A Review on the Mullins Effect in Tough Elastomers and Gels

Tough elastomers and gels have garnered broad research interest due to their wide-ranging potential applications.However,during the loading and unloading cycles,a clear stress softening behavior can be observed in many material systems,which is also named as the Mullins effect.In this work,we aim to provide a complete review of the Mullins effect in soft yet tough materials,specifically focusing on nanocomposite gels,double-network hydrogels,and multi-network elastomers.We first revisit the experimental observations for these soft materials.We then discuss the recent developments of constitutive models,emphasizing novel developments in the damage mechanisms or network representations.Some phenomenological models will also be briefly introduced.Particular attention is then placed on the anisotropic and multiaxial modeling aspects.It is demonstrated that most of the existing models fail to accurately predict the multiaxial data,posing a significant challenge for developing future anisotropic models tailored for tough gels and elastomers.

Deformable micro-continua in which quantum mysteries reside

Deformable micro-continua of highly localized nature are found to exactly exhibit all quantum effects commonly known for quantum entities at microscopic scale.At every instant,the spatial configuration of each such micro-continuum is prescribed by four spatial distributions of the mass,the velocity,the internal stress,and the intrinsic angular momentum.The deformability features of such micro-continua in response to all configuration changes are identified with a constitutive equation that specifies how the internal stress responds to the mass density field.It is shown that these microcontinua are endowed with the following unique response features:(i)the coupled system of the nonlinear field equations governing their dynamic responses to any given force and torque fields is exactly reducible to a linear dynamic equation governing a complex field variable;(ii)this fundamental dynamic equation and this complex field variable are just the Schrodinger equation and the complex wave function in quantum theory;and,accordingly,(iii)the latter two and all quantum effects known for quantum entities are in a natural and unified manner incorporated as the inherent response features of the micro-continua discovered,thus following objective and deterministic response patterns for quantum entities,in which the physical origins and meanings of the wave function and the Schrodinger equation become self-evident and,in particular,any probabilistic indeterminacy becomes irrelevant.

A Unified Approach Toward Simulating Constant and Varying Amplitude Fatigue Failure Effects of Metals with Fast and Efficient Algorithms

A new finite strain elastoplastic J2-flow model is established with an explicit formulation of work-hardening and softening effects up to eventual failure,in which both a new flow rule free of yielding and an asymptotically vanishing stress limit are incorporated.The novelties of this new model are as follows:(i)Fatigue failure effects under repeated loading conditions with either constant or varying amplitudes are automatically characterized as inherent response features;(ii)neither additional damage-like variables nor failure criteria need to be involved;and(iii)both high-and low-cycle fatigue effects may be simultaneously treated.A fast and efficient algorithm of high accuracy is proposed for directly simulating high-and medium-high-cycle fatigue failure effects under repeated loading conditions.Toward this goal,a direct and explicit relationship between the fatigue life and the stress amplitude is obtained by means of explicit and direct procedures of integrating the coupled elastoplastic rate equations for any given number of loading-unloading cycles with varying stress amplitudes.Numerical examples suggest that the new algorithm is much more fast and efficient than usual tedious and very time-consuming integration procedures.

Notes on micro-continua exhibiting quantum effects

1 Uniqueness concerning exact linearization Most recently[1–2],the Schr¨odinger equation governing the quantum effects has been shown to be derivable as exact linearization from the following nonlinear field equations governing the dynamic responses of the newly discovered quantum-continua[1–2].