A membrane finite element based on position applied to the contact of fabrics with rigid surfaces

Resumo

In this paper, a total Lagrangian and position based formulation of membrane finite elements is
employed to solve dynamic problems of contact between a non-tensioned fabric and a rigid surface. The geometric
nonlinearity is naturally considered in this positional strategy, resulting in a simple description of the membrane
elements by mapping gradients for the initial and current configuration. The dynamic solution is obtained by the
classical Newmark-β method using alternative parameters to improve numerical stability in contact analysis. The
Newton-Raphson procedure is used to solve the set of nonlinear equations. To enforce contact conditions, the
penalty technique and the Lagrange multipliers are employed. A representative example for an isotropic fabric
with frictionless contact is presented and results shown that the proposed numerical approach is effective for this
class of problems, properly evaluating large displacements and dynamic draping.