Micromechanics Analysis Code With Generalized Method of Cells (MAC/GMC) is a comprehensive, user-friendly, efficient computer program that predicts the elastic and inelastic thermomechanical responses of continuous and discontinuous composite materials with arbitrary internal microstructures and reinforcement shapes. This program enables the efficient analysis of composite structures subjected to complex thermomechanical load histories. MAC/GMC won second place in the 1997 NASA Software of the Year competition and has been applied in industrial, government, and academic settings to such diverse composite-material structures as turbine parts, tires, and even brain tissues.

The predictive capability of MAC/GMC rests on the mathematical model known as the generalized method of cells (GMC)— a continuum-based model of micromechanics that provides closed-form expressions for the macroscopic response of a composite material in terms of the properties, sizes, shapes, and responses of the individual constituents or phases that make up the material. The viscoplastic and fatigue-life characteristics of the constituents or phases, are in turn, represented by advanced, physics-based mathematical submodels.

The GMC also incorporates expressions that relate stress and strain fields within individual constituents to macroscopically applied stresses and strains via stress-concentration factors. These expressions make possible the investigation of failure processes at the microscopic level at each step of applied-load history. The GMC also affords a capability for studying the influence of the strengths of bonds of fiber/matrix interfaces; this is an important capability because the strengths of these bonds strongly influence the progression of damage.

MAC/GMC enhances the basic capabilities of the GMC by providing a modular software framework wherein one can take advantage of any or all of the following options:

  • Various thermal, mechanical (stress or strain), and thermomechanical load histories can be imposed.
  • Different integration algorithms can be selected.
  • Any of a variety of constitutive submodels for constituent materials can be selected from a library of such models or implemented via a subroutine defined by the user.
  • Any of a variety of fiber architectures (unidirectional, laminate, and woven) can be selected from a library of representative volume elements or be defined by user.
  • A postprocessing subprogram for graphical display of microscopic and macroscopic field quantities is available (MACPOST).

The most outstanding feature of MAC/GMC is its ability to accurately model composites with laminated and woven fiber architectures at minimal cost and with minimal input by the user. MAC/GMC can be executed in conjunction with standard linear and nonlinear finite-element analysis programs for cost-effective design and analysis of large structures, including fully time-dependent deformation behavior of constituents. It is also possible to model porosity, damage, interfacial regions around inclusions, and deterioration of interfaces. Multiaxial states of stress or strain can be applied and predicted accurately, regardless of the orientations of fibers.

One advantage of the use of constitutive submodels is that any type of simple or combined loading (e.g., multiaxial stress) can be applied, irrespective of symmetry or asymmetry, and without resorting to different boundary-condition application strategies. An analytical macro elastic-thermo-inelastic constitutive law offers the advantage of reducing the amount of memory needed in a finite-element structural-analysis code; it also enables coupling of optimization algorithms with the solution for automated tailoring of the material and structure under analysis. Furthermore, this formulation has been shown to predict macroscopic behavior accurately, given only a few subcells within a repeating cell.

This work was done by Steven M. Arnold of Glenn Research Center, Brett A. Bednarcyk of Ohio Aerospace Institute, and Thomas E. Wilt and Daniel E. Trowbridge of the University of Akron. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Machinery/Automation category.

Inquiries concerning rights for the commercial use of this invention should be addressed to

NASA Glenn Research Center
Commercial Technology Office
Attn: Steve Fedor
Mail Stop 4 —8
21000 Brookpark Road
Cleveland
Ohio 44135.

Refer to LEW-16870


NASA Tech Briefs Magazine

This article first appeared in the June, 2000 issue of NASA Tech Briefs Magazine.

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