The paper presents a thin-film acoustic metamaterial designed to absorb low-frequency sound at resonance frequencies ranging from 100 to 1,000 Hz. The metamaterial consists of an elastic membrane decorated with asymmetric rigid platelets, which induce flapping motions that lead to large elastic curvature energy density at their perimeters. This energy density is concentrated in small volumes, minimally coupled to the radiation modes, forming an open cavity that enhances absorption. The samples achieve near-unity absorption at frequencies where the sound wavelength is three orders of magnitude larger than the membrane thickness. Finite element simulations and experimental measurements show excellent agreement, demonstrating that the system can absorb up to 86% of acoustic waves at 170 Hz and 99% at lower frequencies. The mechanism involves the high curvature energy density at the platelet perimeters, which is confined and not radiated, leading to strong absorption. The study also explores the tunability of absorption peaks and the effectiveness of the metamaterial under oblique incidence.The paper presents a thin-film acoustic metamaterial designed to absorb low-frequency sound at resonance frequencies ranging from 100 to 1,000 Hz. The metamaterial consists of an elastic membrane decorated with asymmetric rigid platelets, which induce flapping motions that lead to large elastic curvature energy density at their perimeters. This energy density is concentrated in small volumes, minimally coupled to the radiation modes, forming an open cavity that enhances absorption. The samples achieve near-unity absorption at frequencies where the sound wavelength is three orders of magnitude larger than the membrane thickness. Finite element simulations and experimental measurements show excellent agreement, demonstrating that the system can absorb up to 86% of acoustic waves at 170 Hz and 99% at lower frequencies. The mechanism involves the high curvature energy density at the platelet perimeters, which is confined and not radiated, leading to strong absorption. The study also explores the tunability of absorption peaks and the effectiveness of the metamaterial under oblique incidence.