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Professor Grima (on Sabbatical Leave from October 2021 till September 2023) normally lectures in the area of physical and computational chemistry and runs courses in mathematics for chemistry undergraduates. He was instrumental in the establishment of the Metamaterials Unit, a Unit operating under the auspices of the Faculty of Science to host the research work on mechanical metamaterials and related systems and was its first coordinator (till September 2021). He is the Rector's Delegate for DegreePlus, a programme aimed at providing all university students with the opportunity to augment their academic studies with additional skills and experiences that can enhance their character and employability.

His research group works on materials exhibiting negative properties such as negative Poisson's ratios (auxetic), negative thermal expansion and/or negative compressibility (negative bulk modulus). The research entails the testing, modelling and/or simulation of the mechanical properties of materials in an attempt to discover or design materials with these unusual properties. Particularly interesting results include the discovery of negative Poisson's ratios in graphene, tendons, the zeolite class of materials, the design of various networked polymeric auxetics and, the development of models for predicting the mechanical properties of auxetic foams and of microporous polymers. Some of these discoveries have a number of very important technical implications (e.g. the discovery of negative Poisson's ratios in zeolites opens many new possibilities towards the use of zeolites as tunable filters). The group has hosted a number of international conferences and workshops and co-edited various international journal special issues.

In addition to this, Professor Grima has been involved in a number of biomechanics projects which range from the biomechanics of the chest to sports biomechanics with particular emphasis on fixed-seat rowing, a sport he also practices.