Please see whether the following references may be of help to you. 

1) Book: "Molybdenum Disulphide Lubrication" By A.R. Lansdown, Elsevier, 1999.

2) For Shear and Young's moduli: Andras Kis et al., Advanced Materials, 15, 2003, page 733.

3) "Nonlinear elastic behavior of two-dimensional molybdenum disulfide", Ryan C. Cooper et al., PHYSICAL REVIEW B 87, 035423 (2013).

4) "MOLYBDENUM DISULPHIDE IN LUBRICATION. A REVIEW", J. P. G. FARR, Wear, 35 (1975) 1-22.

In case you need further/specific information on MoS2 (used as a solid lubricant because of its low friction properties), you need to search in journals related to wear/tribology. 

Possibly helpful reference: A. Castellanos-Gomez, M. Poot, G.A. Steele, H.S.J. van der Zant, N. Agraït, G. Rubio-Bollinger, "Elastic properties of freely suspended MoS2 nanosheets", Advanced Materials, 24(6) 2012, 772–775; http://onlinelibrary.wiley.com/doi/10.1002/adma.201103965/abstract

The specific heat of molybdenum disulphide (MoS2) can be found (e.g.) at: O. Kubaschewski, C.B. Alcock, P.J. Spencer, "Materials Thermochemistry", 6th ed., Pergamon Press, 1993.

The following literature may be useful for your research

We perform classic molecular dynamics simulations to comparatively investigate the mechanicalproperties of single-layer MoS2 and a graphene/MoS2/graphene heterostructure under uniaxialtension. We show that the lattice mismatch between MoS2 and graphene will lead to an spontaneousstrain energy in the interface. The Young’s modulus of the heterostructure is much larger than thatof MoS2. While the stiffness is enhanced, the yield strain of the heterostructure is considerably

smaller than the MoS2 due to lateral buckling of the outer graphene layers owning to the applied mechanical tension

Mechanical properties of MoS2/graphene heterostructures

Jin-Wu Jiang1,a) and Harold S. Park2

APPLIED PHYSICS LETTERS 105, 033108 (2014)

arxiv.org › cond-mat