Machine-learned constitutive relations for mechanoluminescent ZnS:Cu–PDMS composites

Materials with novel properties, such as emerging smart materials, offer a design challenge to researchers who want to make use of their unique behaviors. The complex nature of these material responses can be difficult to model from a physics-based understanding as a full description of the multi-physics, multi-scale, and non-linear phenomena requires expertise from various scientific disciplines. Some new smart materials, such as the mechanoluminescent (ML) copper-doped zinc sulfide (ZnS:Cu)-embedded in polydimethylsiloxane (PDMS) (ZnS:Cu–PDMS), lack a constitutive model or an agreement on the mechanisms of action behind the unique material properties. As constitutive equations are essential to engineer devices, with existing knowledge gap in underlying physics of smart materials, a viable approach is to use empirical data for deriving constitutive equations. However, it is challenging to derive constitutive equations on non-linear, multi-variate, and multi-physics relationship using conventional data processing approaches due to the size and complexity of the empirical data. In this work, a machine learning framework is proposed for ones to derive constitutive equations using empirical data for novel materials. The framework is validated by creating constitutive models for ZnS:Cu–PDMS elastomeric composites undergoing a variety of tensile load patterns. To avoid confinement of the models to the programming environment, in which they are developed, numerical fits of the machine-learned models are created as constitutive equations for the non-linear, multi-variate, and multi-physics ML properties. These models can be used when designing ML ZnS:Cu–PDMS to develop devices to harness the unique ML properties.