In a vast number of engineering fields like medicine,aerospace or robotics,materials are required to meet unusual performances that simple homogeneous materials are often not able to fulfil.Consequently,many efforts are currently devoted to develop future generations of materials with enhanced properties and unusual functionalities.In many instances,biological systems served as a source of inspiration,as in the case of cellular materials.Commonly observed in nature,cellular materials offer useful combinations of structural properties and low weight,yielding the possibility of coexistence of what used to be antagonistic physical properties within a single material.Due to their peculiar characteristics,they are very promising for engineering applications in a variety of industries including aerospace,automotive,marine and constructions.However,their use is conditional upon the development of appropriate constitutive models for revealing the complex relations between the microstructure's parameters and the macroscopic behavior.From this point of view,a great variety of analytical and numerical techniques have been proposed and exhaustively discussed in recent years.Noteworthy contributions,suggesting different assumptions and techniques are critically presented in this review paper.
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