A porosity-based model of dynamic compaction in under-dense materials

Abstract

Under-dense metals including micro-architectured structures and stochastic foams provide a combination of low weight, high strength-to-weight ratio, high permeability, and low stiffness, which make them desirable materials for a variety of applications. Specifically, their energy absorption capabilities under dynamic compressive loads are desirable. However, under high loading rates there are several challenges in performing accurate simulations of under-dense materials—primarily, the responses of materials with high, low, and zero porosity are difficult to accurately predict with a single model. A general model that tracks porosity and pore geometry and is flexible for a variety of matrix material constitutive responses has yet to be produced. This work outlines such a model and applies it to high loading rate simulations that demonstrate the model’s ability to address a variety of stress states. The approach is to extend a porosity model meant for isolated porosity of low-to-modest volume fraction to the application space of under-dense materials. Calibration parameters are used to account for complex mechanisms as well as the effects of the geometries of various under-dense materials. This results in a general, versatile, and flexible model. A study of the model’s sensitivity to calibration parameters is shown along with qualitative and quantitative comparisons to direct numerical simulations (DNS) and predictions resulting from impact velocities and flyer structures for which the model is not calibrated. This model can simulate a range of compaction conditions and is less computationally intense than direct numerical simulations which gives it utility in the design of micro-architected materials for impact mitigation, energy absorption, and other applications.