近些年，基于物理的弹性体仿真成为计算机图形学的研究热点。有限元仿真由于其仿真结果真实感强，逐渐变得流行，广泛应用在计算机动画、影视特效、电子游戏、虚拟现实中。弹性体的形变仿真，其形变效果很大程度取决于弹性体的材料模型。然而，几乎所有的应用都集中在常见的超弹性材料模型，包括非线性St.VenantKirchhoff材料、非线性Neohookean材料、共旋线性材料等。尽管我们可以通过设计材料的参数，如杨氏模量、泊松系数获得多样的超弹性材料，但是这种方法却是十分限制的。

为了获得更加丰富的真实的材料，本文介绍了一种稳定的超弹性材料设计方法。
本文首先介绍了一种分离形式的材料本构模型。由于分离形式的材料本构模型在物理解释和数学计算上都有着很好的优势，这使得材料设计更加方便。
但是，随意设计材料很容易导致形变体不稳定、仿真失败等问题，所以本文研究的关键在于设计稳定的超弹性材料。基于此目的，本文首先提出了材料稳定性条件。
并且，围绕着材料稳定性条件，本文给出了有效的用户友好的材料设计方法，可以更加直观方便地设计出稳定的超弹性材料。
由于真实世界的材料更多的是各向异性材料，本文进一步给出了稳定的正交异性材料设计方法。

此外，基于分离形式的材料本构模型，本文也讨论了鲁棒的基于分离形式的材料本构模型的有限元仿真方法，使得本文所设计的材料可以正确稳定的仿真。

最后，本文通过多组实验以及对比实验证明了本文方法的有效性正确性，可以设计出稳定的超弹性材料。

Recently, physically-based simulation of 3D elastic objects has become a hotspot in computer graphics. The Finite Element Method (FEM) has evolved into a popular tool for simulation of deformable objects in many applications, such as computer animation, special effects in movies, computer games and virtual reality because of its strong simulation results. The deformation effect of the elastomer depends largely on the material. However, almost all applications focus on standard elastic materials, including nonlinear St.VenantKirchhoff, nonlinear Neohookean and corotated linear materials, based on which only the material properties of Young’s modulus and Poisson’s ratio can be adjust to produce limited deformation effects.

In order to obtain more realistic and interesting deformation behavior, we introduce a convenient and intuitive method to model new materials. In this paper, we first introduce a separable material constitutive model, which have a certain attraction from both the physical and mathematical perspectives and makes material modeling more convenient. However, the casual modeling of materials can easily lead to deformation of the instability, simulation failure and other issues. So, we focus on how to design stable materials and propose a list of material stabilization conditions. Moreover, we give a useful and user-friendly way to satisfy the conditions. As the materials in real world are usually anisotropic materials, we gives a method of modeling stable orthotropic materials.

In addition, we argue robust stretch-based FEM simulations for large deformation with our modeled nonlinear isotropic and orthotropic materials.

Lastly, we prove the validity of the proposed method by multiple experiments and comparative experiments and we can model stable hyperelastic materials.