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A new concept of dynamic potential (macrostress potential or macrostrain-rate potential), which has two components, i.e., deformation and kinetic potentials for heterogeneous materials under intense dynamic loading, is proposed using a micromechanical approach. In particular, for voided nonlinear materials, the approximate expression of the macrostress potential is derived through an upper bound approach. Simplified physical models for ductile porous materials (aggregates of voids and ductile matrix) are employed with the matrix material taken as power-law thermal viscoplastic and incompressible. Approximate velocity fields for the matrix are adopted to derive the dynamic loading criterion and an approximate functional form of the dynamic loading criterion is developed. The inertial, rate sensitivity, and thermal effects are directly included in the expressions of the macrostress potential and the dynamic loading function. Various features of the loading function are numerically investigated in detail. Numerical analysis reveals that both the dynamic growth of voids and the loading surface have strong rate dependence and temperature dependence. Experimental data, theoretical analysis, and numerical modeling indicate that the inertial and thermal effects play a very important role in the dynamic behavior of the voided nonlinear materials. © 1997 American Institute of Physics.