  
Author(s):  
F. Cleri
Keyword(s):  
Continuum Mechanics ◽  
Constitutive Relations ◽  
Point Of View ◽  
Atomic Scale ◽  
Continuum Models ◽  
Cohesive Law ◽  
Macroscopic Models ◽  
Scale Models ◽  
Level Information ◽  
Set Up

AbstractThe validity and predictive capability of continuum models of fracture rests on basic informations whose origin lies at the atomic scale. Examples of such crucial informations are, e.g., the explicit form of the cohesive law in the Barenblatt model and the shear-displacement relation in the Rice-Peierls-Nabarro model. Modem approaches to incorporate atomic-level information into fracture modelling require to increase the size of atomic-scale models up to millions of atoms and more; or to connect directly atomistic and macroscopic, e.g. finite-elements, models; or to pass information from atomistic to continuum models in the form of constitutive relations. A main drawback of the atomistic methods is the complexity of the simulation results, which can be rather difficult to rationalize in the framework of classical, continuum fracture mechanics. We critically discuss the main issues in the atomistic simulation of fracture problems (and dislocations, to some extent); our objective is to indicate how to set up atomistic simulations which represent well-posed problems also from the point of view of continuum mechanics, so as to ease the connection between atomistic information and macroscopic models of fracture.

Uncertainty in Collapse Strength Prediction of Sandwich Pipelines

2021 ◽  
Author(s):  
U. Bhardwaj ◽  
A. P. Teixeira ◽  
C. Guedes Soares
Keyword(s):  
Probabilistic Models ◽  
Uncertainty Propagation ◽  
Simulation Method ◽  
External Pressure ◽  
Design Parameters ◽  
Collapse Strength ◽  
Parameters Uncertainty ◽  
Wide Range ◽  
Model Predictions ◽  
Strength Models

Abstract This paper assesses the uncertainty in the collapse strength of sandwich pipelines under external pressure predicted by various strength models in three categories based on interlayer adhesion conditions. First, the validity of the strength models is verified by comparing their predictions with sandwich pipeline collapse test data and the corresponding model uncertainty factors are derived. Then, a parametric analysis of deterministic collapse strength predictions by models is conducted, illustrating insights of models’ behaviour for a wide range of design configurations. Furthermore, the uncertainty among different model predictions is perceived at different configurations of outer and inner pipes and core thicknesses. A case study of a realistic sandwich pipeline is developed, and probabilistic models are defined to basic design parameters. Uncertainty propagation of models’ predictions is assessed by the Monte Carlo simulation method. Finally, the strength model predictions of sandwich pipelines are compared to that of an equivalent single walled pipe.

scholarly journals Research and Modeling of Viscoelastic Behavior of Elastomeric Nanocomposites

2021 ◽  
pp. 76-87
Author(s):  
V. D Kislitsyn ◽  
K. A Mokhireva ◽  
V. V Shadrin ◽  
A. L Svistkov
Keyword(s):  
Constitutive Relations ◽  
Viscoelastic Behavior ◽  
Polymer Materials ◽  
Material Structure ◽  
Softening Effect ◽  
Single Walled Nanotubes ◽  
Wide Range ◽  
Significant Difference ◽  
The Matrix ◽  
Entire History

The paper presents results of studying mechanical properties of polymer composites depending on types of filler particles (granular - carbon black, nanodiamonds; layered - graphene plates; fibrous - single-walled nanotubes). These nanofillers differ greatly from each other in their structure and geometry. A significant difference in behavior of nanocomposites was revealed even with little introduction of particles into the elastomer. The highest level of reinforcement of the matrix was obtained when single-wall nanotubes and detonation nanodiamonds were used as fillers. The viscoelastic properties and the Mullins softening effect [1-4] were investigated in experiments performed with material samples subjected to complex uniaxial cyclic deformation. In these experiments, the amplitude of deformations was changed step by step; and at each step a time delay was specified to complete rearrangement processes of the material structure. It was found that a pronounced softening effect after the first cycle of deformation and significant hysteresis losses occur in the material filled with single-walled nanotubes. These characteristics are insignificant for the rest of nanocomposites until elongation increases twofold. In accordance with the obtained results, a new version of the mathematical model to describe properties of the viscoelastic polymer materials was proposed. The constants of the constitutive relations were calculated for each material; the theoretical and experimental load curves were compared. As a result, the introduced model is able to describe the behavior of elastomeric nanocomposites with a high accuracy. Moreover, this model is relatively easy to use, suitable for a wide range of strain rates and stretch ratios and does not require the entire history of deformation as needed for integral models of viscoelasticity.

scholarly journals Constitutive relations for compressible granular flow in the inertial regime

2019 ◽  
Vol 874 ◽  
pp. 926-951 ◽  
Author(s):  
D. G. Schaeffer ◽  
T. Barker ◽  
D. Tsuji ◽  
P. Gremaud ◽  
M. Shearer ◽  
...  
Keyword(s):  
Steady State ◽  
Granular Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Practical Interest ◽  
Time Dependent ◽  
Direct Result ◽  
Wide Range ◽  
Inertial Regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology that does not suffer from such defects is proposed. In the framework of compressible $I$-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.

Quantification of O2 consumption and arterial pressure as independent determinants of coronary flow

1987 ◽  
Vol 252 (3) ◽  
pp. H545-H553 ◽  
Author(s):  
I. Vergroesen ◽  
M. I. Noble ◽  
P. A. Wieringa ◽  
J. A. Spaan
Keyword(s):  
Coronary Artery ◽  
Arterial Pressure ◽  
Coronary Flow ◽  
Left Main Coronary Artery ◽  
External Pressure ◽  
Arterial Blood Flow ◽  
O2 Consumption ◽  
Left Main ◽  
Arterial Blood ◽  
Wide Range

The steady-state relationship between coronary arterial blood flow (CBF) and both myocardial O2 consumption (MVO2) and coronary arterial pressure (P) was explored in anesthetized dogs and goats. Both species were subjected to constant pressure perfusion of the left main coronary artery by an external pressure-controlling circuit. In addition a group of goats was studied with normal aortic perfusion using an occluder around the left main coronary artery to vary coronary arterial pressure. The statistical analysis revealed that despite the direct effect of P on MVO2 (the Gregg effect) the effects of both variables on CBF were independent and linear over a wide range of P and MVO2 so that multiple regression analysis with a linear equation (CBF = a X P + b X MVO2 + c) gave an excellent fit which was not improved by the introduction of an addition interactive term b3MVO2 X P. The mean correlation coefficient for all animals was greater than 0.9. From these data we conclude that any factor regulating coronary arterial flow would be influenced by both MVO2 and perfusion pressure in an independent way. This study characterizes the stationary behavior of local coronary flow control. Hence, it specifies quantitatively the relations to be predicted by hypotheses aiming to explain this control mechanism.

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