Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Robust Solution Procedure for Hyperelastic Solids with Large Boundary
  Deformation   Compressible Mooney-Rivlin theory has been used to model hyperelastic solids,
such as rubber and porous polymers, and more recently for the modeling of soft
tissues for biomedical tissues, undergoing large elastic deformations. We
propose a solution procedure for Lagrangian finite element discretization of a
static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the
case in which the boundary condition is a large prescribed deformation, so that
mesh tangling becomes an obstacle for straightforward algorithms. Our solution
procedure involves a largely geometric procedure to untangle the mesh: solution
of a sequence of linear systems to obtain initial guesses for interior nodal
positions for which no element is inverted. After the mesh is untangled, we
take Newton iterations to converge to a mechanical equilibrium. The Newton
iterations are safeguarded by a line search similar to one used in
optimization. Our computational results indicate that the algorithm is up to 70
times faster than a straightforward Newton continuation procedure and is also
more robust (i.e., able to tolerate much larger deformations). For a few
extremely large deformations, the deformed mesh could only be computed through
the use of an expensive Newton continuation method while using a tight
convergence tolerance and taking very small steps.

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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga