This study presents a computational approach for the deformation analyses of problems in cell and developmental biology. Cells and embryos are viewed mechanically as axisymmetric shell-like bodies containing a body of incompressible material. The analysis approach is based on the finite element method. It is comprised of three finite element ingredients: (1) an axisymmetric shell/membrane element valid for modeling finite bending, shearing and stretching; (2) a volume constraint algorithm for modeling the membrane-bound incompressible material; and (3) a contact algorithm for modeling the mechanical interactions between deformable bodies. Part II of this study will demonstrate how these three ingredients can be applied to analyze mechanical experiments on cells. This same method is also useful for simulating embryonic shape changes during development.

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