| It is of great significance and will be a guidance for us to discuss the multi-field couplings considering chemical reactions for solving practical problems in the field of energy,manufacture,medicine and some other areas,since materials show different dynamic evolution processes in the coupling mechanism with multifield attributions.The research of elastic-viscoplastic materials have attracted extensive attention for its complex properties and broad-ranging contents while being studyed in solid mechanics.The characteristic is that it contains combination of elastic,viscous or plastic effects.Based on the continuum theory,this paper carried out the theoretical modeling and analysis of thermo-electro-chemo-mechanically couplings for elastic-viscoplastic materials especially to further understand the influence of chemical process,and our work specifically completed as follows:A coupled theoretical framework of electrochemical active elastic-viscoplastic materials with finite deformation is established at first.Consider a continuum body which allows heat transfer-mass transfer-chemical reaction-large deformation,the deformation gradient is decomposed into elastic and inelastic parts,the electric displacement is decomposed into reversible and irreversible parts,and we introduced a viscoplastic deformation rate described by the extent of chemical reaction in kinematics.Based on conservation equations,Clausius Duhem inequality and the first constitutive relation,the second Piola-Kirchhoff stress,electrochemical potential,entropy,electric field strength,chemical affinity and other internal variables are related to elastic strain,total diffusion concentration,temperature,the reversible electric displacement,the extent of chemical reaction and other factors involved,with linear phenomenological relations being used to describe the dynamic evolution equations of each field respectively.We especially used the Nernst-Planck electrodiffusion equation and gave the updated Lagrange description of evolution of reversible reaction,quasi-order reaction,parallel reaction and continuous reaction to describe the dynamic processes of diffusion and chemical reaction in this paper.Finally,the corresponding initial conditions and boundary conditions are given for the subsequent numerical examples.Merits of the above theory are that it can both involve energy conversion,change of substances and electron / ion transfer,describe the coupling of electrochemical reaction-diffusion-current-heat flux-stress-deformation and help to realize the multi-field simulation of elastic-viscoplastic materials.Secondly,the viscoelastic soft material which is considered as a matter between solid and ideal fluid is modeled,and the absorption-pseudo order reaction-large deformation process of hydrogel under external electrified is analyzed.In order to understand the interaction between diffusion absorption and pseudo order reaction accurately,we distinguish diffusion induced volume ratio and reaction induced volume ratio from the total change,and divide the total concentration of absorbing into the sum of reacted and unreacted parts.Then the total concentration of absorption is modified with the unreacted part in the electrodiffusion kinetic equation,and the quasi-order reaction is considered in the reaction kinetic equation which is believed that is mainly related to the concentration of absorbed substance,but has nothing to do with the solid-state concentration in hydrogel.By solving the equilibrium equation of stress and the steady-state equation of reaction,we obtain the solution of two steady-state problems.By considering the time scales that after diffusion reaches equilibrium,the reaction happens,the first transient-state problem is calculated.The force balance,diffusion and chemical evolution equations are solved simultaneously,and the effect on the deformation of hydrogel are shown by the characteristic time ratio which stands for distinct proportion of the diffusion time scale and reaction time scale.Then,the elastic-viscoplastic metal materials with the characteristics of plastic and viscous effect are modeled,and the degradation-parallel reaction-small deformation process of Ni anode in solid oxide fuel cell,the insertion of lithium-reversible reactionlarge deformation process of solid electrolyte in all-solid-state lithium battery during discharge process are analyzed respectively.By introducing an internal variable to represent the degree of degradation and associating it with the growth of unit extent of oxidation to form a new state quantity which representing the degradation-reaction process,the former uses theory in continuum damage mechanics,and the stress-free / constraint growth of oxidation problems are solved while ignoring the reverse of reaction.It shows that the forces restrain reaction in time space and degree.The latter simplifies the problem of interfacial reaction to a one-dimensional transient deformation problem.Similarly,with the characteristic time ratio being used to show the corresponding proportion of diffusion time scale and reaction time scale,the stretching ratio of lithium embedded in solid electrolyte in the vertical direction,the electrochemical potential,volume ratio of insertion and volume ratio of chemical expansion along the interface with diffusion dominated,reaction dominated or diffusion-reaction competitive process are obtained,which helps to put forward beneficial ideas of battery manufacture in power supply.In the end,this proposed generalized thermo-electro-chemo-mechanically coupling theory with large deformation framework is not only suitable for modeling and analysis of hydrogels,solid oxide fuel cells and all-solid-state lithium batteries,but also for other viscoelastic soft materials and elastic-viscoplastic metal materials with multi-field coupling problems considering chemical reactions.In this paper,we introduce new independent state variables and concepts of the characteristic time ratio etc.,and numerical solution of the stress-dependent constitutive model and steady-state / transientstate examples with diffusion-reaction-deformation process are obtained. |
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