Addressing the effects of material non-linearities on wellbore stresses using stress- and strain-dependent elastic moduli

Two elastic constitutive models accounting for pre-peak non-linear (NL) effects are formulated and applied to deformation analysis around circular openings in rock. These models present extension of the constitutive equations of linear elasticity (LE) to NL materials obtained by replacing classic elastic moduli Ko (bulk modulus), and Go (shear modulus) of linear elasticity with stress- or strain-dependent functions introduced in a form of power series. Model parameters are identified from uniaxial compression tests, and a numerical examples showing linear and NL stress distributions in a hollow cylinder are presented.