Bayesian calibration of material properties for shape memory alloys from nanoindentation data

Shape memory alloys (SMAs) are materials with exceptionally high recoverable strains and temperature-sensitive material response, seeing growing use in medical and aerospace applications. Nanoindentation is an experimental method where a shaped tip indenter is pushed into a material surface while recording applied force and penetration depth, providing information about material deformation. We study the problem of inferring thermomechanical properties of SMAs given experimentally obtained indentation curves at nano-micron scales. We propose to use a Bayesian hierarchical model to simultaneously incorporate (1) spatially-varying material properties resulting from sampling and spatial variation in the local grain structure at each indentation site; (2) a surrogate model for the response surface of the computationally expensive constitutive model informed by a small sample of finite element simulations; and (3) a discrepancy for the missing physics in the constitutive model. The resulting Bayesian analysis characterizes SMA material properties with associated uncertainty employing data acquired from adaptively selected indentation locations and multimodal indenter tip shapes.