A plastic-damage material model for foam concrete under blast loads

Abstract

Foam concrete is a prospective material in defense engineering to protect structures subjected to intense dynamic loadings such as impact and blast through wave impedance mismatch as well as energy absorption. In the near-field of intense dynamic loadings, the foam concrete is always suffered from a high-pressure stress state associating with complex failures such as pore collapse, shear fracture and tensile fracture. A well-established material model is needed to capture above-mentioned behaviors. In this paper, a plastic-damage material model for foam concrete is proposed focused on its mechanical behavior under high pressures. Firstly, a closed form yield function, a partially-associative flow rule and a new piecewise hardening law are introduced. The yield function is composed of a fracture function describing the mechanical behavior due to microcracks and a continuous cap function describing the mechanical behavior due to pores. The partially-associative flow rule is used to avoid the overestimation of plastic strain induced by the classical associative flow rule. In particular, a new piecewise hardening law is proposed instead of frequently-used exponential ‘‘crush curve’’, which is flexible for fitting test data and can capture the experimentally-observed increase of unloading bulk modulus with increase of pressure. The rate dependency of yield surface is considered to capture the strain-rate effect of foam concrete. And then three independent damage indexes with clear physical background are proposed to describe irreversible degradation caused by microcrack growth and pore collapse. The shear damage caused by shear cracks, tensile damage caused by tensile cracks, and hydrostatic compression damage caused by pore collapse, are separately identified and proposed in the framework of continuum damage mechanics. The proposed model is embedded into the LS-DYNA through the subroutine of user-defined material model. Its performances for predicting complex failures under various stress states at a Gaussian point level are numerically evaluated using a single element, and further used to predict blast response of foam concrete. All the numerical predictions agree with test data well.