Bending models for thin flexible objects

Abstract

Textiles usually exhibit much larger resistance to in-plane deformation than to bending deformation. However, the latter essentially determines the formation of folds and wrinkles which in turn govern the overall appearance of the cloth. The resulting numerical problem is inherently stiff and hence susceptible to instability. This overview is devoted to a closer investigation of bending deformation. Approaches known from the field of engineering can describe the problem of bending in a physically accurate way. However, the nature of the governing equations is such that they cannot be discretised with the standard methods currently used in cloth simulation. Since curvature is a central variable, we introduce related concepts from differential geometry and describe the transition to the discrete setting. Different approaches are discussed and demands on an approach for correctly modelling the bending behaviour of cloth are formulated.