Multibody systems have widespread applications in diverse fields such as robotics, entertainment, and animation. Their capability to model and simulate intricate interactions among interconnected bodies makes them invaluable in various domains. However, complexity arises with factors like non-smooth contact handling, nonlinearity in flexible joints, and parallelization challenges. We introduce a stable and highly parallel GPU algorithm within affine body dynamics for solving constrained multibody dynamics with nonlinear constraints.Our innovation involves reformulating constrained multibody dynamics into a variational form, treating the system as a set of affine bodies connected with peridynamic bonds. This formulation provides a unified model for affine body dynamics, constraints, and contact within the peridynamics framework.It also facilitates the integration of the semi-implicit successive substitution method to solve nonlinear optimization in a global-local iterative manner. The proposed method obviates the necessity of assembling a global Hessian, rendering it highly suitable for efficient implementation on GPUs.This allows real-time simulation of intricate interactions involving both rigid and flexible bodies, encompassing contact, joint constraints, and friction.

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