Theoretical, numerical and experimental results examining thermoviscous losses in sonic crystals are presented in this work, enabling the fabrication and characterization of an acoustic metamaterial absorber with complex-valued anisotropic inertia. The formulations developed can be written with no unknown or empirical coefficients, due to the structured lattice of the sonic crystals and organized layering scheme, and it is shown that higher filling fraction arrangements can be used to provide a large enhancement in the loss factor. To accurately describe these structures in a realizable experimental configuration, confining structures are needed which modify the effective properties, due to the thermal and viscous boundary layer effects within the sonic crystal lattice. Theoretical formulations are presented which describe the effects of these confined sonic crystals, both individually and as part of an acoustic metamaterial structure, and is demonstrated experimentally in an acoustic impedance tube. It is observed that confined sonic crystals demonstrate an increase in the viscous losses and a reduction in the effective bulk modulus, enabling better acoustic absorber performance through improved impedance matching and enhanced absorption. ; Comment: The following article has been submitted to the Journal of the Acoustical Society of America (JASA). After it is published, it will be found at http://scitation.aip.org/JASA