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A sustainable future requires products to be recyclable. An important process in recycling is shredding where materials joined in multi-material structures are liberated or detached. Until now, no physics-based models exist to describe shredding processes adequately. The proposed approach uses finite element simulations to model the shredding of a multi-material structure (steel and fiber-reinforced polymers with an adhesion joint) in a rotary shredder based on previous experimental investigations. Simulations successfully replicate the shredding phenomena, but the stochastic nature of the process results in different load cases making a strict quantitative comparison between simulations and experiments challenging. Comparing similar load cases of two experiments and the corresponding simulations, the estimated liberation degree ranges from 56 % to 100 % (63 % to 99 % in experiments). The estimated energy consumption varies from 1.4 kWh/t to 1.7 kWh/t (1.0 kWh/t to 1.4 kWh/t in experiments), marking a significant step in achieving a reasonable physics-based estimation of required energy. However, the number of fiber-reinforced polymer fragments is underestimated, ranging from 22 to 50 fragments (50 to 78 in experiments). The presented method is a novel contribution to recyclability assessment and recycling-oriented design.