The hypothesis that strain has a permeating influence on ferroelastic, magnetic and superconducting transitions in 122 iron pnictides has been tested by investigating variations of the elastic and anelastic properties of a single crystal of Ba(Fe0.957Co0.043)2As2 by Resonant Ultrasound Spectroscopy as a function of temperature and externally applied magnetic field. Non-linear softening and stiffening of C66 in the stability fields of both the tetragonal and orthorhombic structures has been found to conform quantitatively to the Landau expansion for a pseudoproper ferroelastic transition which is second order in character. The only exception is that the transition occurs at a temperature (TS ≈ 69 K) ~10 K above the temperature at which C66 would extrapolate to zero ( ≈ 59 K). An absence of anomalies associated with antiferromagnetic ordering below TN ≈ 60 K implies that coupling of the magnetic order parameter with shear strain is weak. It is concluded that linear-quadratic coupling between the structural/electronic and antiferromagnetic order parameters is suppressed due to the effects of local heterogeneous strain fields arising from the substitution of Fe by Co. An acoustic loss peak at ~50-55 K is attributed to the influence of mobile ferroelastic twin walls that become pinned by a thermally activated process involving polaronic defects. Softening of C66 by up to ~6% below the normal – superconducting transition at TC ≈ 13 K demonstrates an effective coupling of the shear strain with the order parameter for the superconducting transition which arises indirectly as a consequence of unfavourable coupling of the superconducting order parameter with the ferroelastic order parameter. Ba(Fe0.957Co0.043)2As2 is representative of 122 pnictides as forming a class of multiferroic superconductors in which elastic strain relaxations underpin almost all aspects of coupling between the structural, magnetic and superconducting order parameters and of dynamic properties of the transformation microstructures they contain.RUS facilities in Cambridge were established through grants from the Natural Environment Research Council and the Engineering and Physical Sciences Research Council of Great Britain to MAC.: EP/I036079/1, NE/B505738/1, NE/F17081/1. The work presented here was funded specifically through NE/F17081/1. AC magnetic measurements were carried out using the Advanced Materials Characterisation Suite, funded by EPSRC Strategic Equipment Grant EP/M000524/1. PM acknowledges funding from the Winton Programme for the Physics of Sustainability
