Mechanics of mechanochemically responsive elastomers Qiming Wang a,b , Gregory R. Gossweiler c , Stephen L. Craig c , Xuanhe Zhao a,b,d,n a Soft Active Materials Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139, USA b Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC27708, USA c Department of Chemistry, Duke University, Durham, NC27708, USA d Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA02139, USA article info Article history: Received 23 January 2015 Received in revised form 15 April 2015 Accepted 15 May 2015 Available online 27 May 2015 Keywords: Mechanochemistry Stimuli-responsive polymer Spiropyran Constitutive model Interpenetrating-network model Chain-length distribution abstract Mechanochemically responsive (MCR) polymers have been synthesized by incorporating mechanophores – molecules whose chemical reactions are triggered by mechanical force – into conventional polymer networks. Deformation of the MCR polymers applies force on the mechanophores and triggers their reactions, which manifest as phenomena such as changing colors, varying fluorescence and releasing molecules. While the activation of most existing MCR polymers requires irreversible plastic deformation or fracture of the polymers, we covalently coupled mechanophores into the backbone chains of elastomer networks, achieving MCR elastomers that can be repeatedly activated over multiple cycles of large and reversible deformations. This paper reports a microphysical model of MCR elastomers, which quantitatively captures the interplay between the macroscopic de- formation of the MCR elastomers and the reversible activation of mechanophores on polymer chains with non-uniform lengths. Our model consistently predicts both the stress–strain behaviors and the color or fluorescence variation of the MCR elastomers under large deformations. We quantitatively explain that MCR elastomers with time-in- dependent stress–strain behaviors can give time-dependent variation of color or fluor- escence due to the kinetics of mechanophore activation and that MCR elastomers with different chain-length distributions can exhibit similar stress–strain behaviors but very different colors or fluorescence. Implementing the model into ABAQUS subroutine further demonstrates our model's capability in guiding the design of MCR elastomeric devices for applications such as large-strain imaging and color and fluorescence displays. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction Polymers capable of chemical reactions in response to external mechanical stimuli offer great promise for developing future sensors, memories, displays and photomodulators (Beyer and Clausen-Schaumann, 2005; Caruso et al., 2009; Sagara and Kato, 2009). Recent years, a novel strategy for fabricating mechanochemically responsive (MCR) polymers has been developed by covalently incorporating molecules capable of force-triggered chemical reactions, or so-called mechan- ophores, into polymer networks (Beyer and Clausen-Schaumann, 2005; Black et al., 2011a; Caruso et al., 2009; Kean and Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmps Journal of the Mechanics and Physics of Solids http://dx.doi.org/10.1016/j.jmps.2015.05.007 0022-5096/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author at: Soft Active Materials Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. E-mail address: zhaox@mit.edu (X. Zhao). Journal of the Mechanics and Physics of Solids 82 (2015) 320–344