The past two decades have been marked by the ever increased interest into the development of various types of metamaterials, i.e. architected materials exhibiting properties beyond those achievable through chemistry and microstructure. A class of metamaterials designed to manipulate the propagation of elastic/acoustic waves is of particular interest here as it opens unprecedented possibilities for a broad class of applications ranging from noise/vibration insulation, to acoustic cloaking, acoustic lenses going beyond the diffraction limits, seismic isolation, tunable waveguides, adaptive passive vibration control, acoustic diodes, and many more. Various physical principles are being harnessed for obtaining metamaterials’ extraordinary properties. This work focuses on metamaterials based on one of these principles, i.e. the localized resonance, which is of a particular interest for subwavelength applications, i.e. when the wavelength being manipulated is (significantly) larger compared to the size of the metamaterial units. In this talk, first several examples of locally resonant subwavelength metamaterials will be given, e.g. with application to vibration control, enhanced and negative angle reflection, and transmission amplification, in addition to the more conventional application to transmission attenuation. Next, the need for modelling techniques that allow the analysis and design of subwavelength metamaterial domains of finite sizes, complex geometries and non-trivial, non-harmonic loadings, possibly involving non-linearities will be discussed. As a good candidate, transient computational homogenization methodology will be presented. The approach is applicable to general non-linear problems [1], while in linear cases it may be reduced to provide the closed-form homogenized effective constitutive relations [2]. Several examples will illustrate the performance of the methodology. REFERENCES [1] T.F.W. van Nuland, P.B. Silva, A. Sridhar, M.G.D. Geers and V.G. Kouznetsova, Transient analysis of nonlinear locally resonant metamaterials via computational homogenization. Mathematics and Mechanics of Solids, 24, pp. 3136–3155, 2019. [2] A. Sridhar, V.G. Kouznetsova and M.G.D. Geers, Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum. Computational Mechanics, 57, pp. 423–435, 2016.