A recent (2009) Mark Horstemeyer's publication "Multiscale Modeling: A Review" gives an excellent introduction to this subject.
From the hierarchical multiscale modeling paradigm, we have developed some macroscale constitutive models that can be used in a production mode (MSU DMG Plasticity-Damage 1.0, MSF 1.0, ImageAnalyzer) and others that are research versions. The production codes have user's manuals and a theoretical manual and have been used in practice to solve complex engineering problems using finite element analysis. The codes that are research codes (EMMI, TP, etc) have not enjoyed the wealth of application and might not have a user's manual or a theoretical manual. We caution the user that there is some risk in using the research version of the codes.
The links to activities and codes for various scales can be found below:
See the complete list of codes used for multiscale simulations at CAVS, together with the documentation, instructions how to use it, and example input decks.
Some of these codes can be browsed and downloaded from our Repository of codes, under open source license.
MSU ISV Plasticity-Damage 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.
The DMG model is implemented as an ABAQUS user material (UMAT and VUMAT) subroutines for production run finite element simulations. For consistency, the same UMAT is utilized for model calibration (determining the material constants) by the DMGfit tool. The calibrated model constants can be directly merged by DMGfit into the "USER MATERIAL, CONSTANTS" section an existing ABAQUS input deck.
The DMG model in the UMAT and VUMAT codes as well as a stand-alone DMGfit tool are available from the online code repository.
A user guide for the DMGfit tool based on the updated DMG model (55p-v1p1) may be found here.
Microstructural Characterization Tool for Stereological Parameters
ImageAnalyzer is a utility for calculating some of the material microstructural quantities from an optical image of a material (only a picture is needed) that can be directly used in the MSU DMG Plasticity-Damage model 1.0 and the MultiStage Fatigue MSF 1.0 model. Groups of pixels in the image that satisfy user-specified criteria are interpreted to be objects (particles, grains, voids, etc.). Associated with each object are the following quantities: area, centroid, number density, area fraction, first nearest neighbor distance, major axis length, minor axis length, and orientation.
- The area is the number of pixels in the object.
- The centroid’s x-coordinate is calculated as the average of the x-coordinates of the pixels in the object. The y-coordinate for the centroid is found similarly.
- The number density is the count of particles, voids, etc. measured as a function of total area in the region of interest
- The area fraction is the two dimensional area of particles, voids, etc. divided by the total area in the region of interest
- The first nearest neighbor distance for an object is the distance of its centroid to the centroid of the nearest object.
- The major axis length is the length of the major axis of the ellipse that encapsulates the object.
- The minor axis length is the length of the minor axis of the ellipse.
- The orientation is the degree angle between the x-axis and the major axis of the ellipse.
The aspect ratio is the ratio of the major axis length over the minor axis length. Thus the aspect ratio is bounded below by 1, in which case the object would be a circle. Area and length are calculated in pixels; these are converted in microns and microns2 using the scale (microns per pixel) of the image.
The following material properties in the DMGfit program are derived from the above quantities:
- property(37) - particle size (dn)
- property(38) - particle volume (or area) fraction (fn)
- property(39) - coalescence factor (cd1)
- property(41) - grain size or dendrite cell size (DCS)
- property(44) - initial void volume (or area) fraction
The number density and area fraction can be used to monitor the void/crack nucleation and total damage, respectively, employed in the material model.
A stand-alone ImageAnalyzer tool are available from the online code repository. A prototype of the online version of the ImageAnalyzer tool is available as well. Please refer to the documentation (CAVS Technical Report MSU.CAVS.CMD.2007-R0039.pdf; ImageAnalyzer-Tutorial.pptx) to learn how to use this tool.
MSF is a high fidelity multistage fatigue model that predicts the number of fatigue cycles required to cause the appearance of a measurable crack. The model incorporates microstructural features to the fatigue life predictions for crack incubation, microstructurally small crack growth, and long crack growth stages in both high cycle and low cycle regimes. Section 2 provides a theoretical basis for the MSF model. Section 3 is the MSF model user's manual. Section 4 describes a software utility for calibrating the MSF model constants from experimental data. The theoretical basis of the MSF model is described in draft of the CAVS Technical Report: MSU.CAVS.CMD.2009-R0XXX.doc. The model is based upon McDowell, DL, Gall, K, Horstemeyer, MF, and Fan, J., "Microstructure-Based Fatigue Modeling of Cast A356-T6 Alloy," Engineering Fracture Mechanics, Vol. 70, pp. 49-80, 2003. The model can be used stand-alone or as a post-processor to finite element simulations. It can also admit the microstructural heterogeneities that are distributed within a structural component.
A stand-alone MSF tool is available from the online code repository. A prototype of the online version of the MSF tool is available as well. Please refer to the documentation (draft of the CAVS Technical Report: MSU.CAVS.CMD.2009-R0XXX.doc, online help and tutorial) to learn how to use this tool.
Evolving Microstructure Model of Inelasticity is described in emmi_fit.pdf is a research code and not a production code yet; EMMI is a non-dimensionalized preliminary version of the MSU DMG 1.0 production code. There will be a future production release version MSU EMMI 2.0 that will merge the MSU DMG 1.0 code with research upgrades over time.
Visco-Plastic Self-Consistent model (VPSC7b)
The VPSC model is a crystal plasticity code that is used for polycrystal analysis and is described in draft of the CAVS Technical Report: MSU.CAVS.CMD.2009-R000XX-VPSC7b_gui.docx
Recently, a modified embedded-atom method (MEAM) potential was developed for saturated hydrocarbons and hydrocarbon-based polymers, such as polyethylene and polypropylene, that would be suitable for reactive molecular dynamics simulations of these materials at the nanoscale. For more details about the potential and the C/H parameters, please visit MEAM for Hydrocarbons.
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (MSU-TP) 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. . 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  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.
- ↑ M. F. Horstemeyer, "Multiscale Modeling: A Review," Practical Aspects of Computational Chemistry", ed. J. Leszczynski and M.K. Shukla, Springer Science+Business Media, pp. 87-135, 2009
- ↑ J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA
- ↑ Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)
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