SBIR-STTR Award

This proposal presents two novel approaches for the modeling of interface and interphase phenomena in composite material systems. From the computational perspective new developments include integration of Discontinuous Galerkin ideas with the variational multiscale finite element methods for a precise description of the fiber-matrix interface. The second approach is developed for a mixture theory that is governed by a homogenized set of equations. A two-level split of the deformation map into an elastic component and a phase/damage evolution component leads to two-level description with embedded interphases and damage evolution, leading to fatigue and failure. These methods possess enhanced stability properties as compared to the standard Galerkin methods, and a built-in error estimation module that helps distinguish modeling errors from numerical errors, a feature that is not present in any of the competing numerical method currently available. Another significant feature of our methods is the notion of maximization of entropy production that yields the driving criterion for damage evolution. A third significant feature is that both methods accommodate p-refinement feature that leads to higher than quadratic convergence in the L2 norm with quadratic or higher interpolation functions.

Benefit:
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Keywords:
Mixture Theory, Chemical Kinetics, Maximization Of Entropy Production, Damage And Fatigue, Finite Element Method, Variational Multiscale Method, Sinc Method, Error Estimation

This proposal presents two novel approaches for characterizing manufacturing induced damage in fibrous composites. New developments include integration of discontinuous Galerkin ideas with the variational multiscale finite element methods for the modeling of interface and interphase phenomena in these material systems. The second approach is developed for a mixture theory that is governed by a homogenized set of equations. A two-level split of the deformation map into an elastic component and a phase/damage evolution component leads to two-level description with embedded interphases and damage evolution. These methods possess enhanced stability properties as compared to the standard Galerkin methods, and they come equipped with built-in error estimation modules that help distinguish modeling errors from numerical errors. A significant feature of our methods is a thermodynamically consistent damage driving criterion that relates interphase damage to fatigue life prediction in composites. Both methods accommodate p-refinement feature that leads to higher than quadratic convergence in the L2 norm with quadratic or higher interpolation functions.

Benefit:
The SBIR program emphasizes that the research and development effort should lead to a marketable product. With that in view, Advanced Computational Technology will perform code development parts of phase II in a modular form that can be integrated with other commercial finite element analysis packages via the User Defined Modular Interconnects. This will help in easy transfer of the developed technology to practical application in the industry. With the advanced solutions that our methods will facilitate, with integrated graphics tools for easy visualization and comprehension of the intricate stress fields, and with the orders-of-magnitude effect of the interphase on the fatigue life of fibrous composites, these computational tools will help optimize the composite manufacturing processes adopted in the industry. We anticipate that these tools will be of great interest to the aerospace, defense and sports industry.

Keywords:
Fibrous Composites, Interface And Interphase, Phase Change And Damage Evolution, Chemical Reactions And Thermal Effects, Mixture Models, Multiscale Finite Element Methods, Err