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We present a study of elastic metamaterial that possesses multiple localresonances. We demonstrated that the elastic metamaterial can havesimultaneously three negative effective parameters, i.e., negative effectivemass, effective bulk modulus and effective shear modulus at a certain frequencyrange. Through the analysis of the resonant field, it has been elucidated thatthe three negative parameters are induced by dipolar, monopolar and quadrupolarresonance respectively. The dipolar and monopolar resonances result into thenegative band for longitudinal waves, while the dipolar and quadrupolarresonances cause the negative band for transverse waves. The two bands have anoverlapping frequency regime. A simultaneously negative refraction for bothlongitudinal waves and transverse waves has been demonstrated in the system.

Elastic metamaterial with simultaneously negative Mass Density, Bulk Modulus and Shear Modulus