With a basis of previously developed upper bound analysis, the conditions required for homogeneous deformation in a composite material tensile specimen are determined. As in the earlier work, relative strength of reinforcing particles, particle-matrix bonding, geometry variations, environmental pressure, and the possibility of void formation are all included in the analysis. The necessary conditions for homogeneous deformation are provided as explicit expressions for allowable ranges of relative particle strength and relative environmental pressure. A detailed procedure for graphical presentation is provided and examples are used to demonstrate the application and typical results.

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