IGsim is a tiny C++ FEM simulation library. It has implemented functions which calculate deformation energy, force and sitffness matrix of neo-hookean material and some other tools which are handy for 3D FEM based simulation.
It is a header-only library, mainly mimic the design philosophy of libigl. You do not need to compile anything to use, just include IGsim headers (e.g. #include <IGsim/elastic_neohookean.h>) and run. Most are tailored to operate on a generic triangle mesh stored in an n-by-3 matrix of vertex positions V, an m-by-3 matrix of triangle indices F or an m-by-4 matrix of tetrahedron indices T.
IGsim uses the Eigen library heavily, mainly as input/output data container and matrix algebra interface. The representation of meshes is coordinated with libigl, and you can refer to libigl's tutorial for more information.