Alan T. Zehnder

Background: The relationship between molecular-scale chain scission and bulk viscoelasticity in soft polymer networks remains incompletely understood, particularly in multiple network elastomers, where energy dissipation arises from the interaction between irreversible chain-scission damage and reversible time-dependent mechanics. Objective: This study aims to elucidate how cumulative, progressive chain-scission damage influences bulk viscoelasticity in double network elastomers through both experiments and constitutive modeling. Methods: A non-swelling, platinum-cured silicone double network elastomer was synthesized and served as a model system to investigate damage-induced effects on viscoelasticity. Cyclic tensile loading was applied to introduce systematically controlled chain-scission damage. The changes in viscoelastic properties were characterized via stress relaxation tests and dynamic mechanical analysis. A constitutive model coupling hyperelasticity with damage-induced viscosity through stretch-mediated chain-scission kinetics and chain-length-dependent disentanglement kinetics was established to describe the observed damage-viscosity coupling. Results: Experiments revealed that cumulative bond breaking in the double network elastomer contributes not only to Mullins-type softening but also to measurable increases in apparent relaxation time and viscoelastic dissipation rate. The proposed model successfully reproduced damage-related effects, including both irreversible primary hysteresis caused by network damage and narrower, persistent secondary hysteresis due to damage-induced viscoelastic dissipation. Conclusion: Although the damage-induced viscoelastic dissipation was small compared to the energy directly dissipated by bond breaking, our results provide direct experimental evidence and quantification that internal molecular damage can modulate bulk time-dependent constitutive behavior. These findings lay the foundation for predictive modeling of dissipative mechanics mediated by damage–viscoelasticity coupling in complex multiple network elastomers.

We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the oscillations using interferometry. Devices of different dimensions are used to introduce frequency detuning, and short silicon bridges connecting the micro-beams are used as mechanical coupling between the oscillators. The region of synchronization is plotted for the MEMS system in the detuning vs. coupling parameter space and compared with the numerical analysis of a corresponding, lumped-parameter model. Three states of oscillations are observed i.e. the drift state, quasi-periodic state, and the synchronized state. The numerical model also distinguishes between in-phase and out-of-phase synchronization where out-of-phase synchronization is observed at low coupling strengths and low frequency detuning.

We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the oscillations using interferometry. Devices of different dimensions are used to introduce frequency detuning, and short silicon bridges connecting the micro-beams are used as mechanical coupling between the oscillators. The region of synchronization is plotted for the MEMS system in the detuning vs. coupling parameter space and compared with the numerical analysis of a corresponding, lumped-parameter model. Three states of oscillations are observed i.e. the drift state, quasi-periodic state, and the synchronized state. The numerical model also distinguishes between in-phase and out-of-phase synchronization where out-of-phase synchronization is observed at low coupling strengths and low frequency detuning.2022-0140

In this work, we experimentally investigate the dynamics of pairs of opto-thermally driven, mechanically coupled, doubly clamped, silicon micromechanical oscillators, and numerically investigate the dynamics of the corresponding lumped-parameter model. Coupled limit cycle oscillators exhibit striking nonlinear dynamics and bifurcations in response to variations in system parameters. We show that the input laser power influences the frequency detuning between two non-identical oscillators. As the laser power is varied, different regimes of oscillations such as the synchronized state, the drift state, and the quasi-periodic state are mapped at minimal and high coupling strengths. For non-identical oscillators, coexistence of two states, the synchronized state and the quasi-periodic state, is demonstrated at high coupling and high laser power. Experimentally, this bistability manifests as irregular oscillations as the system rapidly switches between the two states due to the system’s sensitive dependence on initial conditions in the presence of noise. We provide a qualitative comparison of the experimental and numerical results to elucidate the behavior of the system. [2022-0005]

In this work, we experimentally investigate the dynamics of pairs of opto-thermally driven, mechanically coupled, doubly clamped, silicon micromechanical oscillators, and numerically investigate the dynamics of the corresponding lumped-parameter model. Coupled limit cycle oscillators exhibit striking nonlinear dynamics and bifurcations in response to variations in system parameters. We show that the input laser power influences the frequency detuning between two non-identical oscillators. As the laser power is varied, different regimes of oscillations such as the synchronized state, the drift state, and the quasi-periodic state are mapped at minimal and high coupling strengths. For non-identical oscillators, coexistence of two states, the synchronized state and the quasi-periodic state, is demonstrated at high coupling and high laser power. Experimentally, this bistability manifests as irregular oscillations as the system rapidly switches between the two states due to the system's sensitive dependence on initial conditions in the presence of noise. We provide a qualitative comparison of the experimental and numerical results to elucidate the behavior of the system.