About Built-in Time Domain Simulation Models

Time Domain Simulation Models

In the time domain, there are five available deformation modes for you to choose from: Uniaxial, Biaxial, Planar, Simple Shear and, Volumetric. When you select a deformation mode during test data import you are choosing a built-in simulation model that will be available for calibration. The figure below illustrates the directions of the nominal stresses and strains for the Uniaxial, Biaxial, Planar and, Simple Shear and the uniform stretches for the Volumetric mode.

The table below contains a list of labels for the stress and strain symbols in the figure. The convention used in the Material Calibration app is that the transverse and lateral directions are respectively aligned with the global 2- and 3-directions.

Table 1. Stress and Strain Labels
Symbol	Label
$ϵ_{U}$	Nominal Uniaxial Strain
$T_{U}$	Nominal Uniaxial Stress
$ϵ_{P}$	Nominal Planar Strain
$T_{P}$	Nominal Planar Stress
$ϵ_{B}$	Nominal Biaxial Strain
$T_{B}$	Nominal Biaxial Stress
$J$	Volume Ratio
$p$	Pressure
$γ$	Nominal Shear Strain
$T_{S}$	Nominal Shear Stress
$T_{L}$	Nominal Lateral Stress
$ϵ_{L}$	Nominal Lateral Strain
$T_{T}$	Nominal Transverse Stress
$ϵ_{T}$	Nominal Transverse Strain

The simulations for all the deformation modes are based upon a homogenous deformation. This is typically a good assumption for isotropic materials or orthotropic materials whose primary directions align with the deformation field with a reasonable amount of deformation. For test data that includes inhomogeneous deformation, such as plastic necking, a FE-based model might be more appropriate, otherwise you should remove the test data past necking from the set before running a calibration in non FE-based mode.

Uniaxial Deformation Mode

The Uniaxial deformation mode simulates a standard uniaxial test. The simulation is driven by the imported uniaxial strain as a function of time. Conditions of zero stress in the transverse and lateral directions and zero shear strains are enforced.

In numerical execution mode the available responses from the simulation are the uniaxial stress and nominal lateral strain. The analytical execution mode supports uniaxial stress response, but the nominal lateral strain is only available for hyperfoam materials. During a calibration, the objective function is a measure of the difference between the active imported response test data and the computed responses from the simulation.

Biaxial Deformation Mode

The Biaxial deformation mode simulates a standard biaxial test. The simulation is driven by the imported biaxial strain as a function of time. The strain in the transverse direction is constrained to be equal to the biaxial strain, i.e., $ϵ_{T} = ϵ_{B}$ Conditions of zero stress in the lateral direction and zero shear strains are enforced.

In numerical execution mode the available responses from the simulation are the biaxial stress and nominal lateral strain. The analytical execution mode supports biaxial stress response, but the nominal lateral strain is only available for hyperfoam materials. During a calibration, the objective function is a measure of the difference between the active imported response test data and the computed responses from the simulation.

Planar Deformation Mode

The Planar deformation mode simulates a standard planar test. The simulation is driven by the imported planar strain as a function of time. Conditions of zero strain in the transverse direction, zero stress in the lateral direction, and zero shear strains are enforced.

In numerical execution mode the available responses from the simulation are the planar stress and nominal lateral strain. The analytical execution mode supports planar stress response, but the nominal lateral strain is only available for hyperfoam materials. During a calibration, the objective function is a measure of the difference between the active imported response test data and the computed responses from the simulation.

Simple Shear Deformation Mode

The Simple Shear deformation mode simulates a standard simple shear test. The simulation is driven by the imported nominal shear strain as a function of time. Conditions of zero strain in the transverse and lateral directions and zero shear strains in the global 13- and 23-directions are enforced.

In numerical execution mode the available responses from the simulation are the nominal shear stress and nominal lateral stress. The analytical execution mode supports nominal shear stress response, but the nominal lateral stress is only available for hyperfoam materials. During a calibration, the objective function is a measure of the difference between the active imported response test data and the computed responses from the simulation.

Volumetric Deformation Mode

The Volumetric deformation mode simulates a standard volumetric test. The simulation is driven by the imported volume ratio as a function of time. The volume ratio is due to a uniform compressive stretch ( $λ_{V}$ ) that is enforced in all three directions. Conditions of zero shear strains are enforced.

In numerical execution and analytical execution modes the available response from the simulation is the pressure. During a calibration, the objective function is a measure of the difference between the imported pressure test data and the computed pressure from the simulation.