A damage model to simulate nanoindentation tests of lamellar bone at multiple penetration depth

Mechanical intrinsic anisotropy and architectural arrangements of building blocks of lamellar bone confer mechanical and structural anisotropy to the tissue as well as a size dependence observed in mechanical laboratory tests able to probe material samples at different sizes. Instrumented indentation tests is an effective experimental tool which is well suited to investigate both the above described peculiar features of the lamellar bone tissue. In this work a computational model is presented, able to simulate the mechanical response of lamellar bone subject to nanoindentation tests. The aim of the model is to represent: i) the direction dependent response, and ii) the decrease of the indentation modulus with increasing penetration depth. To these purposes, an anisotropic constitutive law has been implemented into a commercial finite element code with an asymmetric tension/compression yield criterion and transversely isotropic strength properties by a suitably modified Drucker-Prager yield function. In addition, a continuum damage model has been implemented by means of a scalar function reducing the values of entries of the undamaged anisotropic elastic tensor. Numerical results have shown the ability of the model to fit the experimental measures carried out along axial and transverse directions on bovine lamella bone.