### Overview

The Macroscale is a continuum point, where one develops the constitutive model
for the structural scale finite element simulations and is able
to downscale by defining the requirements and admitting the subscale
information with the use of internal state variables. We are concerned here
with model calibration, model validation, and experimental stress-strain
curves. Model calibration is related to correlating constitutive model
constants with experimental data from homogeneous stress states like uniaxial
compression. Model validation is related to comparing predictive results with
experimental results that arise from heterogeneous stress states like a notch
tensile test. Experimental stress-strain curves can include different strain
rates, temperatures, and stress states (compression, tension, and torsion).

The macroscale can also be thought to apply to cyclic behavior like fatigue.
Here there is also model calibration, model validation, and experimental data.
Model calibration is related to strain-life curves (or stress-life curves).
Model validation is related to mean stress effects and multi-axial stress
states.

Finally, to garner more information about the information bridges between
length scales go to the

ICME Education page.

#### Human Head/Brain Models

The Mississippi State University Brain model uses an elastic viscoplastic
material model to capture the rate dependent nonlinear behavior of the human
brain (Prabhu et al “Coupled experiment/finite element analysis on the
mechanical response of porcine brain under high strain rates” Journal of the
Mechanical Behavior of Biomedical Materials). This brain model has been
calibrated to high rate testing of porcine tissue and used to optimize helmet
performance (K.L. Johnson et al, “Constrained topological optimization of a
football helmet facemask based on brain response” Materials & Design).

#### Internal State Variable Plasticity-Damage (MSU ISV-DMG) Model

The Mississippi State University Internal State Variable (ISV)
plasticity-damage model (DMG) production version 1.0
is being released along with its model calibration tool (DMGfit). The model
equations and material model fits are explained in CAVS Technical Report:
MSU.CAVS.CMD.2009-R0010.pdf. This model is based upon Bammann, DJ, Chiesa, ML,
Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite
Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and
Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and
Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State
Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and
Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity
and failure in a metal alloy. It can be initialized to have different
heterogeneous microstructures within the finite element mesh.

#### Johnson-Cook Flow Stress (JC) Model

The Johnson-Cook (JC) constitutive model is an empirically based flow model
originally intended for the prediction of inelastic deformation in solid
materials. The Johnson-Cook plasticity model has terms that account for the
strain hardening, strain rate, and temperature sensitivity of a material. The
Johnson-Cook model has been extended to account for damage progression based
upon strain rate, temperature, and pressure conditions.

#### Mechanical Threshold Stress (MTS) Model

The Mechanical Threshold Stress (MTS) Model is a flow stress model that
considers the effects of dislocation motion and interaction on macroscale
deformation. The MTS model proposes the use of the mechanical threshold
stress (described as the material flow stress at 0K) as an internal state
variable. The MTS is formulated as a combination of dislocation mechanisms
generation and recovery, strain rate, and temperature terms. The MTS variable
is related to the flow stress of the material in conjunction with strain-rate
dependent scaling factors thus capturing and relating the internal microscale
evolution of the material to the macroscale stress-strain material behavior.

#### MultiStage Fatigue (MSF) Model

The multi-stage fatigue (MSF) model predicts the amount of fatigue cycling
required to cause the appearance of a measurable crack, the crack size as a
function of and loading cycles. The model incorporates microstructural features
to the fatigue life predictions for incubation, microstructurally small crack
growth, and long crack growth stages in both high cycle and low cycle regimes.

#### ThermoPlastic Internal State Variable (TP-ISV) Model

The Mississippi State University Internal State Variable (ISV) model for
thermoplastics (TPISV) version 1.0 is being released along with its model
calibration tool (TPfit). The model equations and material model fits are
decribed in Bouvard et al. [2010][14]. This polymer based ISV model is able to
capture the history effects of a thermoplastic polymer tested under different
stress states and strain rates. The modeling approach follows current
methodologies used for metals [15] based on a thermodynamic approach with
internal state variables. Thus, the material departs from spring-dashpot based
models generally used to predict the mechanical behavior of polymers. To select
the internal state variables, we have used a hierarchical multiscale approach
for bridging mechanisms from the molecular scale (see Atomistic Deformation of Amorphous Polyethylene) to the
continuum scale. The continuum constitutive model applied a formalism using a
three-dimensional large deformation kinematics and thermodynamics framework.
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations
were then simplified to the one-dimensional case in order to fit the model
parameters using MATLAB software.

#### WARP3D - Open Source Code for 3D Nonlinear Analysis of Solids

WARP3D is a research code for the solution of
large-scale, 3-D solid models subjected to static and dynamic loads. The
capabilities of the code focus on fatigue & fracture analyses primarily in
metals.

#### Zerilli-Armstrong Flow Stress (ZA) Model

The Zerilli-Armstrong (ZA) model is a flow stress model based upon dislocation
mechanics. The ZA plasticity model accounts for the effects of temperature
and strain rate while also considering contribution of dislocation density,
microstructural stress intensity, and material grain size. Material parameters
within the ZA model are dependent upon the crystalline structure of the
material.