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• Side impact on an ice island drifting ice floes. A strike from the side of the island
is modeled.
The results are recorded in the form of two-dimensional patterns of the distribution
of elastic wave velocities in the medium, the components of the stress tensor, as well
as the Mises stresses in the plane of the drilling well. Then the data obtained can
be used for a detailed analysis of the results and their visual display in the form of
two-dimensional visualizations.
13.3 Mathematical Model and Numerical Method
In this section, we consider a methodology of the problem solution. In Sect. 13.3.1, the
mathematical model is represented. Section 13.3.2 is devoted to numerical method,
while Sect. 13.3.3 is about the boundary and contact boundary conditions used in
problem. The criterion of ice island destruction is described in Sect. 13.3.4, while
Sect. 13.3.5 is devoted to the drill model used in problem with drill strikes.
13.3.1 Linear Elastic Medium Model
A complete system of equations of state of a continuous linear elastic medium and
an acoustic field is solved [12].
ρ
∂ V i
∂t
=
∂ T ji
∂ x j
,
∂ T i j
∂t
= λ
k
∂ V k
∂ x k
I i j + μ
∂ V i
∂ x j
+
∂ V j
∂ x i
,
where V i is the velocity components, T ji is the components of tension tensor, ρ is the
density of medium, λ and μ are the Lame coefficients, and I ij is the component of
unit tensor. Using vector of variables
u =
V x , V y , V z , T xx , T yy , T zz , T xy , T xz , T yz
,
the equation system we can represent as
∂
u
∂t
+
i=1,2,3
A i
∂
u
∂ξ i
= 0.