scholarly journals Constitutive relations for materials with strain state dependent properties

2021 ◽  
pp. 52-62
Author(s):  
E. V Lomakin ◽  
P. V Tishin
Keyword(s):  
Stress Tensor ◽  
Constitutive Relations ◽  
Strain Tensor ◽  
Experimental Studies ◽  
Mechanical Tests ◽  
Analytical Treatment ◽  
Proportional Loading ◽  
Defining Relations ◽  
State Dependent ◽  
Uniqueness Of The Solution

Many materials demonstrate a dependence of mechanical properties on the type of stressed or deformed states. This is most noticeable in the dependence of the processes of shear and bulk deformation. Such materials include rocks, structural graphite, concrete, some grades of steel, cast iron, and aluminum. The main properties of these materials are an absence of a "single curve" relationship between the intensity of stresses and the intensity of deformations. Under shear conditions, bulk deformations can occur. Such materials can be described by constitutive equations that depend on the parameter of the type of a stress state, which is the ratio of the first invariant of the stress tensor to the stress intensity. Thus, these defining relations give the dependence of the strain tensor components on the stress tensor components. Such defining relations can be quite cumbersome, and therefore do not allow an analytical treatment to obtain defining relations that give the dependence of the components of the stress tensor on the components of the strain tensor. The paper proposes the constitutive relations obtained from the analysis of test results of various materials, which properties depend on the type of deformed state. Conditions are derived for material constants that ensure the uniqueness of the solution of boundary value problems. Based on experimental data obtained under the conditions of the proportional loading of various rocks: limestone and talcochlorite, as well as the results of mechanical tests of several grades of concrete, the constants of the mathematical model are determined. The results of the experimental studies are compared with theoretical dependencies predicted by the model. The limited applicability of the proposed constitutive relations is established.

Towards a Unified Solution Method for Fluid-Structure Interaction Problems: Progress and Challenges

2006 ◽  
Author(s):  
G. Papadakis ◽  
C. G. Giannopapa
Keyword(s):  
Stress Tensor ◽  
Solution Method ◽  
Constitutive Relations ◽  
Fluid Structure Interaction ◽  
Strain Tensor ◽  
Internal Stresses ◽  
Fluid Structure ◽  
Structure Interaction ◽  
The Difference ◽  
Fundamental Equations

The paper presents the progress in the development of a novel unified method for solving coupled fluid-structure interaction problems as well as the associated major challenges. The new approach is based on the fact that there are four fundamental equations in continuum mechanics: the continuity equation and the three momentum equations that describe Newton’s second law in three directions. These equations are valid for fluids and solids, the difference being in the constitutive relations that provide the internal stresses in the momentum equations: in solids the stress tensor is a function of the strain tensor while in fluids the viscous stress tensor depends on the rate of strain tensor. The equations are written in such a way that both media have the same unknown variables, namely the three velocity components and pressure. The same discretisation technique (finite volume) and solution method (segregated approach) are used irrespective of the medium. Also the same methodology to handle the pressure-velocity coupling is employed. A common set of variables as well as a unified discretisation and solution method leads to a strong coupling between the two media and is very beneficial for the robustness of the algorithm. Significant challenges include the derivation of consistent boundary conditions for the pressure equation in boundaries with prescribed traction as well as the handling of discontinuity of pressure at the fluid-structure interface.

Torsion of a Viscoelastic Cylinder

2000 ◽  
Vol 67 (2) ◽  
pp. 424-427 ◽  
Author(s):  
R. C. Batra ◽  
J. H. Yu
Keyword(s):  
Stress Tensor ◽  
Constitutive Relation ◽  
Linear Relation ◽  
Constitutive Relations ◽  
Strain Tensor ◽  
Time History ◽  
Cauchy Stress ◽  
Kirchhoff Stress Tensor ◽  
History Of ◽  
Energy Dissipated

Finite torsional deformations of an incompressible viscoelastic circular cylinder are studied with its material modeled by two constitutive relations. One of these is a linear relation between the determinate part of the second Piola-Kirchhoff stress tensor and the time history of the Green-St. Venant strain tensor, and the other a linear relation between the deviatoric Cauchy stress tensor and the left Cauchy-Green tensor, its inverse, and the time history of the relative Green-St. Venant strain tensor. It is shown that the response predicted by the latter constitutive relation is in better agreement with the test data, and this constitutive relation is used to compute energy dissipated during torsional oscillations of the cylinder. [S0021-8936(00)00502-X]

A note on the wave equation for a class of constitutive relations for nonlinear elastic bodies that are not Green elastic

2016 ◽  
Vol 23 (2) ◽  
pp. 148-158 ◽  
Author(s):  
R Meneses ◽  
O Orellana ◽  
R Bustamante
Keyword(s):  
Wave Equation ◽  
Stress Tensor ◽  
Constitutive Relations ◽  
Strain Tensor ◽  
Nonlinear Function ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Travelling Wave ◽  
Elastic Bodies ◽  
New Type

A class of constitutive relations for elastic bodies has been proposed recently, where the linearized strain tensor is expressed as a nonlinear function of the stress tensor. Considering this new type of constitutive equation, the initial boundary value problem for such elastic bodies has been expressed only in terms of the stress tensor. In this communication, this new type of nonlinear wave equation is studied for the case of a one-dimensional straight bar. Conditions for the existence of the travelling wave solutions are given and some self-similar solutions are obtained.

scholarly journals DEFORMATION MONITORING OF RETROFITTED SHORT CONCRETE COLUMNS WITH LASER SENSOR

2016 ◽  
Vol XLI-B5 ◽  
pp. 765-769
Author(s):  
E. Ö. Avsar ◽  
M. F. Celik ◽  
E. Binbir ◽  
A. E. Arslan ◽  
D. Çokkeçeci ◽  
...  
Keyword(s):  
Laser Scanning ◽  
Reference Sample ◽  
Experimental Studies ◽  
Construction Materials ◽  
Mechanical Tests ◽  
Deformation Monitoring ◽  
Laser Sensor ◽  
Scanning Method ◽  
Compression Load ◽  
Short Columns

This paper presents one of the applications of monitoring mechanical tests carried out in Construction Materials Laboratory of Istanbul Technical University. In Turkey, as in many countries, large amount of existing buildings exposed to seismic hazard, therefore various analytical and experimental studies are being conducted to contribute to the solution of the problem. One of the new generation retrofitting techniques is to strength the structural members by using Fiber Reinforcing Polymer (FRP). This study summarize the results of monitoring of deformations short concrete column samples under the incremental compression load. In this study, result of two rectangular short columns are given. One of them was tested as a reference sample, the other sample were tested after strengthening by PET reinforced polymer composite materials. Besides conventional displacement and strain measurement systems, laser scanning method was used to get three dimensional deformed shape of sample at each selected steps.

scholarly journals On continuum damage mechanics

2019 ◽  
Vol 52 (3) ◽  
pp. 125-147
Author(s):  
Kari Juhani Santaoja
Keyword(s):  
Stress Tensor ◽  
Effective Stress ◽  
Elastic Strain ◽  
Damage Mechanics ◽  
Volume Fraction ◽  
Strain Tensor ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
The Matrix ◽  
Elastic Strain Tensor

A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fraction f , which has a clear physical meaning, and the elastic strain tensor \Bold {ε}^e with the damage-elastic strain tensor \Bold {ε}^{de}. The postulate of strain equivalence with the effective stress concept was reformulated and applied to a case where the response of the matrix obeys Hooke’s law. In contrast to many other studies, in the derived relation between the effective stress tensor \Bold {\Tilde{σ}} and the stress tensor \Bold {σ}, the tensor \Bold {\Tilde{σ}} is symmetric. A uniaxial bar model was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.

Constitutive Modeling of Asphalt Bound Granular Materials: Applications to Sand Asphalt

2002 ◽  
Author(s):  
J. Murali Krishnan ◽  
K. R. Rajagopal
Keyword(s):  
Granular Materials ◽  
Asphalt Concrete ◽  
Constitutive Modeling ◽  
Hot Mix Asphalt ◽  
Constitutive Relations ◽  
Experimental Studies ◽  
Compressive Creep ◽  
Multiple Natural Configurations

In the earlier paper, we developed constitutive relations for two kinds of hot mix asphalt, viz., asphalt concrete and sand asphalt using the framework of materials with multiple natural configurations. In the present paper, we apply the framework that we developed for sand asphalt to study compressive creep experiments. Experimental studies of Wood and Goetz (1959) are used to compare with the predictions of the 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 Contributions of Strain Energy and PV-work on the Bending Behavior of Uncoated Plain-woven Fabric Air Beams

2007 ◽  
Vol 2 (1) ◽  
pp. 155892500700200 ◽  
Author(s):  
Paul V. Cavallaro ◽  
Ali M. Sadegh ◽  
Claudia J. Quigley
Keyword(s):  
Strain Energy ◽  
Constitutive Relations ◽  
Mechanical Tests ◽  
Woven Fabric ◽  
Beam Model ◽  
Bending Performance ◽  
Macro Scale ◽  
Beam Bending ◽  
Bending Behavior ◽  
Homogenization Methods

The bending performance of fabric air beams varies significantly from conventional beams. Both are dependent upon the constitutive relations of the material, but air beams are further dependent upon the thermodynamics of the internal air. As the governing energy balance demonstrates, air beam bending is dependent upon strain energy and PV-work (air compressibility). The relative importance of these terms will vary with pressure, volume changes and shear deformations. To this point, a swatch of uncoated plain-woven fabric was subjected to mechanical tests and its material properties determined. Attempts at using the stress-strain measurements in air beam models, assumed constructed with the same fabric, were made. The models accounted for fluid-structure interactions between the air and fabric. Homogenization methods were used and were necessary to provide computational efficiencies for the macro-scale air beam model while attempts were made to incorporate the combined extension and shear behaviors observed during the material tests. Bending behavior was numerically investigated for several constitutive cases. The models were solved with the ABAQUS-Explicit program over a range of pressures. The fabric strain energy and PV-work were tracked and compared. It was concluded that strain energy and PV-work must be considered in deflection analyses of uncoated plain-woven fabric air beams.

Wolff’s Law of Trabecular Architecture at Remodeling Equilibrium

1986 ◽  
Vol 108 (1) ◽  
pp. 83-88 ◽  
Author(s):  
S. C. Cowin
Keyword(s):  
Stress Tensor ◽  
Bone Tissue ◽  
Constitutive Relation ◽  
Cancellous Bone ◽  
Strain Tensor ◽  
Constitutive Relationship ◽  
Trabecular Architecture ◽  
Fabric Tensor ◽  
Principal Axes ◽  
Wolff’S Law

An elastic constitutive relation for cancellous bone tissue is developed. This relationship involves the stress tensor T, the strain tensor E and the fabric tensor H for cancellous bone. The fabric tensor is a symmetric second rank tensor that is a quantitative stereological measure of the microstructural arrangement of trabeculae and pores in the cancellous bone tissue. The constitutive relation obtained is part of an algebraic formulation of Wolff’s law of trabecular architecture in remodeling equilibrium. In particular, with the general constitutive relationship between T, H and E, the statement of Wolff’s law at remodeling equilibrium is simply the requirement of the commutativity of the matrix multiplication of the stress tensor and the fabric tensor at remodeling equilibrium, T* H* = H* T*. The asterisk on the stress and fabric tensor indicates their values in remodeling equilibrium. It is shown that the constitutive relation also requires that E* H* = H* E*. Thus, the principal axes of the stress, strain and fabric tensors all coincide at remodeling equilibrium.

Sign in / Sign up

Export Citation Format

Share Document