Workshop on Mathematical Challenges in Brittle Material Failure

The Army Research Office funded an invitation-only workshop entitled "Identifying Mathematical Challenges Associated with Failure of Brittle Materials" at the Johns Hopkins University, Maryland on May 20-21, 2019. The workshop brought together mathematicians, statisticians, and mechanics of materials researchers with diverse academic and research backgrounds to discuss the state-of-the-art in brittle material failure prediction and to identify new directions for future research. Three specific goals of the workshop were: (1) to identify the state-of-the-art for modeling failure of brittle materials (e.g., ceramics, glasses); (2) to discuss the major mathematical and statistical challenges experienced by academics and scientists studying brittle failure; and (3) to propose novel and unexplored research collaborations between mechanics researchers and mathematicians to address the identified challenges. By virtue of the Army Research Office's interests and the expertise of participants, these three goals were broadly pursued within the context of understanding and predicting dynamic behavior of brittle materials. This document provides a summary of workshop presentations, discussions, and recommendations for future work (and research funding) that emerged from the workshop. The recommendations for future work are organized into four major thrusts: (i) defining robust quantities of interest; (ii) understanding and modeling variability and stochasticity; (iii) model parameter importance and calibration; and (iv) transitioning from discrete to continuum behaviors. For each thrust, specific future work discussed in the workshop is described in this article.