Mesh generation difficulties can be avoided when a background mesh rather than a mesh that conforms to the geometry is used for the analysis. The geometry is represented by equations and is independent of the mesh and is immersed in the background mesh. The solution to boundary value problems is approximated or piece-wise interpolated using the background mesh. The main challenge is in applying the boundary conditions because the boundaries may not have any nodes on them. Implicit boundary method has been used for linear static and dynamic analysis and has shown to be an effective approach for imposing boundary conditions but has never been applied to nonlinear problems. In this paper, this approach is extended to large deformation nonlinear analysis using the Total Lagrangian formulation. The equations are solved using the widely used modified Newton-Raphson method with loads applied over many load steps. Several test examples are studied and compared with traditional finite element analysis software for verification.

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