To characterize the response of progressively damaged glassy polymers due to the presence and evolution of voids, yield functions and flow rules were developed systematically for a pressure-dependent matrix following the modified von Mises criterion. A rigid-perfectly plastic material was first assumed. The upper bound method was used with a velocity field which has volume preserving and shape changing portions. Macroscopic yield criterion in analytical closed form was first obtained for spherical voids which is valid for all possible macroscopic strain rate fields. Macroscopic yield criteria in analytical closed form were then obtained for cylindrical voids for the special cases of axisymmetric and plane-strain modes of deformation. The upper-bound solutions were subsequently improved to better match analytical solutions for pure hydrostatic loading. Characteristics of the yield function as a function of pressure dependency and void fraction were studied in detail. Generalization of the model for spherical voids to include elasticity as well as strain hardening of the matrix was then obtained. An example for the uniaxial response of a progressively damaged material was then used to illustrate one possible application of the full set of constitutive equations. [S0021-8936(00)02902-0]
Yield Functions and Flow Rules for Porous Pressure-Dependent Strain-Hardening Polymeric Materials
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Dec. 15, 1998; final revision, June 22, 1999. Associate Technical Editor: A. K. Mal. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Lee, J. H., and Oung, J. (June 22, 1999). "Yield Functions and Flow Rules for Porous Pressure-Dependent Strain-Hardening Polymeric Materials ." ASME. J. Appl. Mech. June 2000; 67(2): 288–297. https://doi.org/10.1115/1.1305278
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