Abstract: This paper presents a new, physically based model for performing finite element simulation of deformable objects in which all quantities - strain, stress, displacement, etc. - are computed entirely in local frames of reference. In our framework, subdivision solids with non-homogeneous material properties, such as mass and deformation distributions, can be defined throughout continuous, volumetric domains. This capability enables an animator or virtual sculptor to exert fine-level control over deforming objects and to define a wide variety of physical behaviors. Furthermore, since all quantities pertinent to physical simulation are computed locally, our model facilitates both large-scale and small-scale deformations, as well as rigid or near-rigid transformations. We demonstrate applications of our framework in animation and interactive sculpting and show that interactive simulation of non-trivial, volumetric shapes is possible with our methodologies.