On the validity range of strain-gradient elasticity: A mixed static-dynamic identification procedure

Abstract

Wave propagation in architectured materials, or materials with microstructure, is known to be dependent on the ratio between the wavelength and a characteristic size of the microstructure. Indeed, when this ratio decreases (i.e. when the wavelength approaches this characteristic size) important quantities, such as phase and group velocity, deviate considerably from their low frequency/long wavelength values. This well-known phenomenon is called dispersion of waves. Objective of this work is to show that straingradient elasticity can be used to quantitatively describe the behaviour of a microstructured solid, and that the validity domain (in terms of frequency and wavelength) of this model is sufficiently large to be useful in practical applications. To this end, the parameters of the overall continuum are identified for a periodic architectured material, and the results of a transient problem are compared to those obtained from a finite element full field computation on the real geometry. The quality of the overall description using a strain-gradient elastic continuum is compared to the classical homogenization procedure that uses Cauchy continuum. The extended model of elasticity is shown to provide a good approximation of the real solution over a wider frequency range.

An experimental evidence of the failure of Cauchy elasticity for the overall modeling of a non-centro-symmetric lattice under static loading

“…A weak-scale separation ratio ( = m M = 1 8 ) is considered for producing both the numerical and the experimental sample. This ratio lies between the bounds identified in [33] and is chosen so as to magnify the higher-order kinematics. For both materials, numerical uniaxial tension tests are performed in order to design the real experiment.…”

“…In the same reference, it is shown that an extension of classical elasticity, called strain-gradient elasticity, is able to model the observed phenomenon. In [33], the validity range of this enrichment is studied. It results that the use of a strain-gradient continuum as an overall medium improves the continuous description for scale separation ratios ( = m M ) between 1/6 and 1/20.…”

Computational Homogenization of Architectured Materials

“…For more details about the mechanics of generalized continua, see [5,75,180]. The study of structures made of architectured materials has been the object of intensive research in the last few years [168], and has resulted in promising results concerning the development of architectured metamaterials for acoustic [175,177] and elastodynamic applications [174,176].…”

Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

“…and the projections on the tangent plane to the deformed surface as well as on the normal direction n. The identification of the introduced material parameters may be performed using the methods discussed in [56][57][58][59][60][61][62].…”