Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics.The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics is given.The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given.The forms of variable orders fractional Noether conserved quantities corresponding to Noether symmetry generators solutions of the model under different conditions are discussed in detail,and it is found that the expressions of variable orders fractional Noether conserved quantities are closely dependent on the external nonconservative forces and material parameters of the neuron.

Theoretical and experimental study on multiscale coupled Mohr-Coulomb shear strength criterion of fibre-reinforced sand

Fibre-reinforced sand(FRS)is a multiphase and multiscale geo-material,which is widely used in geotechnical engineering as supporting structure of excavation of underground space and reinforcement of foundation of underground structures,and its strength is determined by the properties of the heterogeneous substances of the FRS and their coupling mechanical responses.In order to investigate the influence of fibre characteristics and mechanical properties on the shear strength of the FRS,according to the microscopic interface slip effect generated by the interaction between sand particles and the interaction between these particles and fibre,the material phase of the FRS is divided to conceptualize a micro cell element of the FRS that is capable of reflecting the internal material characteristic information of the FRS.Moreover,based on the coordinated deformation condition between fibres and sand particles at the microscale and the couple stress theory that is capable of effectively describing the discontinuous mechanical responses at the sand-fibre interface,a mesomechanism-based multiscale Mohr–Coulomb shear strength criterion of the FRS is derived,and the yield locus of the FRS is also drawn on the p plane.Furthermore,a series of FRS samples with different fibre content and fibre length were prepared by adopting the freezing method,and consolidated and drained triaxial compression tests were conducted on these samples to validate the proposed multiscale coupled Mohr–Coulomb shear strength criterion.Results show that the multiscale coupled Mohr–Coulomb shear strength criterion is capable of effectively reproducing and predicting the yield strength of the FRS.The yield locus of the FRS extends outwards as fibre content and fibre length increase.The yield stress of the FRS predicted by the proposed multiscale coupled Mohr–Coulomb shear strength criterion is in good agreement with that of the test result.

A review of multiscale expansion of low permeability reservoir cracks

The study of rock crack propagation by multi-scale method is of great significance to comprehensively and accurately understand the law of rock crack evolution.In this paper,the theoretical,experimental and numerical methods from macroscale,mesoscale and microscale used for crack propagation in recent years are summarized and analyzed.Firstly,the evolution mechanism of the crack and the related research status are analyzed from a single scale.Secondly,multi-scale theory,modeling,meshing algorithm and macro-mesoscopic parameters are reviewed in the multi-scale coupling method.Through the analysis of the results published in recent years,it is considered that the following aspects need to be further studied:the characteristic parameters of the rock are different at different scales,so the extraction of the characteristic parameters under different scales is essential to modeling and coupling;the heterogeneity of rock and the prefabrication of cracks are greatly affected by human factors,so that 3D printing will be a good breakthrough to build the model of crack owing to its accurate control on the distribution and the size of cracks.The internal stress field of the rock is complex and varied,and the generation and expansion of the microcracks in the process of crack propagation are closely related to the surrounding environment.Therefore,it is of great importance to combine theoretical,experimental and numerical research with practical engineering.

Quantifying the solid electrolyte interphase stress induced capacity fading of lithium-ion batteries via a multiscale mechanicalelectrochemical coupling model

The solid electrolyte interphase(SEI)is widely recognized as a critical factor leading to the capacity fading of lithium-ion batteries(LIBs).Although SEI stress-related mechanical failure caused by the expansion or contraction of active materials upon cycles is well documented,previously reported SEI components and overpotential varying phenomena due to SEI stress and their effects on the electrochemical performance are poorly understood.Here,we establish a quantitative correlation between capacity fading and the SEI stress by considering its effects on side reactions,especially SEI component evolution,in a multiscale mechanical-electrochemical coupling model.Furthermore,the capacity fading behaviors of two typical cells(Li[NiMnCo]O_(2) as the cathode,and graphite and silicon as the anode,respectively)were adopted as numerical examples to demonstrate its potential utility and applications.Stress within the SEI was indeed found to play a predominant role in the capacity fading of the graphite and silicon anodes,resulting in 27%and 69%of the total capacity loss after 200 and 100 cycles at 1 C,respectively.This study provides valuable mechanical insights into the variations of SEI properties related to the capacity degradation and SEI optimization and design for LIBs.