Material Model for Creep-Assisted Microcracking Applied to S2 Sea Ice

Abstract

A material model is presented that includes the following deformation mechanisms: the instantaneous response of ice due to distortion of crystal lattices, creep, the formation of microcrack nuclei due to creep, the formation of microcracks, and deformation due to microcracks. The new material model has a strict foundation on deformation mechanisms. This constitutive equation was applied to sea ice for engineering applications through implementation in the Abaqus explicit code by writing a VUMAT subroutine. The computed results show that the model correctly predicts the uniaxial tensile and the uniaxial compressive strengths of ice. The computed compressive strength versus strain-rate relation takes an almost linear relation when expressed in the log–log coordinates, which fits well with the data obtained from the literature. The material model shows the Hall–Petch type of strength dependency on the grain size.

On continuum damage mechanics

“…(4.3.6a)] shows. A similar partition is obtained for rectilinear microcracks in a two-dimensional body [12] and for penny-shaped microcracks in a three-dimensional body [30]. Based on Equations (11) and (14) where is the elastic strain tensor, is the damage strain tensor, is the ε e ε d ε sw porosity swelling strain tensor and is the inelastic strain tensor.…”

“…Model (37) 2 is valid for a Hookean matrix deformation with spherical microvoids [see Equation (20)]. According to Santaoja [11,30,36], it is valid for a Hookean matrix deformation with penny-shaped microcracks and for rectilinear microcracks in a 2D solid [12], although for these latter two cases the damage strain tensor has to be made symmetric. Therefore, Equations (38) are valid for g d these three types of material behaviours.…”

“…It can be a scalar, vector or tensor of any order. Instead of the variable , it is preferable to introduce variables that are connected to the microstructure D of the material, such as the void volume fraction , which is the topic of this f paper, and the microcrack densities introduced by Santaoja [11], [12]. Both the Q r void volume fraction and microcrack densities enter into the theory of f Q r continuum thermodynamics as internal variables, being thus a vital part of continuum thermodynamics.…”