Electro-chemo-thermo-mechanical couplings, wherein electro-chemo-thermal processes interact with mechanical deformation, govern the behavior of a wide class of multi-functional materials and devices. Typical examples are batteries and shape-morphing devices that comprise electrodes separated by (liquid or solid) electrolyte. In these systems, ionic transport, electrochemical reactions, and electric fields are intrinsically coupled with deformation, both in the bulk material and, not the least, at interfaces. In this paper we consider, at the outset, the generic situation when ions and electrons coexist (at the considered scale of continuum). To retain maximal generality, we then consider the interface as an “energetic” surface that is equipped with its own balance and constitutive equations. It is thereby tacitly assumed that the interface is “imperfect” in the sense that kinematic as well as flux variables are discontinuous across the interface. We develop a generic thermodynamically consistent framework, while restricting to small strain kinematics, that provides constraints on constitutive relations for the bulk material, as well as for the interface, from mechanical, electric, chemical and thermal viewpoints. A particular challenge is offered by extending Ampere’s and Faraday’s laws, as well as establishing the proper definition of the Poynting vector (representing the electro-magnetic power), to interfaces. As illustrations of the canonical framework, under isothermal conditions, we consider three specific systems: (a) An electronic conductor of dissimilar material with electronic interface, (b) an ionic conductor of dissimilar material with ionic interface, (c) electrode/electrolyte with electronic interface. The latter may represent a halfcell, wafering a Solid Electrolyte Interphase (SEI), in a battery or in a shape-morphing device. The electro-chemical activity in the interface is modeled by classical and non-classical models of Butler–Volmer type, which are shown to be thermodynamically consistent.
Attenuating low-frequency vibrations in piping systems remains a significant challenge for conventional passive vibration control techniques. This work presents a computational framework for the large-deformation analysis and design of flexible curved-beam-based quasi-zero-stiffness (QZS) resonators and demonstrates their application to low-frequency metamaterial pipes. The framework combines the chain beam constraint model (CBCM) with non-uniform rational B-splines (NURBS) to efficiently capture the nonlinear response of flexible curved beams and enable iterative geometric design. Exploiting the geometric flexibility of NURBS, the curved beam is tailored to realize prescribed QZS characteristics. The optimized curved beam is subsequently employed to construct a QZS resonator, where pre-compression is introduced to tailor the equivalent linear stiffness about the static equilibrium configuration. Under small-amplitude excitation, the resonator is represented by an equivalent spring–mass system and periodically integrated into a pipe. Flexural wave propagation is analyzed using the transfer matrix method for infinite periodic pipes and wave approach for finite pipes, with results validated by finite element simulations. The results demonstrate that pre-compression enables tunable low-frequency flexural wave bandgaps. Parametric analyses reveal that damping mainly affects attenuation, whereas the unit-cell length, resonator mass, equivalent stiffness, and mass–stiffness ratio govern the bandgap characteristics.
Highly filled particulate-reinforced composites exhibit pronounced finite-deformation nonlinearity, rate dependence, stress relaxation, and damage-induced softening under complex loading histories. Conventional finite-deformation viscoelastic damage models commonly use the same nonequilibrium variables to describe both the stress enhancement generated during finite-rate loading and the subsequent relaxation during strain holding. This treatment assigns the two responses to the same internal states and characteristic time scales, obscuring their distinct evolution and limiting model transferability across loading paths. Here, a solid propellant is studied as a representative highly filled composite. Cyclic relaxation tests and tensile tests performed over a range of strain rates reveal a transient rate-enhancement effect that is activated during loading and decays during holding. Motivated by this observation, a finite-deformation viscoelastic damage model is developed in which transient rate-enhancement and nonequilibrium stress relaxation are governed by independent internal variables and evolution laws. A physics-informed hierarchical identification procedure separately determines the parameters associated with equilibrium response, relaxation, damage, and rate-enhancement. The model reproduces rate-dependent loading-holding responses, multi-step stress relaxation, and cyclic Mullins softening, and is implemented in a three-dimensional finite element framework through a user material subroutine. The simulations capture localized deformation and progressive damage in complex geometries, while comparison with independent biaxial experimental data supports the transferability of parameters identified from uniaxial data to multiaxial loading conditions. The formulation provides a physically interpretable framework for highly filled composites under complex loading histories.
