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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.

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).

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. 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.

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.

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.

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.

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 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.

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.

MSU DMG v1.0 is an example of a plasticity-damage internal state variable model, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the Image Analysis tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.

A video tutorial for calibrating DMG is found here.

The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:- one element compression for aluminum A356 (ABAQUS-Implicit)
- one element compression for aluminum A356 (ABAQUS-Explicit)
- one element tension for aluminum A356 (ABAQUS-Implicit)
- one element tension for aluminum A356 (ABAQUS-Explicit)
- one element simple shear for aluminum A356 (ABAQUS-Implicit)
- one element simple shear for aluminum A356 (ABAQUS-Explicit)

One element explicit compression A356 input decks Model Validation simulations include the following: notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit).

The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') here, or can be viewed online by clicking 'view' for each of the files.

The macroscale tools also include fatigue analysis tools. One example is the MultiStage Fatigue (MSF) model, which also admits microstructural information to help quantify the number of cycles for crack incubation, the number of cycles in the Microstructurally Small Crack (MSC) regime, and the number of cycles in the long crack (LC) regime. The amount of cycles that is experienced in each regime depends on the manufacturing process and the type of material.

MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.

One element tension for Polycarbonate (ABAQUS-Explicit)

To learn how to use the parameters fitting routine, you can refer to the documentation (TPGui User Manual, TPGui Tutorial).

A stand-alone TP tool is available from the online code repository. Please refer to the documentation (online help and tutorial) to learn how to use this tool.