Comput Mech DOI 10.1007/s00466-012-0778-7 ORIGINAL PAPER A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets Ravindra Duddu · Haim Waisman Received: 26 March 2012 / Accepted: 7 August 2012 © Springer-Verlag 2012 Abstract We present a Lagrangian finite element formu- lation aimed at modeling creep fracture in ice-sheets using nonlocal continuum damage mechanics. The proposed for- mulation is based on a thermo-viscoelastic constitutive model and a creep damage model for polycrystalline ice with dif- ferent behavior in tension and compression. In this paper, mainly, we detail the nonlocal numerical implementation of the constitutive damage model into commercial finite ele- ment codes (e.g. Abaqus), wherein a procedure to handle the abrupt failure (rupture) of ice under tension is proposed. Then, we present numerical examples of creep fracture under four-point bending, uniaxial tension, and biaxial tension in order to illustrate the viability of the current approach. Finally, we present simulations of creep crack propagation in idealized rectangular ice slabs so as to estimate calving rates at low deformation rates. The examples presented dem- onstrate the mesh size and mesh directionality independence of the proposed nonlocal implementation. Keywords Ice mechanics · Creep fracture · Anisotropic damage · Finite element simulation · Nonlocal integral R. Duddu (B ) · H. Waisman Department of Civil Engineering and Engineering Mechanics, Columbia University, 610 Seeley W. Mudd Building, 500 West 120th Street, Mail Code 4709, New York, NY 10027, USA e-mail: rduddu@gmail.com; ravidra.duddu@vanderbilt.edu Present Address: R. Duddu Department of Civil and Environmental Engineering, Vanderbilt University, 400 24th Avenue South, 274 Jacobs Hall, Nashville, TN 37212, USA 1 Introduction Creep fracture plays an important role in the calving of ice- bergs from glaciers and in the catastrophic collapse of ice- shelfs [1]. A better understanding of creep fracture mechanics is required to estimate the loss of mass from polar ice-sheets and to predict the consequent sea-level change. Field obser- vations indicate that the calving process involves initiation and propagation of large fractures or rifts in ice-sheets and ice-shelfs [2]. Current theoretical models for estimating calv- ing rates and rift propagation rates are based on linear elastic fracture analysis and so they do not consider the effects of viscoelastic creep deformation [3–7]. Computational models can help us gain new insights into the processes leading to glacial calving and ice-sheet fracture, however, the numeri- cal aspects of viscoelastic creep fracture simulation need to be addressed. Therefore, in this paper, we present a finite element formulation for modeling creep fracture based on nonlocal continuum damage theory that is applicable at low deformation rates encountered in glaciers. The material response of polycrystalline ice that consti- tutes glaciers is highly nonlinear, viscoelastic, and aniso- tropic [8]. This nonlinear behavior of ice is due to the nucleation and progressive accumulation of distributed flat and planar micro-cracks. Therefore, in the case of ice it is sufficient to consider only damage [9], unlike metals where both damage due to micro-defects and plasticity due to dis- locations needs to be considered [10]. Since it is difficult to account for the micro-cracks individually, continuum dam- age theory [11] is used to describe the creep damage and eventual rupture of ice [12–14]. Herein, we employ a creep damage model for ice, based on the Murakami model [15, 16], that captures the temperature and stress-state dependent mechanical response of ice [17]. In addition, the anisotropy 123