Fracture mechanics theories rely on assumptions that state-of-the-art cannot verify, being limited by spatial resolution and maximum sample sizes. To this end, a collaboration between ACMD in Boulder and the NIST Center for Neutron Research is developing a novel measurement technique capable of measuring 3D strain tensor fields using neutron imaging at structurally relevant length scales. The inverse problems related to reconstructing scalar quantities (e.g. bone or tissue density as in X-ray CT or MRI scans) are well-known; however strain tensors offer an additional challenge due to the directional variation of the tensor projection as the sample is rotated. Solving this problem will require novel data analysis techniques that are quantitative, transferrable and computationally efficient.  Domains for advancement might include tensor tomography algorithm, microscale mechanical modeling or training advanced neural net architectures.