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Abstract Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell–matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.

The evolution of crack tip displacement and strain fields during uniaxial, room temperature, low‐cycle fatigue experiments of Nickel superalloy compact tension specimens was measured by a digital image correlation approach and was further used to validate a cyclic plasticity model and corresponding deformation calculations made by a finite elements methodology. The experimental results provided data trends for the opening displacements and near crack tip strains as function of cycles. A finite element model was developed to capture test conditions for a measured crack size. The model captures crack tip plasticity by using a constitutive model calibrated against stress‐strain measurements performed on a round bar. Similar quantities were extracted from the model predictions to compare with the digital image correlation measurements for model validation purposes. This type of direct comparison demonstrated that the computational model was capable to adequately capture the crack opening displacements at various stages of the specimen's fatigue life, providing in this way a tool for quantitative cyclic plasticity model validation. In addition, this integrated experimental‐computational approach provides a framework to accelerate our understanding related to interactions of fatigue test data and models, as well as ways to inform one another.

The development of high-fidelity mechanical property prediction models for the design of polycrystalline materials relies on large volumes of microstructural feature data. Concurrently, at these same scales, the deformation fields that develop during mechanical loading can be highly heterogeneous. Spatially correlated measurements of 3D microstructure and the ensuing deformation fields at the micro-scale would provide highly valuable insight into the relationship between microstructure and macroscopic mechanical response. They would also provide direct validation for numerical simulations that can guide and speed up the design of new materials and microstructures. However, to date, such data have been rare. Here, a one-of-a-kind, multi-modal dataset is presented that combines recent state-of-the-art experimental developments in 3D tomography and high-resolution deformation field measurements.