Simulation of Hyperelasticity 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 allow 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 computations for geometry-based methods. 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 an element's blended shape. This process is done dynamically to update a material's stiffness in real-time, for any number of materials, regardless of linear or non-linear material curves.