Lew's interests lie in the broad area of computational solid mechanics. He is concerned with the fundamental design and mathematical analysis of material models and numerical algorithms, with the ultimate goal of reducing uncertainty and increasing trust and reliability of computational engineering tools in solid mechanics. Current projects include: a) the creation of new tools to optimize and characterize high-fidelity atomic force microscopy images, with particular emphasis in soft, polymeric materials; b) the creation of coarse-grained computational models of polymer networks, with the goal of better understanding the mechanical behavior of elastomers and a number of biological entities, such as the cell cytoskeleton; c) the creation of robust numerical methodologies to solve problems in which discontinuities may ubiquitously appear, such as massively fragmented solids. Within these projects the group is attacking fundamental questions in computational dynamics, nonlinear elasticity, and statistical mechanics.