On the compatibility conditions of finite deformations

arXiv:2509.10525v1 Announce Type: new
Abstract: This paper examines the intuitive meaning of the Saint–Venant compatibility equation known from the linear theory of deformations. The linearized theory is typically obtained from the relations of finite deformation theory by neglecting higher-order terms. We show how to formulate the compatibility conditions for finite deformations and how the well-known equation for small deformations follows from this formulation.