Abstract: The mechanical memory of fabrics often leads to persistent wrinkles, which reflect key physical properties and habitual wear patterns. Simulating these wrinkles accurately is essential for visual plausibility in digital garments, yet no dedicated approach exists for inferring the parameters that govern their formation due to the lack of precise datasets and estimation methods. We introduce Fabric-101, an inclusive, accurate, and extendable fabric dataset comprising over 101 common fabrics following textile standards. Unlike existing datasets, it captures three physically distinct deformation components (i.e., self-recoverable (elastic), recoverable (friction-driven), and unrecoverable (plastic)), from cyclic loading-unloading measurements. Building on this data, we propose a differentiable cloth simulator combining an elasto-plastic model with friction, designed to capture recoverable and unrecoverable wrinkle formation. Our simulator is differentiable and uses adjoint method to learn fabric physical parameters from the measured hysteresis curves, learning fabric-specific wrinkle behaviors. Through extensive experiments, we demonstrate that our model reproduces persistent wrinkles that are visually and physically similar to real fabrics across diverse materials and motions. Dataset and code are available in https://github.com/GongDeshan/Fabric_101_for_Wrinkles.