A versatile implicit computational framework for continuum-kinematics-inspired peridynamics

Continuum-kinematics-inspired peridynamics (CPD) has been recently proposed as a novel reformulation of peridynamics that is characterized by one-, two- and three-neighbor interactions. CPD is geometrically exact and thermodynamically consistent and does not suffer from zero-energy modes, displacement oscillations or material interpenetration. In this manuscript, for the first time, we develop a computational framework furnished with automatic differentiation for the implementation of CPD. Thereby, otherwise tedious analytical differentiation is automatized by employing hyper-dual numbers (HDN). This differentiation method does not suffer from round-off errors, subtractive cancellation errors or truncation errors and is thereby highly stable with superb accuracy being insensitive to perturbation values. The computational framework provided here is compact and model-independent, thus once the framework is implemented, any other material model can be incorporated via modifying the potential energy solely. Finally, to illustrate the versatility of our proposed framework, various potential energies are considered and the corresponding material response is examined for different scenarios.