Multifield Coupling Response Analysis Of Three-dimensional Elastomers Based On Fractional Order Strain

The classical Fourier theory of heat conduction holds that the speed of heat propagation is infinite.This view is inconsistent with experimental results.Experiments have shown that heat waves propagate at a finite speed,which has led to the generalized theory of thermoelasticity.Generalized thermoelastic theory mainly includes: one thermal relaxation time Lord-Shulman(L-S)theory,two thermal relaxation time Green-Lindsay(G-L)theory,and green-Naghdi(G-N)theory without energy dissipation.For anomalous conduction,anomalous diffusion,viscoelastic materials,biological materials,porous materials,organic materials,and piezoelectric materials,the thermoelastic behavior is difficult to describe with classical thermoelastic theory and generalized thermoelastic theory.Since fractional calculus has successfully solved isochronous curve integral equations,it has been widely used in various fields.Fractional calculus operators have been introduced to describe the memory-dependent effects of elastomer.Fractional-order generalized thermoelastic theory has been established.Based on the generalized thermoelastic theory of fractional order strain,this paper uses the fractional order to describe the memory-dependent effect,establishes a three-dimensional semi-infinite elastic body multiple-field coupling problem,and studies the memory-dependent and size-dependent effects when subjected to thermal shock.Studies that consider the dynamic response of memory-dependent effects when taking into account;studies that consider memory-dependent effects and material characteristics and temperature when subjected to thermal shock.The details are as follows:(1)Establish a three-dimensional isotropic homogeneous elastomer model with free surface under thermal shock.The Nonlocal model of Eringen is used to describe the size-dependent effect.The coupled governing equations considering size-dependent effect and memory-dependent effect are applied to the three-dimensional half-space model.After dimensionless processing,the Laplace transform,double Fourier transform and inverse numerical transformation are used to solve the coupled governing equations,and the dimensionless temperature,stress,strain and displacement physical quantities are obtained under different fractional order and size-related parameters distribution law.The results show that fractional-order parameters and size-related parameters have limited effects on thermal waves and significant effects on mechanical waves.(2)Establish a three-dimensional isotropic homogeneous elastomer model with free surface under the action of a moving heat source,and apply a coupled governing equation considering memory-dependent effects to a three-dimensional half-space model.Thedistribution laws of dimensionless temperature,stress,strain and displacement under different moving heat source velocities and fractional parameters are derived.The results show that the fractional order parameters have a limited effect on the heat wave,while the moving heat source speed parameter has a certain effect on the heat wave;the fractional order parameters and the moving heat source speed have a significant effect on the mechanical wave.(3)Establish a three-dimensional isotropic homogeneous elastomer model with free surface affected by thermal shock.A linear function of temperature is used to describe the temperature dependence of material properties.A coupling control equation that considers memory-dependent effects is introduced into the temperature dependence of material properties.For 3D half-space models.The coupling governing equations for different hysteresis factor,fractional-order parameters,and temperature-related parameters are derived,and the distribution laws of dimensionless temperature,stress,and strain for each physical quantity are obtained.The results show that the effects of hysteresis factor and fractional order parameters and temperature-related parameters are similar,with limited effects on thermal waves and significant effects on stress and displacement.