Dissipation Potential Research Articles

A Dissipative Green’s Function Approach to Modeling Gravity Waves behind Submerged Bodies

Potential flow-based methods are common in early design stages because of their associated speed and relative simplicity. By separating the resistance components of a ship into viscous and wave resistance, an inviscid method such as potential flow can be used for wave resistance determination. However, gravity waves are affected by viscosity and decay with time and distance. It has, therefore, long been assumed that the inclusion of a damping parameter in potential flow would better model the wave resistance. This article presents a Kelvin-Neumann dissipative potential flow model. A Rayleigh damping term is inserted into the Navier-Stokes equations to capture the decay of waves. A new 3D Green’s function based on the Havelock-Lunde formulation is derived by the use of a Fourier transform. An upper limit for the Rayleigh damping term is found by comparison with experiments and a possible improvement on conventional potential flow models for the wave making resistance prediction of a submerged ellipsoid is proposed.

Energetic upscaling strategy for grain growth. II: Probabilistic macroscopic model identified by Bayesian techniques

This paper is the second part of an energetic upscaling strategy to simulate grain growth at the macroscopic scale with state variables that contain statistical descriptors of the grain structure. The first part was dedicated to the derivation of a fast mesoscopic model of grain growth based on orientated tessellation updating method, which consists in a succession of Voronoi-Laguerre tessellations obtained by establishing an evolution law directly on the parameters defining the tessellations. In this contribution, the final step of the upscaling strategy is detailed by deriving macroscopic evolutions laws of the state variables representing statistical distributions of the grain structure. The approach relies on macroscopic free energy and dissipation potentials that are identified not axiomatically, but using a large database of mesoscopic computations. The macroscopic energy is found to be purely deterministic, although the dissipation necessitates to introduce a probabilistic framework. Indeed, an epistemic uncertainty arises due to the loss of information in the reduction of the amount of data between the detailed mesoscopic state and the statistical macroscopic state (i.e., several mesoscopic states can share the same macroscopic state). Classical Bayesian inference has been used to identify the probability density functions associated to the epistemic uncertainty. From the computational point of view, this work can be used to simulate grain growth at very large scale with short computation time, while processing rich statistical information about the grain structure, such as statistical indicators of the grain boundary character distribution. The resulting stochastic macroscopic model has been compared to several particular mesoscopic evolutions, and good agreement is observed. However, the macroscopic model still requires an experimental validation.

Seasonal characteristics of boundary layer over a high-altitude rural site in Western India: implications on dispersal of particulate matter.

The temporal variability of the planetary boundary layer height (PBLH) over Mahabaleshwar was studied for a period of 1 year from 1 December 2015 to 30 November 2016 using microwave radiometer (MWR) observations. The PBLH over Mahabaleshwar was found to be the highest during the pre-monsoon (March-May) season and lowest during the winter (December-February) season. The seasonal mean of PBLH was estimated to be 339±88 m during winter, 485±70 m during pre-monsoon, 99±153 m during monsoon, and 438±24 m during post-monsoon season. Frequency distribution analysis of PBLH during pre-monsoon season revealed that the formation of turbulence internal boundary layer (TIBL) is evident. In contrast, cold and moist air mass during the monsoon season enhances the wind shear with lower buoyancy term which results in lowering of PBLH. The comparison of PBLH between MWR and radiosonde observations shows a good correlation (r2 = 0.66, p=0.001). The growth rate was observed to be 388 m/h during pre-monsoon, 206 m/h during winter, 57 m/h during monsoon, and 167 m/h during post-monsoon season. The seasonal mean concentration of PM2.5 was found to be 42.3±4.6 μg/m3during winter, 33.4±8.7 μg/m3 during pre-monsoon, 6.6±2.2 μg/m3 during monsoon, and 26.1±1.7 μg/m3during post-monsoon season. The effect of higher loading of scattering-type aerosol (dust particle) was also investigated as a case study. The analysis reveals the inverse relationship between the PBL height variability and the particulate loading indicating the importance of aerosol direct effect. Analysis of the ventilation coefficient (Vc) revealed that the dissipation potential was higher (1736 m2/s) during pre-monsoon season as compared to (1191 m2/s, 455m2/s, and 1580 m2/s) winter, monsoon, and post-monsoon seasons.

Quantification of Shape Memory Alloy Damping Capabilities Through the Prediction of Inherent Behavioral Aspects

In this work the time response of pseudoelastic Shape Memory Alloy (SMA) wires is numerically simulated. In particular, the effect of their operation under partial phase transformation is investigated and quantified. Additionally, the effect of the thermomechanical coupling under cyclic operation is evaluated both under adiabatic and natural convection conditions. To this end, proper finite element models are generated considering a low-frequency harmonic sinusoidal excitation. The effect of the partial transformation and thermomechanical coupling on the operation of the SMA is highlighted by comparison with respective results acquired by finite element models which neglect the modified hardening function that accounts for the partial loops. The results suggest that the latent heat produced during forward transformation highly affects the energy dissipation potential of SMAs. The hardening behavior also affects the transformation evolution and therefore impacts the amount of heat generation/absorption. Although both phenomena, when accounted for, result in the prediction of an altered hysteresis area and consequently different dissipation capabilities, the scope of the paper is to highlight their importance on the calculated values of dissipated energy and loss factor. These quantities are of particular interest since they constitute crucial design parameters for the development of smart dampers employing SMA materials.

Incremental variational homogenization of elastoplastic composites with isotropic and Armstrong-Frederick type nonlinear kinematic hardening

In order to investigate the behavior of elastoplastic composites exhibiting both isotropic and nonlinear kinematic hardening, we extend the Double Incremental Variational (DIV) formulation of Lucchetta et al. (2019), based on both the incremental variational principles introduced by Lahellec and Suquet (2007) and the formulation proposed by Agoras et al. (2016). However, the Armstrong-Frederick model (Armstrong and Frederick), which is very often used to describe nonlinear kinematic hardening and refers to the framework of non-associated plasticity (Chaboche, 1977), cannot be handled within the framework of generalized standard materials as required by the incremental variational principles on which the DIV formulation relies. That is why we work with an approximation of this model, namely the modified Chaboche model (Chaboche, 1983). As the dissipation potential associated with this model depends on internal variables, we have to extend the incremental variational principles of Lahellec and Suquet to such a situation. Then, we apply twice the variational procedure of Ponte Castañeda (1991), first to linearize the local behavior and then to deal with the intraphase heterogeneity of the thermoelastic Linear Comparison Composite (LCC) induced by the linearisation step. The resulting thermoelastic LCC with per-phase homogeneous properties is homogenized by classical linear schemes. We develop and implement this new incremental variational procedure for two-phase matrix-inclusions composites with an isotropic elastoplastic matrix exhibiting combined isotropic and nonlinear kinematic hardening. For various cyclic loadings, the predictions of the proposed DIV formulation compare favorably with Finite Element simulations based on the Armstrong-Frederick model.

Dynamically consistent coarse-grain simulation model of chemically specific polymer melts via friction parameterization.

Coarse-grained (CG) models of polymers involve grouping many atoms in an all-atom (AA) representation into single sites to reduce computational effort yet retain the hierarchy of length and time scales inherent to macromolecules. Parameterization of such models is often via "bottom-up" methods, which preserve chemical specificity but suffer from artificially accelerated dynamics with respect to the AA model from which they were derived. Here, we study the combination of a bottom-up CG model with a dissipative potential as a means to obtain a chemically specific and dynamically correct model. We generate the conservative part of the force-field using the iterative Boltzmann inversion (IBI) method, which seeks to recover the AA structure. This is augmented with the dissipative Langevin thermostat, which introduces a single parameterizable friction factor to correct the unphysically fast dynamics of the IBI-generated force-field. We study this approach for linear polystyrene oligomer melts for three separate systems with 11, 21, and 41 monomers per chain and a mapping of one monomer per CG site. To parameterize the friction factor, target values are extracted from the AA dynamics using translational monomer diffusion, translational chain diffusion, and rotational chain motion to test the consistency of the parameterization across different modes of motion. We find that the value of the friction parameter needed to bring the CG dynamics in line with AA target values varies based on the mode of parameterization with short-time monomer translational dynamics requiring the highest values, long-time chain translational dynamics requiring the lowest values, and rotational dynamics falling in between. The friction ranges most widely for the shortest chains, and the span narrows with increasing chain length. For longer chains, a practical working value of the friction parameter may be derived from the rotational dynamics, owing to the contribution of multiple relaxation modes to chain rotation and a lack of sensitivity of the translational dynamics at these intermediate levels of friction. A study of equilibrium chain structure reveals that all chains studied are non-Gaussian. However, longer chains better approximate ideal chain dimensions than more rod-like shorter chains and thus are most closely described by a single friction parameter. We also find that the separability of the conservative and dissipative potentials is preserved.

An explicit dissipative model for isotropic hard magnetorheological elastomers

Hard magnetorheological elastomers (h-MREs) are essentially two phase composites comprising permanently magnetizable metallic inclusions suspended in a soft elastomeric matrix. This work provides a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible h-MREs. Energy dissipates in such hard-magnetic composites primarily via ferromagnetic hysteresis in the underlying hard-magnetic particles. The proposed constitutive model is thus developed following the generalized standard materials framework, which necessitates suitable definitions of the energy density and the dissipation potential. Moreover, the proposed model is designed to recover several well-known homogenization results (and bounds) in the purely mechanical and purely magnetic limiting cases. The magneto–mechanical coupling response of the model, in turn, is calibrated with the aid of numerical homogenization estimates under symmetric cyclic loading. The performance of the model is then probed against several other numerical homogenization estimates considering various magneto–mechanical loading paths other than the calibration loading path. Very good agreement between the macroscopic model and the numerical homogenization estimates is observed, especially for stiff to moderately-soft matrix materials. An important outcome of the numerical simulations is the independence of the current magnetization to the stretch part of the deformation gradient. This is taken into account in the model by considering an only rotation-dependent remanent magnetic field as an internal variable. We further show that there is no need for an additional mechanical internal variable. Finally, the model is employed to solve macroscopic boundary value problems involving slender h-MRE structures and the results match excellently with experimental data from literature. Crucial differences are found between uniformly and non-uniformly pre-magnetized h-MREs in terms of their pre-magnetization and the associated self-fields.

Behavior of steel-reinforced composite concrete columns under combined axial and lateral cyclic loading

This study presents the experimental and numerical investigations on structural steel-reinforced concrete (SRC) columns under combined axial and lateral cyclic loadings. The main parameters evaluated are the peak lateral strength, mode of failure, hysteretic response, stiffness degradation, and energy dissipation potential of SRC columns. A parametric study has been conducted using a finite element software ABAQUS to predict the flexural capacity of the SRC columns under varying axial load levels and to evaluate the reliability of the design guidelines of Eurocode 4 (2004) and AISC 360-16 (2016) in predicting the axial load (P) - bending moment (M) interaction behavior of SRC columns. In the tension damage regions, the experimental and numerical data points mostly lie within or on the unfactored P-M envelopes of both these standards. However, the data points are found to fall outside the P-M envelopes in the compression damage region. For the SRC columns designed to fail in the compression damage, the Eurocode 4 (2004) provisions showed a more reliable prediction of the failure loads under the uniaxial bending condition.

Thermal and mechanical properties of epoxy resin reinforced with modified iron oxide nanoparticles

AbstractEpoxy polymers, having good mechanical properties and thermal stability, are often used for engineering applications. Their properties can be further enhanced by the addition of iron oxide (Fe3O4) nanoparticles (NPs) as fillers to the resin. In this study, pristine Fe3O4 NPs were functionalized with polydopamine (PDA), (3‐glycidoxypropyl)trimethoxysilane (GPTMS), and (3‐aminopropyl)trimethoxysilane (APTES). X‐ray diffraction and scanning electron microscopy (SEM) were used to study any changes in the crystal structure and size of the NPs while Fourier‐Transform Infrared Spectroscopy (FTIR) and Thermogravimetric Analysis (TGA) were used to ensure the presence of functional groups on the surface. The mechanical properties of the Fe3O4‐based nanocomposites generally improved except when reinforced with Fe3O4/PDA. The maximum improvement in tensile strength (∼34%) and fracture toughness (∼13%) were observed for pristine Fe3O4‐based nanocomposites. Dynamic mechanical analysis (DMA) showed that the use of any of the treated NPs improved the material's initial storage modulus and had a substantial impact on its dissipation potential. Also, it was observed that the glass transition temperature measurements by DMA and differential scanning calorimetry were below that of pure epoxy. SEM of the cracked surfaces shows that the incorporation of any NPs leads to an enhancement in its thermal and mechanical properties.

A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a aContribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

We demonstrate the stabilization of two-dimensional nonlinear wave patterns by means of a dissipative confinement potential. Our analytical and numerical analysis, based on the generalized dissipative Gross-Pitaevskii equation, makes use of the close analogy between the dynamics of a Bose-Einstein condensate and that of mode-locked fiber laser, operating in the anomalous dispersion regime. In the last case, the formation of stable two-dimensional patterns corresponds to spatiotemporal mode locking, using dissipation-enhanced mode cleaning. We analyze the main scenarios of pattern destabilization, varying from soliton dissolution to its splitting and spatiotemporal turbulence, and their dependence on graded dissipation.

Interface pinning causes the hysteresis of the hydride transformation in binary metal hydrides

Hydriding and dehydriding transitions in bulk and nanocrystalline binary metal hydrides were studied using the Pd-H model system by measuring pressure-composition isotherms with in situ x-ray diffractometry. Nanocrystalline Pd showed a smaller pressure hysteresis, solvus hysteresis, and hysteresis in lattice parameter, compared to bulk Pd. The time-dependence of pressure equilibration was measured after dosing with aliquots of hydrogen, giving equilibration times that were much faster in the single-phase regions than in the two-phase plateaus. In the broad two-phase plateaus, the pressure relaxations were exponential functions of time. An explanation of hysteresis is developed that is based on a dissipative potential barrier that impedes the motion of the interface due to interactions between lattice defects and the two-phase interface. The exponential pressure relaxations and hysteresis are consistent for this mechanism. For a simple model of the pinning potential, the potential barrier maximum is an order of magnitude less than typical grain boundary energies. These pinning effects are substantially different in the nanocrystalline Pd, suggesting differences in the hydriding mechanism.

Harnessing fluctuation theorems to discover free energy and dissipation potentials from non-equilibrium data

The Jarzynski relation, as an equality form of the second law of thermodynamics, represents an exact thermodynamic statement that is valid arbitrarily far away from equilibrium. This remarkable relation directly links the equilibrium free energy difference between two states and the probability distribution of the work done along a process that drives the system from one state to the other. Here, we leverage the Jarzynski equality and a local equilibrium assumption, to go beyond the calculation of free energy differences and also extract the dissipation potential from additional measurements of kinematic field variables (strain and velocity fields). The proposed strategy is exemplified over pulling experiments of mass–spring models obeying overdamped Langevin dynamics, which is a prototype for nanorods, fibrous macro-molecules and the Rouse model of polymers. Different interaction potentials, fluid viscosities and bath temperatures are studied, so as to intrinsically control how close or far away the system is from equilibrium. The data-inferred continuum models are then validated against processes governed by different pulling protocols, thereby demonstrating their predictive capability. The methods presented here represent a first step toward full material characterization from non-equilibrium data of macroscopic observables, which could potentially be obtained from experimental observations.

Thermo-mechanical coupled incremental variational formulation for thermosetting resins subjected to curing process

This study presents an incremental variational formulation (IVF) for the thermo-mechanical problem of resin products subjected to curing, for which a dual dissipation potential (DDP) for the cure state is originally derived in conjunction with that for viscoelasticity. Following the thermodynamically consistent formulation for the time evolution equation of the degree of cure (DOC) of a thermosetting resin and the linear viscoelastic law, we derive these DDPs by way of Legendre-Fenchel transformations with respect to characteristic dissipations. The evolution of DOC is then casted into the flow rule in mathematical theory of plasticity with the introduction of the curing multiplier as a new internal state variable in an analogous fashion to Perzyna’s viscoplastic regularization theory. Then, the pseudo stress is introduced as a new internal state variable to parameterize the derived flow rule of DOC. By virtue of this pseudo stress, we naturally define an incremental variational problem constrained by the parameterized flow rule in order to construct a semi-implicit scheme for the variational constitutive update. The finite element discretization is applied to the governing equations that satisfy the stationary conditions so that we could perform thermo-mechanical analyses of a thermosetting resin subjected to curing with the strong coupling procedure. The verification analysis is conducted to confirm the validity of the numerical result obtained by the proposed method in comparison with that of the conventional framework and followed by a demonstrative numerical example to simulate the stress development and relaxation in a virtual device subjected to different thermal histories.

Exact results for weakly nonlinear composites and implications for homogenization methods

Weakly nonlinear composite conductors are characterized by position-dependent dissipation potentials expressible as an additive composition of a quadratic potential and a nonquadratic potential weighted by a small parameter. This additive form carries over to the effective dissipation potential of the composite when expanded to first order in the small parameter. However, the first-order correction of this asymptotic expansion depends only on the zeroth-order values of the local fields, namely, the local fields within the perfectly linear composite conductor. This asymptotic expansion is exploited to derive the exact effective conductivity of a composite cylinder assemblage exhibiting weak nonlinearity of the power-law type (i.e., power law with exponent m=1+δ, such that |δ|≪1), and found to be identical (to first order in δ) to the corresponding asymptotic result for sequentially laminated composites of infinite rank. These exact results are used to assess the capabilities of more general nonlinear homogenization methods making use of the properties of optimally selected linear comparison composites.

Explicit form of yield conditions dual to a class of dissipation potentials dependent on three invariants

In the paper, a pragmatic approach to finding the dual formulation for isotropic perfectly plastic materials given a dissipation potential dependent on three cylindrical invariants and involving the Ottosen shape function is proposed and illustrated by examples. The main goal is to provide instructions on how to perform the Legendre transformation used when passing from a dissipation potential to its conjugate yield condition and offer some suggestions regarding calibration for particular potentials dependent on the trace of the strain rate tensor and the product of the norm of its deviator and the Ottosen shape function, which covers a wide class of engineering materials. The classic framework for constitutive modelling of thermodynamically consistent materials within the small deformation theory is used. First, general formulae connecting a dissipation potential dependent on three invariants of the strain rate tensor to the coupled yield condition are derived. Then, they are narrowed down for the aforementioned case of dissipation functions dependent on the Lode angle in a way proposed by Ottosen. Finally, three examples are given involving classical potentials: Beltrami’s, Drucker–Prager’s and Mises–Schleicher’s generalised potential using the shape function. Detailed calculations exposing the introduced technique are performed. Also, a method of the calibration of such potentials leading to explicit mathematical formulae is demonstrated, based on the typical tests located on the tension and compression meridians.

Symmetry analysis and equivalence transformations for the construction and reduction of constitutive models

A methodology based on Lie analysis is proposed to investigate the mechanical behavior of materials exhibiting experimental master curves. It is based on the idea that the mechanical response of materials is associated with hidden symmetries reflected in the form of the energy functional and the dissipation potential leading to constitutive laws written in the framework of the thermodynamics of irreversible processes. In constitutive modeling, symmetry analysis lets one formulate the response of a material in terms of so-called master curves, and construct rheological models based on a limited number of measurements. The application of symmetry methods leads to model reduction in a double sense: in treating large amounts number of measurements data to reduce them in a form exploitable for the construction of constitutive models, and by exploiting equivalence transformations extending point symmetries to efficiently reduce the number of significant parameters, and thus the computational cost of solving boundary value problems (BVPs). The symmetry framework and related conservation law analysis provide invariance properties of the constitutive models, allowing to predict the influence of a variation of the model parameters on the material response or on the solution of BVPs posed over spatial domains. The first part of the paper is devoted to the presentation of the general methodology proposed in this contribution. Examples of construction of rheological models based on experimental data are given for setting up a reduced model of the uniaxial creep and rupture behaviour of a Chrome-Molybdenum alloy (9Cr1Mo) at different temperatures and stress levels. Constitutive equations for creep and rupture master responses are identified for this alloy, and validated based on experimental data. Equivalence transformations are exemplified in the context of parameter reduction in fully nonlinear anisotropic fiber-reinforced elastic solids.

Discrete approximation of dynamic phase-field fracture in visco-elastic materials

<p style='text-indent:20px;'>This contribution deals with the analysis of models for phase-field fracture in visco-elastic materials with dynamic effects. The evolution of damage is handled in two different ways: As a viscous evolution with a quadratic dissipation potential and as a rate-independent law with a positively <inline-formula><tex-math id="M1">\begin{document}$ 1 $\end{document}</tex-math></inline-formula>-homogeneous dissipation potential. Both evolution laws encode a non-smooth constraint that ensures the unidirectionality of damage, so that the material cannot heal. Suitable notions of solutions are introduced in both settings. Existence of solutions is obtained using a discrete approximation scheme both in space and time. Based on the convexity properties of the energy functional and on the regularity of the displacements thanks to their viscous evolution, also improved regularity results with respect to time are obtained for the internal variable: It is shown that the damage variable is continuous in time with values in the state space that guarantees finite values of the energy functional.</p>

Numerical simulation of cyclic deformation behavior of SLM‐manufactured aluminum alloys

AbstractThe selective laser melting process has already been developed for many metallic materials, including steel, aluminum, and titanium. The quasi‐static properties of these materials have been found to be comparable or even better than their conventionally manufactured counterparts. However, for their reliable application in operational components, their fatigue behavior plays a critical role. This phenomenon is dominated by several process‐related features, such as surface roughness, remnant porosity, microstructure and residual stresses. The present contribution shows a model which relies on an assumption for the Helmholtz free energy and the dissipation potential. To be more precise: the phase‐field method is applied to simulate the damage evolution, whereas plastic effects are modeled in terms of the isotropic hardening. It is assumed that the damage evolution only occurs in the tension mode of a cyclic load, which is achieved by the decomposition of the stored energy. The numerical results give insight into the evolution of plastic deformations and of damage at a material point and for a chosen mesoscopic sample.

A variational concept and its experimental calibration for temperature‐induced rate‐dependent phase transformations in steel

AbstractIn forming processes of metals, different physical phenomena are observable which may alter the material properties and behavior severely. These observations can be attributed to changes in the surface layer of the material. This research is a part of the transregional collaborative research center SFB/TRR 136 which deals with surface layer modifications in 42CrMo4 steels and aims to determine process independent correlations between material loads and material modifications. These correlations are called process signatures. The present work is concerned with investigating thermally induced solid‐solid phase transformations in steels. An example of a predominantly thermal process is the induction hardening process. In this process, an initially ferritic‐pearlitic structure is at first heated until reaching a temperature that lies above the temperature at which homogeneous austenite is formed. During this heating process, the steel undergoes diffusion‐driven phase transformations which are heating‐rate‐ and time‐dependent. After sufficiently long incubation, a homogeneous austenitic microstructure is obtained. Then, the specimen temperature is lowered at a very high cooling rate. This invokes high‐temperature rates on the microstructure and results in an austenitic‐martensitic phase transformation, see e.g. [1]. Based on the Principle of the Minimum of the Dissipation Potential (PDMP) as presented in [2], the austenitic‐martensitic transformation has been widely discussed in the context of shape memory alloys. We present a material model which is also able to show the ferritic‐austenitic transformation. The individual phase transitions are modeled using a rate‐ and transformation‐process‐dependent formulation of the dissipation potential. The presented material model is finally tested with numerical simulations.

Bio-inspired surface modification of iron oxide nanoparticles for active stabilization in hydrogels.

Biological materials employ a variety of dynamic interactions in sophisticated composite structures to function adaptively on different time and length scales. Inspired by such designs we develop a novel surface modification approach to promote dynamic interactions between nanoparticles and polymer chains in physical and double network hydrogels. Physical hydrogels are formed via reversible complexation of borate ions with poly(vinyl alcohol) (PVA) and chemical crosslinks are introduced by electron beam irradiation. Dopamine is used for surface modification of magnetic iron oxide nanoparticles (MNPs) in two different ways: the direct treatment results in anchoring via catechol groups, whereas the indirect method leaves the catechol group on the free surface of MNPs. Although the former particles show very good colloidal stability, they lower the network connectivity, which results in lower plateau modulus, faster terminal relaxation, and lower yield stress, presumably due to imposing an extra distance between PVA chains. In contrast to this passive design, the latter particles actively reinforce the network by forming clusters of physical bonds between catechol groups of the individual particles and the monodiol complexes of the borate ions and PVA chains. Moreover, the additional complexes formed upon the introduction of nanoparticles with active surfaces provide further energy dissipation potential and therefore enhance the toughness. This approach can help develop novel hydrogels with superior toughness and multiple stimuli-responsiveness.