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.

Stury of Post-Failure Constitutive Relation Based on SMP Criterion

2013 ◽  
Vol 790 ◽  
pp. 405-409
Author(s):  
Jian Ming Zhu ◽  
Ze Xiang Wu ◽  
Qi Zhao ◽  
Chong Yang
Keyword(s):  
Residual Stress ◽  
Elastic Modulus ◽  
Constitutive Model ◽  
Constitutive Relation ◽  
Strain Softening ◽  
Friction Angle ◽  
Peak Friction Angle ◽  
Confining Pressures ◽  
Intermediate Variables ◽  
Nonlinear Elastic

In this paper, based on SMP criteria, combination of strain softening of rock material mechanics theory, the after peak friction angleφfor the intermediate variables, the residual strainεto express the after peak nonlinear elastic modulusE, and finally establish a unified non-linear constitutive model of the rock peak residual stress. Combination Xiao Guanzhuang Eastern Mine typical breakdown rock of diorite triaxial test , get stress-strain curves for different confining pressures by this model. It shows that peak constitutive relation of this study can simulate the experimental results, prove the rationality of the model.

scholarly journals A Modified Fractional Maxwell Numerical Model for Constitutive Equation of Mn-Cu Damping Alloy

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2020
Author(s):  
Baoquan Mao ◽  
Rui Zhu ◽  
Zhiqian Wang ◽  
Yuying Yang ◽  
Xiaoping Han ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Constitutive Relation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Maxwell Model ◽  
Nonlinear Viscoelastic ◽  
Fractional Maxwell Model ◽  
Hysteretic Characteristics ◽  
Nonlinear Elastic

To better describe its constitutive relation, we need a new constitutive equation for an important nonlinear elastic material, Mn-Cu damping alloy. In this work, we studied the nonlinear and hysteretic characteristics of the stress-strain curve of the M2052 alloy with the uniaxial cyclic tensile test with constant strain rate. The strain rate and amplitude correlations of M2052 resembled those of nonlinear viscoelastic material. Therefore, we created a new constitutive equation for the M2052 damping alloy by modifying the fractional Maxwell model, and we used the genetic algorithm to carry out numerical fitting with MATLAB. By comparing with the experimental data, we confirmed that the new constitutive equation could accurately depict the nonlinear constitutive relation and hysteretic property of the damping alloy. Taken together, this new constitutive equation for Mn-Cu damping alloy based on the fractional Maxwell model can serve as an effective tool for further studies of the constitutive relation of the Mn-Cu damping alloys.

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.

Parameter Estimation of the Mechanical Behavior of the Artery Using a Nonlinear Least Square Method With a Noise Model

2008 ◽  
Author(s):  
Shahrokh Zeinali ◽  
Jongeun Choi ◽  
Seungik Baek
Keyword(s):  
Parameter Estimation ◽  
Blood Vessel ◽  
Mechanical Behavior ◽  
Constitutive Relation ◽  
Environmental Changes ◽  
Constitutive Relations ◽  
Estimation Method ◽  
Least Square ◽  
Noise Model ◽  
Bias Error

Although it is well known that blood vessels adapt and remodel in response to various biomechanical stimuli, quantifying changes in constitutive relation corresponding to environmental changes is still challenging. Especially, when the dimension of blood vessel is small, the uncertainties in experimental measurements become significant and make it difficult to precisely estimate parameters of constitutive relations for mechanical behavior of the blood vessel. Hence without considering measurement error in displacement, a conventional nonlinear least square (NLS) method results in a biased parameter estimation. In this paper, we propose a new parameter estimation method to eliminate such bias error and provide more accurate estimated parameters for a constitutive relation using a weighted nonlinear least square (WNLS) method with a noise model. We first applied the proposed technique to a set of synthesized data with computer generated white noises and compared the fitting results to those of the NLS method without the noise model. We also applied our method to experimental data sets from mechanical tests of rabbit basilar and mouse carotid arteries and studied parameter sensitivity of the constitutive model.

Simulation of Frictional Sliding Under Impact Shear Loading

2004 ◽  
Author(s):  
Demir Coker ◽  
Alan Needleman ◽  
George Lykotrafitis ◽  
Ares J. Rosakis
Keyword(s):  
Constitutive Relation ◽  
Wave Speed ◽  
Constitutive Relations ◽  
Shear Loading ◽  
Stress And Strain ◽  
Sliding Modes ◽  
Elastic Plates ◽  
Frictional Sliding ◽  
State Dependent ◽  
Dynamic Loading Conditions

Results from recent and ongoing investigations of frictional sliding under dynamic loading conditions are discussed. The configuration analyzed consists of two identical elastic plates with an interface characterized by a rate- and state-dependent frictional law. The calculations are carried out within a framework where two constitutive relations are used: a volumetric constitutive relation between stress and strain and a surface constitutive relation that characterizes the frictional behavior of the interface. The simulations discussed predict a variety of sliding modes including a crack-like mode and several pulse-like modes as well as circumstances where the sliding tip speed can exceed the longitudinal wave speed.

scholarly journals A thermodynamic basis for implicit rate-type constitutive relations describing the inelastic response of solids undergoing finite deformation

2020 ◽  
Vol 25 (12) ◽  
pp. 2222-2230
Author(s):  
David Cichra ◽  
Vít Průša
Keyword(s):  
Constitutive Relation ◽  
Finite Deformation ◽  
Constitutive Relations ◽  
Plastic Response ◽  
Inelastic Response ◽  
Perfectly Plastic ◽  
Novel Approach ◽  
Elastic Perfectly Plastic ◽  
Rate Type ◽  
Thermodynamic Basis

Implicit rate-type constitutive relations utilising discontinuous functions provide a novel approach to the purely phenomenological description of the inelastic response of solids undergoing finite deformation. However, this type of constitutive relation has so far been considered only in the purely mechanical setting, and the complete thermodynamic basis is largely missing. We address this issue, and we develop a thermodynamic basis for such constitutive relations. In particular, we focus on the thermodynamic basis for the classical elastic–perfectly plastic response, but the framework is flexible enough to describe other types of inelastic response as well.

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

1999 ◽  
Vol 122 (1) ◽  
pp. 48-50 ◽  
Author(s):  
J. Jovanovic´ ◽  
I. Otic´
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Effective Viscosity ◽  
Constitutive Relations ◽  
Reynolds Stresses ◽  
Reynolds Stress Tensor ◽  
The Mean ◽  
Mean Strain

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]

scholarly journals Elastica of Non-Prismatic and Nonlinear Elastic Cantilever Beams under Combined Loading

2019 ◽  
Vol 9 (5) ◽  
pp. 877 ◽  
Author(s):  
Joon Lee ◽  
Byoung Lee
Keyword(s):  
Cross Sections ◽  
Neutral Axis ◽  
Constitutive Law ◽  
Combined Loading ◽  
Cantilever Beams ◽  
Uniform Loading ◽  
Loading System ◽  
Beam Parameters ◽  
Nonlinear Elastic ◽  
Nonlinearly Elastic

This study presents the elastica of non-prismatic cantilever beams with rectangular cross-sections that are subjected to combined loading. The considered beams are nonlinearly elastic and obey Ludwick’s constitutive law. The combined loading system used in this study provides uniform loading, tip point loading, and tip couple loading individually or in combination. This loading system can create a total of seven loading cases that have not been covered in the literature. Ordinary differential equations governing the large deformed shapes of the elastica of the beams are derived and solved numerically. The effects of beam parameters on elastica behavior, including tip responses and strains and stresses loaded onto the cross-sections, were studied. It was observed that the exponential constant of the mechanical properties is very sensitive to elastica behavior. The results also demonstrate that the stresses near the neutral axis are larger with a larger exponential constant.

Behavior of Unidirectional Sandwich Panels With a Bi-Linear “Soft” Core: High Order Approach

2000 ◽  
Author(s):  
Hilla Schwarts-Givli ◽  
Yeoshua Frostig
Keyword(s):  
Constitutive Relation ◽  
Constitutive Relations ◽  
Order Theory ◽  
Solution Procedure ◽  
Load Level ◽  
High Order ◽  
Core Material ◽  
Normal Stresses ◽  
Convergence Criteria ◽  
Level Increase

Abstract A closed-form high-order theory for the analysis of a sandwich panel with a core made of a material characterized by a bi-linear constitutive relation is presented. The non-linearities in the core are a result of bi-linear constitutive relations of the shear and vertical normal stresses. The governing equations are non-linear in the longitudinal and in the vertical coordinates in general. The solution procedure adopted is an iterative one along with convergence criteria. The numerical examples include two types of core material behaviors; where the first one deals with a bi-linear constitutive relation for the shear stress only; and the second one with a bi-linear constitutive relation for vertical normal stresses only. The results demonstrate the relaxation of the stress concentration involves as the load level increase beyond the yielding level as the secant modulus decrease. In the sequel, a summary and conclusions are presented.

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