The inclusion of this framework will make the
generation of more complex simulations possible, in
which the interaction of diverse models (organs) that
act together can be possible and, in this manner, de
sign simulations with major impact in the medical
area, such as the extraction of a tumor or the fully
physical modeling of one part of the body.
ACKNOWLEDGEMENTS
We would like to thank SOFA Team for the help they
bring. We also Graham Maslin for sharing the scalpel
model.
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APPENDIX A. EXTENDED FINITE
ELEMENT METHOD (XFEM)
The main idea of exploiting the partition of unity
property is to construct basis functions through prod
ucts of classical shape functions and a local enriched
basis; allowing to generate discontinuous elements.
Hence, the equation of the displacements can be cal
culated as
u(x) =
n
∑
i=1
Φ
i
(x)u
i

{z }
classical
+
n
∑
j=1
Φ
j
(x)ψ
j
(x)a
j
 {z }
enrichment
(7)
where Φ
i
(x) are the clasical shape functions; the
discontinuous enrichment functions are denoted by
ψ
j
(x), and the new nodal DOFs as a
j
. The enrich
ment function ψ(x) can be any discontinuous func
tion; commonly, it is the Heaviside function (Eq. 8),
another option is the shifted function deﬁned in Eq. 9.
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