Smoothly varying in‐plane stiffness heterogeneity evaluated under uniaxial tensile stress

Identification of spatially varying stiffness is a challenging, but important, research topic in the mechanics of materials and can provide the necessary information for material suitability, damage, and process control, especially for high‐value applications. One homogeneous and 3 heterogeneous virtual field method (VFM) formulations were used to create a methodology for varying stiffness identification. Two finite element method simulations were used to demonstrate the validity and capability of the formulations. A tensile test protocol was implemented to identify spatially varying stiffness of uniaxial tensile paperboard specimens using digital image correlation. A recently published form of VFM, which enforces global equilibrium in the spatial frequency domain, was used to better examine smoothly varying stiffnesses. Two tensile specimens of a single commercial paperboard, known to contain heterogeneities, were examined, and local stiffnesses were identified. Examination of local equilibrium with VFM was used to explain differences in stiffness identification. A polyethylene terephthalate specimen was used to demonstrate homogeneity.