Isotropic hyper-elasticity, altogether with the equilibrium equations and the usual boundary conditions, are formulated directly on the body ℬ, a three-dimensional compact and orientable manifold with boundary equipped with a mass measure. Pearson–Sewell–Beatty pressure potential on the boundary is recovered, using the Poincaré formula. The existence of such a potential requires conditions, which are formulated as non-holonomic constraints on the configuration space.

中文翻译：

---

超弹性、压力势和非完整约束的内在几何公式

各向同性超弹性与平衡方程和通常的边界条件一起直接在主体 ℬ 上制定，这是一个三维紧凑且可定向的流形，其边界配备了质量度量。使用庞加莱公式恢复边界上的 Pearson-Sewell-Beatty 压力势。这种潜力的存在需要条件，这些条件被表述为对配置空间的非完整约束。