Abstract
In this paper, size effects exhibited by mechanical metamaterials have been studied. When the sizescale of the metamaterials is reduced, stiffening or softening responses are observed in experiments. In order to capture both the stiffening and softening size effects fully, a second-order asymptotic homogenization method based on strain gradient theory is used. By this method, the metamaterials are homogenized and become effective strain gradient continua. The effective metamaterial parameters including the classical and strain gradient stiffness tensors are calculated. Comparisons between a detailed finite element analysis and the effective strain gradient continua model have been made for metamaterials under different boundary conditions, different aspect ratios, different unit cells (closed or open cells) and different topologies. It shows that both stiffening and softening size effects can be captured by using the effective strain gradient continua models.
Highlights
Mechanical metamaterials are of growing interest due to their extraordinary mechanical properties for engineering applications [13,16,30,51]
The aim of the present paper is to provide quantitative comparative studies for metamaterials constructed by repetitive planar lattice structures between direct FEM computations, which are understood as correct solutions, and equivalent effective strain gradient continua
It is intended to investigate the mechanism of size effects and to answer the following question: Do the metamaterial parameters derived by using the second-order asymptotic analysis allow to capture size effects accurately including both stiffening and softening effects?
Summary
Mechanical metamaterials are of growing interest due to their extraordinary mechanical properties for engineering applications [13,16,30,51]. In a recent study [66] size effects of lattice structures were examined by comparing direct FEM computations with an equivalent micropolar elastic model. The aim of the present paper is to provide quantitative comparative studies for metamaterials constructed by repetitive planar lattice structures between direct FEM computations, which are understood as correct solutions, and equivalent effective strain gradient continua. These simulations will examine size effects directly for metamaterials under different boundary conditions, of different aspect ratios, constructed by different unit cells and by different topologies. It is intended to investigate the mechanism of size effects and to answer the following question: Do the metamaterial parameters derived by using the second-order asymptotic analysis allow to capture size effects accurately including both stiffening and softening effects?
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