Training future leaders to understand life cycle assessment data is critical for effective research, business, and sociopolitical decision-making. However, the technical nature of these life cycle reports often makes them challenging for students and other nonexperts to comprehend. Therefore, we outline here the key takeaways from recent economic and life cycle assessments for three major commodity chemicalsethylene, ethylene oxide, and terephthalic acidthat are precursors for plastics, synthetic fibers, and many other consumer products. The five lessons and 10 discussion prompts (provided in the Supporting Information) serve as useful teaching tools for introductory chemistry and chemical engineering courses.

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Discrete modeling of individual damage sites in composites is generally impractical using finite element analysis. A popular alternative is reduction of material properties at those integration points where the stress state exceeds the allowable. This selective reduction of properties results in inhomogeneous properties within an element. Using ordinary finite element interpolation results in severe violation of equilibrium. This paper examines the behavior of the the simplest element, a uniaxial rod element, when selective property reduction is used. Both exact and numerically integrated forms were examined. The results show that errors can be reduced significanly if a robust technique can be developed for representing the damage with a smooth function.