1. Damage and Optimization Models for Analysis and Design of Discontinuous Fiber Composite Structures Ba Nghiep Nguyen Acknowledgements: PNNL’s Computational Science Engineering Initiative – Korolev Vladimir, Brian Tucker (contributors) NSF/DOE/APC Workshop: Future of Modeling in Composites Molding Processes (Design & Optimization Session), June 9-10, 2004, Arlington, Virginia

2. 2 Damage and Optimization Models for Analysis and Design of Discontinuous Fiber Composite Structures Acoustic emission techniques to identify damage Model validation Damage & failure analyses A multiscale mechanistic approach to damage based on micromechanical and continuum damage mechanics descriptions An optimization approach using the optimal control theory accounting for the composite microstructure An experimental procedure for acquiring acoustic emission signals to identify damage PNNL has developed:

3. 3 Damage and Optimization Models for Analysis and Design of Discontinuous Fiber Composite Structures Optimal Control Theory Approach to Short-Fiber Composites Fiber volume fractions Fiber aspect ratios Fiber orientation parameter Optimization of fiber orientation distribution for the plate under tensile loading. The orientations are planar with density: λ Optimizer Using sequential linear programming Determines optimum Finite Element Analysis Resolution of direct & adjoint equations Stress/strain computation Micromechanics Stiffness calculation Derivative of stiffness Derivative Calculator Lagrange Functional Stationarity conditions

4. 4 Current State of the Art in Design and Optimization of Discontinuous Fiber Composites Elastic analysis-based design Micromechanical models rely on material database (fiber volume fraction, aspect ratio, orientation distribution, etc.) to predict effective properties Process modeling to predict fiber orientation Control of process and microstructural parameters to improve composite stiffness Elastic finite element analysis of the as-formed composite structure Nonlinear analysis based design: Phenomenological models rely on material database and testing of specimens Nonlinear micromechanical models derived from the self-consistent and Mori- Tanaka frameworks (e.g. elastic-plastic, damage, creep) PNNL damage models using a multiscale mechanistic approach ORNL micromechanical models Formal optimization methods Only at the beginning Duvaut et al. (2000). “Optimization of Fiber Reinforced Composites,” Composite Structures, 48, 83-89 PNNL optimization model using the optimal control theory

5. 5 Vision on Future Directions Design & optimization methods should be reliable to effectively assist processing & manufacturing of composite components and parts Development of new process and constitutive models accounting for the constituents’ characteristics and properties, and their interaction with each other Interface between process modeling and structural modeling to create and design a composite part through simulations Processing & manufacturing can rely on efficient design & optimization methods rather than on trial-and-error approaches Reduce the number of experimental tests and trial moldings Process modeling Structural modeling Manufacturing

6. 6 Perceived Gaps Where we are now Micromechanical models predict elastic properties and some nonlinear responses Process models provide qualitative predictions of fiber orientations in injection molding Phenomenological constitutive models exist in commercial FE codes for structural analyses Limited interface between process and structural modeling Analysis and design are still based on intensive material database obtained through experiments Initiation of multiscale mechanistic models based on micromechanics and continuum mechanics Where we should be… Accurate micromechanical models accounting for concentrated fiber volume fractions Accurate process models for short- and long-fiber thermoplastic injection molding Constitutive physics-based models for predicting durability and time- dependent behavior Interface between process and structural modeling for linear and nonlinear analyses Optimization methods accounting for process, design and loading variables and constraints Analysis and design should rely on reliable physics-based models to assist processing & manufacturing

7. 7 Research Thrusts Micromechanics Process micromechanics: Effects of fiber content, length on the rheology and fiber orientation Micromechanics of materials: Homogenization accounts for interaction between constituents and defects Continuum mechanics: Need of constitutive models for Fatigue Time dependent behaviors (creep, relaxation,..) Impact Moisture Optimization models accounting for nonlinear behaviors Minimization of damage Improvement of durability (fatigue, creep) Multi-scale modeling From a microstructural to a continuum model