The Discrete Element Method (DEM) is an N-body numerical method widely used to model granular materials with various particle shapes, including complex geometries like spheropolyhedra. A major computational challenge in DEM lies in contact detection, particularly for such complex shapes, which involve multiple simultaneous contact points and intricate geometry requiring costly intersection evaluations. This work focuses on adapting existing methods to efficiently handle spheropolyhedra geometries on GPUs. Two key developments are presented: extending the PCCP (Parallelized by Contact Candidate Pair) algorithm to these complex shapes, which redefines computational granularity by assigning GPU threads to contact pairs, and an optimized memory data layout (SOA) for efficient GPU memory access and data locality. These contributions speed up the contact detection and force calculation phases. The effectiveness of these GPU optimization methods is demonstrated through their implementation in the ExaDEM open-source HPC code, with performance evaluations on NVIDIA A100 and Grace Hopper GPUs. These optimizations enable large-scale simulations, handling from a few hundred thousand to several million particles, while maintaining reasonable simulation times. This work represents a significant advancement in DEM by enabling efficient large-scale simulations with complex particle geometries.