Accurately simulating whether an object will be lifted securely or dropped during grasping is a longstanding Sim2Real challenge. Soft compliant jaw tips are almost universally used with parallel-jaw robot grippers due to their ability to increase contact area and friction between the jaws and the object to be manipulated. However, interactions between the compliant surfaces and rigid objects are notoriously difficult to model. We introduce IPC-GraspSim, a novel grasp simulator that extends Incremental Potential Contact (IPC) - a highly accurate collision + deformation model developed in 2020 for computer graphics. IPC-GraspSim models both the dynamics and the deformation of compliant jaw tips to reduce Sim2Real gap for robot grasping. We evaluate IPC-GraspSim using a set of 2,000 physical grasps across 16 adversarial objects where analytic models perform poorly. In comparison to both analytic quasistatic contact models (soft point contact, REACH, 6DFC) and dynamic grasp simulators (Isaac Gym with FleX), results suggest IPC-GraspSim can predict robustness with higher precision and recall (F1 = 0.85). IPC-GraspSim increases F1 score by 0.03 to 0.20 over analytic baselines and 0.09 over Isaac Gym, at a cost of 8000x and 1.5x more compute time, respectively. All data, code, videos, and supplementary material are available at https://sites.google.com/berkeley.edu/ipcgraspsim.