07/01/1997 09:00 AM
Computer Science
Spring meshes have been used to model elastic material by numerous researchers, with skin, textiles, and soft tissue being typical applications. However, given a specified set of elastic material properties, the question of whether a particular spring mesh accurately simulates those properties, has been largely ignored in the literature. Indeed, from the finite element literature, it would appear that, even for a uniform, isotropic elastic membrane, such a simulation is generally impossible. In two dimensions, given a discretization of a membrane as a triangle mesh, the standard finite element method analyzes each triangle approximately as a membrane with specified elastic properties, computing stresses and strains. An alternative is to regard each edge as a spring, assuming the springs are connected by \"pin-joints\" at the vertices of the discretization. This alternative, called a \"spring mesh\", is computationally more attractive. Previous reports on the technique are silent on the subject of assigning stiffness to the various springs. This paper shows that assigning the same stiffness to all springs fails to simulate a uniform elastic membrane, for equilibrium calculations. A formula for spring stiffness that provides an accurate simulation is then derived.
