scholarly journals The problem of the interaction of a conical indenter with an elastic cylinder

2020 ◽  
pp. 54-63
Author(s):  
Юрий Владимирович Астапов ◽  
Марина Юрьевна Соколова ◽  
Дмитрий Викторович Христич
Keyword(s):  
Numerical Solution ◽  
Nonlinear Response ◽  
Constitutive Relations ◽  
Material Model ◽  
Elastic Cylinder ◽  
Elastic Model ◽  
Rigid Punch ◽  
Hertz Theory ◽  
Fundamental Possibility ◽  
Nonlinear Elastic

В данной работе исследуется поведение эластомера при взаимодействии с жестким штампом, вершина которого имеет форму конуса. В качестве определяющих соотношений используются модель материала Генки и ее обобщение для описания физически-нелинейного отклика. Проведено сравнение результатов численного решения с кривыми, полученными из рассмотрения поставленной задачи в рамках линейной модели с использованием теории Герца. В работах [10, 11] показана принципиальная возможность определения параметров модели гиперупругости на основе определяющих соотношений Генки-Мурнагана из экспериментов по индентированию сферическим штампом. Результаты, полученные в данной работе, могут быть использованы для построения методики определения параметров нелинейно-упругой модели из экспериментов по индентированию коническим штампом. In this paper, we investigate the behavior of an elastomer when interacting with a rigid punch, the top of which is cone-shaped. Hencky’s material model and its generalization to describe the physically nonlinear response are used as the constitutive relations. The results of the numerical solution are compared with the curves obtained from considering the problem in the framework of a linear model using the Hertz theory. The works [10, 11] show the fundamental possibility of determining the parameters of the hyperelasticity model based on the Hencky- Murnaghan constitutive relations from experiments on indentation with a spherical stamp. The results obtained in this work can be used to construct a method for determining the parameters of a nonlinear elastic model from experiments on indentation with a conical stamp.

Finite Deformations of an Elastic Cylinder During Indentation

2018 ◽  
Vol 10 (03) ◽  
pp. 1850026 ◽  
Author(s):  
Yuri Astapov ◽  
Dmitrii Khristich
Keyword(s):  
Cylindrical Specimen ◽  
Constitutive Relations ◽  
Time Derivative ◽  
Strain Tensor ◽  
Elastic Cylinder ◽  
Finite Deformations ◽  
Logarithmic Strain ◽  
Weakly Compressible ◽  
Indentation Problem ◽  
Nonlinear Elastic

The problem about the indentation of the rigid spherical stamp into the cylindrical specimen was considered. The material of the specimen was assumed to be weakly compressible. The formulation of the problem was performed for the case of finite deformations. The method of construction of the constitutive relations in terms of logarithmic strain tensor for elastic media and the variant of the algorithm to take into account the variation of the contact zone were proposed. The expansion of Hencky tensor and its time derivative into the series in powers of Cauchy strain tensor were used to calculate correctly the components of these tensors. Within the indentation problem, we used the model of nonlinear elastic material which provides the best agreement between numerical solution and experimental data among other used types of constitutive relations including various elastic and hypoelastic models.

scholarly journals Analysis and approximation of a strain-limiting nonlinear elastic model

2014 ◽  
Vol 20 (1) ◽  
pp. 92-118 ◽  
Author(s):  
M Bulíček ◽  
J Málek ◽  
E Süli
Keyword(s):  
Elastic Model ◽  
Nonlinear Elastic

scholarly journals Constitutive Modelling and Identification of Parameters of 316L Stainless Steel at Cryogenic Temperatures

2014 ◽  
Vol 8 (3) ◽  
pp. 136-140 ◽  
Author(s):  
Maciej Ryś
Keyword(s):  
Phase Transformation ◽  
Nonlinear Response ◽  
316L Stainless Steel ◽  
Parent Phase ◽  
Secondary Phase ◽  
Material Model ◽  
Transformation Process ◽  
Constitutive Modelling ◽  
Model Parameters ◽  
Two Phase

Abstract In this work, a macroscopic material model for simulation two distinct dissipative phenomena taking place in FCC metals and alloys at low temperatures: plasticity and phase transformation, is presented. Plastic yielding is the main phenomenon occurring when the yield stress is reached, resulting in nonlinear response of the material during loading. The phase transformation process leads to creation of two-phase continuum, where the parent phase coexists with the inclusions of secondary phase. An identification of the model parameters, based on uniaxial tension test at very low temperature, is also proposed.

scholarly journals Identification of Fractional Damping Parameters in Structural Dynamics Using Polynomial Chaos Expansion

2021 ◽  
Vol 2 (4) ◽  
pp. 956-975
Author(s):  
Marcel S. Prem ◽  
Michael Klanner ◽  
Katrin Ellermann
Keyword(s):  
Polynomial Chaos ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Material Model ◽  
Polynomial Chaos Expansion ◽  
Computational Technique ◽  
Chaos Expansion ◽  
Material Damping ◽  
Fractional Damping ◽  
Assembly Technique

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.

Evolutive Laws and Constitutive Relations in Nonlocal Viscoplasticity

2012 ◽  
Vol 152-154 ◽  
pp. 990-996 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Constitutive Relations ◽  
Material Model ◽  
Standard Material ◽  
Viscoplastic Model ◽  
Proposed Model

In the present work the evolutive laws and the constitutive relations for a model of nonlocal viscoplasticity are analyzed. Nonlocal dissipative variables and suitable regularization operators are adopted. The proposed model is developed within the framework of the generalized standard material model. Suitable forms of the elastic and dissipative viscoplastic potentials are defined and the associated constitutive relations are specialized. The evolutive laws for the proposed nonlocal viscoplastic model are presented in a general form which can be suitably specialized in order to include different models of nonlocal viscoplasticity.

A Nonlinear Analysis Formulation for Bend Stiffeners

2007 ◽  
Vol 51 (03) ◽  
pp. 250-258 ◽  
Author(s):  
M. A. Vaz ◽  
C. A. D. de Lemos ◽  
M. Caire
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Nonlinear Analysis ◽  
Cross Section ◽  
Contact Force ◽  
Oil And Gas ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Power Series Expansion ◽  
Gas Production

Bend stiffeners are polymeric structures with a conical shape designed to limit the curvature of flexible risers and umbilical cables at their uppermost connections, protecting them against overbending and from accumulation of fatigue damage. Thus, they are of vital importance to deep water oil and gas production systems. This work develops a mathematical formulation and a numerical solution procedure for the geometrical and material nonlinear analysis of the riser/bend stiffener system considered as a beam bending model. The structures are separately modeled, which allows the numerical calculation of the contact force along the system arc length. The governing differential equations are derived considering geometrical compatibility, equilibrium of forces and moments, and nonlinear asymmetric material constitutive relations, which leads to a shift in the neutral axis position from the cross-section centroid. The eccentricity and the bending moment versus curvature relation for each cross section are numerically calculated and then expressed by a polynomial power series expansion. A set of four first-order nonlinear ordinary differential equations is written and four boundary conditions are specified at both ends. Once the global problem is solved, the contact force may be promptly calculated. A finite difference method is implemented in Fortran code to obtain the numerical solution. A case study is carried out where linear elastic symmetric and nonlinear elastic asymmetric constitutive models are compared and discussed. The results are presented for the riser/bend stiffener deflected configuration, angle, curvature, and contact force distribution. The results demonstrate that an accurate structural analysis of bend stiffeners depends on a precise assessment of the nonlinear asymmetric polyurethane property.

scholarly journals Comparison between Duncan and Chang’s EB Model and the Generalized Plasticity Model in the Analysis of a High Earth-Rockfill Dam

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Weixin Dong ◽  
Liming Hu ◽  
Yu Zhen Yu ◽  
He Lv
Keyword(s):  
Constitutive Models ◽  
Elastic Model ◽  
Plasticity Model ◽  
Rockfill Dam ◽  
Generalized Plasticity ◽  
Rockfill Materials ◽  
Confining Pressures ◽  
Mechanical Behaviours ◽  
Nonlinear Elastic ◽  
Relationship Of

Nonlinear elastic model and elastoplastic model are two main kinds of constitutive models of soil, which are widely used in the numerical analyses of soil structure. In this study, Duncan and Chang's EB model and the generalized plasticity model proposed by Pastor, Zienkiewicz, and Chan was discussed and applied to describe the stress-strain relationship of rockfill materials. The two models were validated using the results of triaxial shear tests under different confining pressures. The comparisons between the fittings of models and test data showed that the modified generalized plasticity model is capable of simulating the mechanical behaviours of rockfill materials. The modified generalized plasticity model was implemented into a finite element code to carry out static analyses of a high earth-rockfill dam in China. Nonlinear elastic analyses were also performed with Duncan and Chang's EB model in the same program framework. The comparisons of FEM results andin situmonitoring data showed that the modified PZ-III model can give a better description of deformation of the earth-rockfill dam than Duncan and Chang’s EB model.

Computational Modeling of Interaction Between Actions and Action Effects of FPSO Topside Structures Subject to Jet Fire

2010 ◽  
Author(s):  
G. M. Katsaounis ◽  
D. Katsourinis ◽  
M. S. Samuelides ◽  
M. Founti ◽  
Jeom Kee Paik ◽  
...  
Keyword(s):  
Computational Modeling ◽  
Constitutive Relations ◽  
Finite Element Program ◽  
Effect Analysis ◽  
Ansys Cfx ◽  
Commercial Code ◽  
Time Histories ◽  
Element Program ◽  
Computational Fluid Dynamics Cfd ◽  
Nonlinear Elastic

This paper presents a computational modeling of accidental fire actions on the topside structures of a floating, production, storage and offloading (FPSO) unit. According to the assumed scenario, the accident results in a jet fire, which loads the structure by temperature increments and pressures generation on their exposed surfaces. Temperature distributions were obtained by computational fluid dynamics (CFD) simulations, using the ANSYS CFX commercial code. The temperature versus time histories computed were first approximated (idealized) by smoother curves, based on fewer time-points, while retaining the maximum and minimum values. A similar procedure was also followed for the pressure variations. For the consequence (action effect) analysis the LSDYNA nonlinear finite element program was employed and the structures were modeled using shell finite elements with nonlinear (elastic-thermal plastic) constitutive relations. On the structure surfaces non coinciding grids were used for the two kinds of analyses (i.e., the CFD and FEM), in order to accommodate the diverse requirements of the different problems. The procedure of assignment the pressure and temperature loadings directly from the CFD results to the FEM model is described and representative results are given through the application of the methodology to a sample problem.

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