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 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.

Rubber Composition–Properties Relationships during Tire Numerical Simulation and Design Optimization

2017 ◽  
Vol 45 (1) ◽  
pp. 71-84 ◽  
Author(s):  
Alexey Mazin ◽  
Alexander Kapustin ◽  
Mikhail Soloviev ◽  
Alexander Karanets
Keyword(s):  
Numerical Simulation ◽  
Design Optimization ◽  
Strain Tensor ◽  
General Purpose ◽  
Orthogonal Functions ◽  
Element Analysis ◽  
Time Investment ◽  
Footprint Analysis ◽  
Composition Properties ◽  
Nonlinear Elastic

ABSTRACT Numerical simulation based on finite element analysis is now widely used during the design optimization of tires, thereby drastically reducing the time investment in the design process and improving tire performance because it is obtained from the optimized solution. Rubber material models that are used in numerical calculations of stress–strain distributions are nonlinear and may include several parameters. The relations of these parameters with rubber formulations are usually unknown, so the designer has no information on whether the optimal set of parameters is reachable by the rubber technological possibilities. The aim of this work was to develop such relations. The most common approach to derive the equation of the state of rubber is based on the expansion of the strain energy in a series of invariants of the strain tensor. Here, we show that this approach has several drawbacks, one of which is problems that arise when trying to build on its basis the quantitative relations between the rubber composition and its properties. An alternative is to use a series expansion in orthogonal functions, thereby ensuring the linear independence of the coefficients of elasticity in evaluation of the experimental data and the possibility of constructing continuous maps of “the composition to the property.” In the case of orthogonal Legendre polynomials, the technique for constructing such maps is considered, and a set of empirical functions is proposed to adequately describe the dependence of the parameters of nonlinear elastic properties of general-purpose rubbers on the content of the main ingredients. The calculated sets of parameters were used in numerical tire simulations including static loading, footprint analysis, braking/acceleration, and cornering and also in design optimization procedures.

Constitutive Relations and Parameter Estimation for Finite Deformations of Viscoelastic Adhesives

2015 ◽  
Vol 82 (2) ◽  
Author(s):  
G. O. Antoine ◽  
R. C. Batra
Keyword(s):  
Constitutive Relation ◽  
Axial Strain ◽  
Constitutive Relations ◽  
Finite Deformations ◽  
Low Velocity Impact ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Cauchy Stress ◽  
Peak Strain ◽  
Material Parameters

We propose a constitutive relation for finite deformations of nearly incompressible isotropic viscoelastic rubbery adhesives assuming that the Cauchy stress tensor can be written as the sum of elastic and viscoelastic parts. The former is derived from a stored energy function and the latter from a hereditary type integral. Using Ogden’s expression for the strain energy density and the Prony series for the viscoelastic shear modulus, values of material parameters are estimated by using experimental data for uniaxial tensile and compressive cyclic deformations at different constant engineering axial strain rates. It is found that values of material parameters using the loading part of the first cycle, the complete first cycle, and the complete two loading cycles are quite different. Furthermore, the constitutive relation with values of material parameters determined from the monotonic loading during the first cycle of deformations cannot well predict even deformations during the unloading portion of the first cycle. The developed constitutive relation is used to study low-velocity impact of polymethylmethacrylate (PMMA)/adhesive/polycarbonate (PC) laminate. The three sets of values of material parameters for the adhesive seem to have a negligible effect on the overall deformations of the laminate. It is attributed to the fact that peak strain rates in the severely deforming regions are large, and the corresponding stresses are essentially unaffected by the long time response of the adhesive.

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.

Nonisothermic Finite Deformations of Hypoelastic Bodies

2016 ◽  
Vol 08 (08) ◽  
pp. 1650099 ◽  
Author(s):  
Yuri Astapov ◽  
Glagolev Vadim ◽  
Khristich Dmitrii ◽  
Markin Alexey ◽  
Sokolova Marina
Keyword(s):  
Variational Formulation ◽  
Deformation Process ◽  
Strain State ◽  
Constitutive Relations ◽  
Finite Deformations ◽  
Reference Configuration ◽  
Deformation Characteristics ◽  
Equilibrium Flow ◽  
Variational Form ◽  
Axisymmetric Bodies

Variational formulation of a coupled thermomechanical problem of anisotropic solids for the case of nonisothermal finite deformations in a reference configuration is shown. The formulation of the problem includes: a condition of equilibrium flow of a deformation process in the reference configuration; an equation of a coupled heat conductivity in a variational form, in which an influence of deformation characteristics of a process on the temperature field is taken into account; constitutive relations for a thermohypoelastic material; kinematic and evolutional relations; initial and boundary conditions. The obtained solutions show the development of stress–strain state and temperature changing in axisymmetric bodies in the case of finite deformations.

Nonlinearly Elastic Constitutive Relation of Anisotropic Aggregate of Cube Crystallites

2020 ◽  
Vol 842 ◽  
pp. 160-167
Author(s):  
Lang Wu ◽  
Ru Yu Yan ◽  
Jun Yao Cai ◽  
Hao Li
Keyword(s):  
Constitutive Relation ◽  
Texture Coefficient ◽  
Constitutive Relations ◽  
Cubic Crystallites ◽  
Voigt Model ◽  
Nonlinear Elastic ◽  
Nonlinearly Elastic

Under Voigt model, Barsch and Johnson gave the formula of nonliearly elastic constitutive relations for isotropic aggregates of cubic crystallites and orthorhambic aggregates of cubic crystallies, respectively. In this paper, a nonlinear elastic constitutive relation based on Voigt model, which is more general than Barsch's and Johnson's results, is derived for the set of anisotropic cubic grains. The anisotropy of metals is described by the texture coefficient.

Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains

2003 ◽  
Vol 70 (6) ◽  
pp. 809-816 ◽  
Author(s):  
V. A. Levin ◽  
K. M. Zingermann
Keyword(s):  
Plane Strain ◽  
Constitutive Equations ◽  
Rigid Motion ◽  
Finite Deformations ◽  
Finite Strains ◽  
Effective Characteristics ◽  
Elastic Materials ◽  
Preliminary Loading ◽  
Nonlinear Elastic

A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane strain, when pores are distributed uniformly.

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