Simulation of Elastic Membranes with Triangulated Spring Meshes UCSC-CRL-97-12

Spring meshes have been used to model elastic material by numerous researchers, with skin, textiles, and soft tissue being typical applications. However, given a speci ed set of elastic material properties, the question of whether a particular spring mesh accurately simulates those properties, has been largely ignored in the literature. In two dimensions, given a discretization of a membrane as a triangle mesh, the standard nite element method analyzes each triangle approximately as a membrane with speci ed 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 sti ness to the various springs. This paper shows that assigning the same sti ness to all springs badly fails to simulate a uniform elastic membrane, for equilibrium calculations. A formula for spring sti ness that provides a more accurate simulation is then derived. Its accuracy is demonstrated on test and practical mesh examples. It is also shown that an exact simulation is not possible, in general.