The Consistent Kinetics Porosity (CKP) Model: A Theory for the Mechanical Behavior of Moderately Porous Solids

A theory is developed for the response of moderately porous solids (no more than {approximately}20% void space) to high-strain-rate deformations. The model is consistent because each feature is incorporated in a manner that is mathematically compatible with the other features. Unlike simple p-{alpha} models, the onset of pore collapse depends on the amount of shear present. The user-specifiable yield function depends on pressure, effective shear stress, and porosity. The elastic part of the strain rate is linearly related to the stress rate, with nonlinear corrections from changes in the elastic moduli due to pore collapse. Plastically incompressible flow of the matrix material allows pore collapse and an associated macroscopic plastic volume change. The plastic strain rate due to pore collapse/growth is taken normal to the yield surface. If phase transformation and/or pore nucleation are simultaneously occurring, the inelastic strain rate will be non-normal to the yield surface. To permit hardening, the yield stress of matrix material is treated as an internal state variable. Changes in porosity and matrix yield stress naturally cause the yield surface to evolve. The stress, porosity, and all other state variables vary in a consistent manner so that the stress remains on the yield surface throughout any quasistatic interval of plastic deformation. Dynamic loading allows the stress to exceed the yield surface via an overstress ordinary differential equation that is solved in closed form for better numerical accuracy. The part of the stress rate that causes no plastic work (i.e-, the part that has a zero inner product with the stress deviator and the identity tensor) is given by the projection of the elastic stressrate orthogonal to the span of the stress deviator and the identity tensor.The model, which has been numerically implemented in MIG format, has been exercised under a wide array of extremal loading and unloading paths. As will be discussed in a companion sequel report, the CKP model is capable of closely matching plate impact measurements for porous materials