Constitutive modeling for high strain rate behavior of ice incorporating a brittle damage response

A great deal of research has been done over the years to study ice as a structural material and several researchers report its mechanical properties in different strain rate regimes, but only a limited amount of data is available in the high strain rate regime, as this area is relevant only to aerospace safety assessments. The Columbia Space Shuttle tragedy motivated a large-scale safety review against the damage of Space Shuttles due to ice or hail impacts. Experiments to study the damage caused by ice to the aircraft structure are very expensive and time consuming considering the wide range of strain rates and velocities. Therefore finite element analysis is a very useful tool to study the behavior of ice and its impacts on aircraft components. The objective of the present work is to develop a constitutive model for ice to study its behavior in the high strain rate regime (within ?10?;2-?10?;4/s)and also to incorporate the brittle damage response observed in ice. The constitutive model of ice in the present work is based on the model proposed by Sain & Narasimhan [16], which captures several significant properties of ice such as strain rate effect and asymmetries in tensile and compressive strength. The damage model incorporated in the constitutive model is based on the model proposed by Ortiz et al. [12], which is an elastic damage model originally adapted from the model used to capture the brittle cracking response in concrete. The model consists of an equivalent strain based damage initiation criterion which is made strain rate dependent using a power law. Later, depending on whether the damage is induced due to tensile or compressive stress separate exponential evolution laws are introduced in the model once the damage initiation occurs. The model is implemented in commercial finite element package ABAQUS and various simulations are performed under uniaxial tension and compression stress states to assess the performance of the constitutive model and also the model predictions are compared with experimental data. A parametric study is performed on the damage model to understand the influence of various damage parameters on the response of ice.