Simulation of Hyper-Elasticity by Shape Estimation

The simulation of complex geometries and non linear deformation has been a challenge for standard simulation methods. There has traditionally been a trade off between performance and accuracy. With the popularity of additive manufacturing and the new design space it enables, the challenges are even more prevalent. Additionally multiple additive manufacturing techniques now enable the use of hyperelastic materials as raw material for fabrication, and multi-material capabilities. This allows designers more freedom, but also introduces new challenges for control and simulation of the printed parts. In this paper, a novel approach to implementing non-linear material capabilities is devised with negligible additional computational for geometry based approaches. Material curves are fitted with a polynomial expression which can determine the tangent modulus, or stiffness, of a material based on strain energy. The moduli of all elements are compared to determine relative shape factors used to establish the blended shape of an element. This process is done dynamically to update the stiffness of a material in real-time, for any number of materials, regardless of linear or non-linear material curves.