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This paper introduces a continuum mechanics based thread model for use in real-time simulation. The model includes both rotary inertia, shear deformation and torsion. It is based on a three-dimensional beam model, using a corotational approach for interactive simulation speeds as well as adaptive mesh resolution to maintain accuracy. Desirable aspects of this model from a numerical and implementation point of view include a true constant and symmetric mass matrix, a symmetric and easily evaluated tangent stiffness matrix, and easy implementation of time-stepping algorithms. From a modeling perspective interesting features are deformation of the thread cross section and the use of arbitrary cross sections without performance penalty.

A family of continuous piecewise linear finite elements for thin plate problems is presented. We use standard linear interpolation of the deflection field to reconstruct a discontinuous piecewise quadratic deflection field. This allows us to use discontinuous Galerkin methods for the Kirchhoff-Love plate equation. Three example reconstructions of quadratic functions from linear interpolation triangles are presented: a reconstruction using Morley basis functions, a fully quadratic reconstruction, and a more general least squares approach to a fully quadratic reconstruction. The Morley reconstruction is shown to be equivalent to the Basic Plate Triangle. Given a condition on the reconstruction operator, a priori error estimates are proved in energy norm and L2 norm. Numerical results indicate that the Morley reconstruction/Basic Plate Triangle does not converge on unstructured meshes while the fully quadratic reconstruction show optimal convergence.