scholarly journals An alternative approach to finite deformation

2018 ◽  
Vol 16 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Marina Trajkovic-Milenkovic ◽  
Otto Bruhns
Keyword(s):  
Constitutive Relations ◽  
Time Derivative ◽  
Distinctive Features ◽  
Eulerian Description ◽  
Objective Time ◽  
Alternative Approach ◽  
Rate Form ◽  
Objective Rate ◽  
Finite Elastoplasticity ◽  
Objective Rates

In elastoplasticity formulation constitutive relations are usually given in rate form, i.e. they represent relations between stress rate and strain rate. The adopted constitutive laws have to stay independent in relation to the change of frame of reference, i.e. to stay objective. While the objectivity requirement in a material description is automatically satisfied, in an Eulerian description, especially in the case of large deformations, the objectivity requirement can be violated even for objective quantities. Thus, instead of a material time derivative in the Eulerian description objective time derivatives have to be implemented. In this work the importance of the objective rate implementation in the constitutive relations of finite elastoplasticity is clarified. Likewise, it shows the overview of the most frequently used objective rates nowadays, their advantages and shortcomings, as well as the distinctive features of the recently introduced logarithmic rate.

Application of Objective Rates in Mechanical Modeling of Solids

1996 ◽  
Vol 63 (3) ◽  
pp. 692-698 ◽  
Author(s):  
W. D. Reinhardt ◽  
R. N. Dubey
Keyword(s):  
Simple Shear ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Logarithmic Strain ◽  
Mechanical Modeling ◽  
Rigid Plastic ◽  
Eulerian Strain ◽  
Objective Rate ◽  
Simple Shear Deformation ◽  
Objective Rates

A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underlying concepts, and allows new rates to be constructed. Mathematical and thermodynamical restrictions on these are shown. As a result, it can be demonstrated that the Eulerian strain rate is an objective rate of logarithmic strain, based on a spin easily derivable from the general form. Interrelations between other known spins and objective rates emerge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latter involving purely isotropic and purely kinematic hardening. The application of the resulting models to the simple shear deformation is shown.

scholarly journals AN OBJECTIVE EXPLICIT FORMULATION BASED ON THE OLDROYD-B CONSTITUTIVE EQUATION

2004 ◽  
Vol 3 (1) ◽  
pp. 36
Author(s):  
G. Mompean ◽  
R. L. Thompson ◽  
P. R. Souza Mendes
Keyword(s):  
Relative Rate ◽  
Time Derivative ◽  
Three Dimensional ◽  
Normal Stress Difference ◽  
Viscoelastic Flows ◽  
Differential Model ◽  
Explicit Formulation ◽  
Objective Time ◽  
Extra Stress ◽  
Good Agreement

In the present paper is shown how to obtain an objective explicit algebraic extra-stress model (AESM) based on differential constitutive equations for viscoelastic flows (Oldroyd B, White-Metzner, Phan-Thien-Tanner, etc). The formulation is developed for three-dimensional time-dependent flows. In a previous work, Mompean, 1998 obtained a non-objective algebraic model. This inconsistency is now removed introducing the relative-rate-ofrotation tensor making the model frame-invariant. A new generalized objective time derivative is also introduced, giving flexibility to the model. Calculations are performed with an Oldroyd B based AESM for a 4:1 contraction flow, showing good agreement with the original constitutive differential model. Several results with particular derivatives are obtained and an analysis guided by a flow type classifier is given. This formulation is able to include a prediction, not present in the Oldroyd B model, the viscometric second normal stress difference, N2.

scholarly journals A Meshless Finite-Point Approximation for Solving the RLW Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
L. Pérez Pozo ◽  
R. Meneses ◽  
C. Spa ◽  
O. Durán
Keyword(s):  
Finite Difference ◽  
Numerical Solution ◽  
Time Derivative ◽  
Mass Energy ◽  
Finite Point ◽  
Long Wave ◽  
Rlw Equation ◽  
Alternative Approach ◽  
Spatial Derivatives ◽  
Energy And Momentum

An alternative meshless finite-point method (FPM) technique for the numerical solution of the Regularized long wave (RLW) equation is presented. In this context, we derive the discretized system by combining finite difference (FD) techniques for the time derivative and FPM for the spatial derivatives. The accuracy of this alternative approach is tested withL2,L∞error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

scholarly journals Mesoscale Simulation to Study Constitutive Properties of TATB/F2314 PBX

Materials ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 3767 ◽  
Author(s):  
Siyu Ge ◽  
Wenying Zhang ◽  
Jian Sang ◽  
Shuai Yuan ◽  
Glenn V. Lo ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Constitutive Relations ◽  
Numerical Data ◽  
Material Point ◽  
Mesoscale Simulation ◽  
Stress Strain ◽  
Simulation Data ◽  
Alternative Approach ◽  
Strain Data ◽  
Different Temperatures

Material Point Method (MPM) mesoscale simulation was used to study the constitutive relation of a polymer bonded explosive (PBX) consisting of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) and a fluorine polymer binder F2314. The stress-strain variations of the PBX were calculated for different temperatures and different porosities, and the results were found to be consistent with experimental observations. The stress-strain relations at different temperatures were used to develop the constitutive equation of the PBX by using numerical data fitting. Stress-strain data for different porosities were used to establish the constitutive equation by fitting the simulation data to an improved Hashion-Shtrikman model. The equation can be used to predict the shear modulus and bulk modulus of the PBX at different densities of the sample. The constitutive equations developed for TATB/F2314 PBX by MPM mesoscale simulation are important equations for the numerical simulations of the PBX at macroscale. The method presented in this study provides an alternative approach for studying the constitutive relations of PBX.

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