scholarly journals A model for magneto-elastic behaviour

2017 ◽  
Vol 50 (3) ◽  
pp. 349-352
Author(s):  
Saivash Danaee ◽  
Reijo Kouhia ◽  
Paavo Rasilo ◽  
Anouar Beloahcen ◽  
Deepak Singh ◽  
...  
Keyword(s):  
Total Energy ◽  
Constitutive Equations ◽  
Strain Tensor ◽  
Elastic Behaviour ◽  
State Variables ◽  
Electric Steel ◽  
Material Parameters ◽  
Green Strain ◽  
Lagrangian Form

In this paper, a coupled magnetoelastic model for isotropic ferromagnetic materialsis presented. The constitutive equations are written on the basis of the total energy in whichthe right Cauchy-Green strain tensor and the Lagrangian form of the magnetic eld strengthare used as the basic state variables. It is also applied to ferromacnetic electric steel for whichthe material parameters are calibrated.

Measurement and Calibration of the Parameters of Hypoplasticity Model for an Iraqi Soil

2020 ◽  
Vol 857 ◽  
pp. 243-252
Author(s):  
Aysar Hassan Subair ◽  
Ala Nasir Aljorany
Keyword(s):  
Constitutive Model ◽  
Void Ratio ◽  
Initial Stresses ◽  
Model Parameters ◽  
State Variables ◽  
Soil Behavior ◽  
Dense Sand ◽  
Hypoplastic Model ◽  
Material Parameters ◽  
Wide Range

There are many constitutive models that have been used to model the mechanical behavior of soils. Some of these models are either unable to represent important features such as the strain softening of dense sand or required many parameters that can be hard to obtain by standard laboratory tests. Because of that, a more reliable constitutive model, which is capable to capture the main features of the soil behavior with easily obtained parameters, is required. The Hypoplasticity model is considered as a promising constitutive model in this respect. It is considered as a particular class of rate non-linear constitutive model at which the stress increment is expressed in a tensorial equation as a function of strain increment, actual stress, and void ratio. The hypoplastic model required only eight material parameters (critical friction angle critical, maximum and minimum void ratio respectively), granular stiffness hs and the model constants n, α, β). The appealing feature of the hypoplastic model is that the material parameters are separated from the state variables (void ratio and the initial stresses). This feature enables the model to simulate the soil behavior under a wide range of stresses and densities with the same set of material parameters. In this research, a brief description of the Hypoplasticity model is presented. Detailed discussions regarding the measurement and calibration of the model parameters of an Iraqi soil are then exposed. It is concluded that only Consolidated Drained (CD) triaxial test, oedometer test, and the well-known limit density tests are needed to get all the parameters of the hypoplasticity model.

scholarly journals On nonlinear thermo-electro-elasticity

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160170 ◽  
Author(s):  
Markus Mehnert ◽  
Mokarram Hossain ◽  
Paul Steinmann
Keyword(s):  
Boundary Value Problem ◽  
Total Energy ◽  
Constitutive Equations ◽  
Cylindrical Tube ◽  
Polymeric Materials ◽  
Temperature History ◽  
Internal Temperature ◽  
Laws Of Thermodynamics ◽  
Electric Loads ◽  
Coupled Loads

Electro-active polymers (EAPs) for large actuations are nowadays well-known and promising candidates for producing sensors, actuators and generators. In general, polymeric materials are sensitive to differential temperature histories. During experimental characterizations of EAPs under electro-mechanically coupled loads, it is difficult to maintain constant temperature not only because of an external differential temperature history but also because of the changes in internal temperature caused by the application of high electric loads. In this contribution, a thermo-electro-mechanically coupled constitutive framework is proposed based on the total energy approach. Departing from relevant laws of thermodynamics, thermodynamically consistent constitutive equations are formulated. To demonstrate the performance of the proposed thermo-electro-mechanically coupled framework, a frequently used non-homogeneous boundary-value problem, i.e. the extension and inflation of a cylindrical tube, is solved analytically. The results illustrate the influence of various thermo-electro-mechanical couplings.

Rheological Equations for Synovial Fluids

1978 ◽  
Vol 100 (4) ◽  
pp. 169-186 ◽  
Author(s):  
W. M. Lai ◽  
S. C. Kuei ◽  
V. C. Mow
Keyword(s):  
Constitutive Equations ◽  
Synovial Joint ◽  
Integral Type ◽  
Material Parameters ◽  
Material Functions ◽  
Synovial Fluids ◽  
Joint Biomechanics ◽  
Differential Type ◽  
The Many ◽  
Rate Type

This review examines a number of theoretical constitutive equations which are applicable to the description of rheological behaviors of synovial fluids. These equations include the integral type, the rate type, the differential type and the generalized new-tonian fluid. Explicit values of the material parameters and/or material functions appearing in these equations are obtained from the many rheological measurements on synovial fluids of the literature. Many of the values of these parameters are taken from the literature, but some are newly computed values obtained by the present authors to make the list of available constitutive equations more extensive, using the existing experimental data. It is hoped that the diversity of the constitutive equations presented here and their appropriate material constants and/or functions will afford researchers in the field of synovial joint biomechanics the choice of a particular constitutive model for synovial fluid to meet their specific purpose.

Constructing Poisson and Dissipative Brackets of Mixtures by using Lagrangian-to-Eulerian Transformation

2010 ◽  
Vol 26 (2) ◽  
pp. 219-228
Author(s):  
K.-C. Chen
Keyword(s):  
Evolution Equations ◽  
Poisson Brackets ◽  
State Variables ◽  
Component Mixture ◽  
Dissipative Part ◽  
Canonical Variables ◽  
Lagrangian Variable ◽  
Two Component ◽  
Lagrangian Form

AbstractThis paper aims to construct the bracket formalism of mixture continua by using the method of Lagrangian- to-Eulerian (LE) transformation. The LE approach first builds up the transformation relations between the Eulerian state variables and the Lagrangian canonical variables, and then transforms the bracket in Lagrangian form to the bracket in Eulerian form. For the conservative part of the bracket formalism, this study systematically generates the noncanonical Poisson brackets of a two-component mixture. For the dissipative part, we deduce the Eulerian-variable-based dissipative brackets for viscous and diffusive mechanisms from their Lagrangian-variable-based counterparts. Finally, the evolution equations of a micromorphic fluid, which can be treated as a multi-component mixture, are derived by constructing its Poisson and dissipative brackets.

On a class of non-dissipative materials that are not hyperelastic

2008 ◽  
Vol 465 (2102) ◽  
pp. 493-500 ◽  
Author(s):  
K.R Rajagopal ◽  
A.R Srinivasa
Keyword(s):  
Physical Meaning ◽  
Constitutive Equations ◽  
Mechanical Response ◽  
Mass Density ◽  
Cauchy Stress ◽  
Response Functions ◽  
State Variables ◽  
Hyperelastic Materials ◽  
Current Mass ◽  
Helmholtz Potential

The purpose of this brief note is to develop fully Eulerian, implicit constitutive equations for the mechanical response of a class of materials that do not dissipate mechanical work in any process. We show that such materials can be modelled by obtaining a form for the Helmholtz potential as a function of the current mass density, the Cauchy stress and certain other parameters that capture anisotropic response. The resulting constitutive equations are of the form , where and are functions of the state variables of the system. The class of materials that can be obtained from such a constitutive relation is considerably more general than conventional Green-elastic hyperelastic materials. Such response functions may be suitable for the modelling of biological tissue where, due to the constant remodelling that takes place, there may be no physical meaning to a ‘reference configuration’.

Anisotropic Behavior of White Matter in Shear and Implications for Transversely Isotropic Models

2013 ◽  
Author(s):  
Ruth J. Okamoto ◽  
Yuan Feng ◽  
Guy M. Genin ◽  
Philip V. Bayly
Keyword(s):  
White Matter ◽  
Strain Tensor ◽  
Experimental Studies ◽  
Transversely Isotropic ◽  
Stretch Ratio ◽  
Fiber Axis ◽  
Fiber Direction ◽  
Material Models ◽  
Green Strain ◽  
The Brain

Experimental studies [1] have shown that white matter (WM) in the brain is mechanically anisotropic. Based on its fibrous structure, transversely isotropic (TI) material models have been suggested to capture WM behavior. TI hyperelastic material models involve strain energy density functions that depend on the I4 and I5 pseudo-invariants of the Cauchy-Green strain tensor to account for the effects of stiff fibers. The pseudo-invariant I4 is the square of the stretch ratio in the fiber direction; I5 contains contributions of shear strain in planes parallel to the fiber axis. Most, if not all, published models of WM depend on I4 but not on I5.

Modelling of Cyclic Plasticity and Viscoplasticity of Directionally Solified DZ125 Superalloy: Part I: Estimating the Parameters of Chaboche Constitutive Equations

2011 ◽  
Vol 295-297 ◽  
pp. 854-858
Author(s):  
Jie Qiong Li ◽  
Li Jun Wang
Keyword(s):  
Constitutive Model ◽  
Test Data ◽  
Creep Test ◽  
Constitutive Equations ◽  
Least Square ◽  
Cyclic Plasticity ◽  
Initial Material ◽  
Material Parameters ◽  
Cyclic Relaxation ◽  
Least Square Procedure

Cyclic plasticity and viscoplasticity of directionally solified superalloy, DZ125, have been described using the Chaboche unified constitutive model. A set of initial material parameters has been determined utilizing the monotonic, cyclic, relaxation and creep test data of DZ125 at 980°C, while an optimum set of material parameters has been obtained by means of least-square procedure.

Comparison of Material Flow Stress Models toward More Realistic Simulations of Friction Stir Processes of Mg AZ31B

2014 ◽  
Vol 783-786 ◽  
pp. 2239-2243 ◽  
Author(s):  
Ali H. Ammouri ◽  
Ramsey F. Hamade
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Constitutive Equations ◽  
Material Model ◽  
The State ◽  
Stir Zone ◽  
State Variables ◽  
Material Models ◽  
Friction Stir ◽  
Comparison Results

Utilizing a proper material model for describing the mechanical behavior of any material is key for a successful simulation of friction stir processing (FSP) where temperature, strain, and strain rate gradients vary abruptly within, and when moving away, from the stirring zone. This work presents a comparison of how faithfully do three different constitutive equations reproduce the state variables of strain, strain rate, and temperature in an FEM simulation of a test-case FSP (1000 rpm spindle speed, and 90 mm/min feed). The three material models considered in this comparison are namely: Johnson-Cook (JC), Sellars-Tegart (ST), and Zerilli-Armstrong (ZA). Constants for these constitutive equations are obtained by fitting these equations to experimental mechanical behavior data collected under a range of strain rates and temperatures of twin-rolled cast wrought AZ31B sheets.It is widely recognized that JC-based models over predicts stress values in the stir zone whereas ST-based models are incapable of capturing work hardening outside of the stir zone. Therefore, a ZA model, being a physical based-HCP specific model, is hereby investigated for its suitability as a material model that would overcome such drawbacks of JC-and ST-based models. The equations from the constitutive models under consideration are fed into an FEM model built using DEFORM 3D to simulate the traverse phases of a friction stir process. Amongst these three material models, comparison results suggest that the HCP-specific ZA model yield better predictions of the state variables: strain, strain rate, and temperature, and, consequently, the estimated values for flow stresses.

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