Damage Gradient Theory And Numerical Simulation Of Medium

In the processing of dielectric materials damage-failure problems, existingclassical Continuum Damage Mechanics ( CDM ) suggests that the stress of materialonly depends on the strain of the point itself and the deformation history, andirrelevant to other points of material. There always exists defects in the material infact, so the material continuity assumption of CDM can not be achieved in the strictsense. the usage of CDM theory to the numerical simulation of mediumdamage-failure phenomenon will appear to depend on the meshence obviously, and itcan not explain the localization phenomenon of medium damage reasonably.Based on the damage theory of thermodynamics, the strain tensor, damagevariable, damage variable gradient is assumed as the internal state variables ofHelmholtz free energy function. By constitutive functional expansion method the freeenergy function for Taylor expansion is implemented near the initial damage ofmaterial and the first ladder degree damage constitutive equation and the equation ofdamage evolution considering the effects of nearage damage gradient in the damagematerial is established. The damage-failure process of medium is descripted by theperspective of damage gradient.The coefficients of first ladder damage constitutive equation and damageevolution equation are analyzed. When the coefficient varies, the first ladder damageconstitutive equation can degenerate into linear elastic stress-strain constitutiveequation, linear elastic damage material damage constitutive equation based on thestrain equivalence hypothesis, isotropic elastic damage constitutive equation anddamage gradient constitutive equation considering the damage first ladder.Based on the theoretical analysis and ANSYS finite element software the damagefailure process of sample is simulated numerically by classical damage model andfirst ladder damage model.The static analysis results is gained by APDL language model, the damage valuefor each node is acquired by choosing reasonable damage evolution in the APDL.Then the cell damage value will be obtained over joint damage value.The unit elasticmodulus is modified by the unit damage value substituted into the damageconstitutive relation. Finally the convergence criteria is satisfied to realize the damagefield numerical simulation through iteration. The damage gradient of node and element for material damage field is considered over node and element finitedifference.Based on the two kinds of theory the results of numerical simulation areanalyzed. The medium damage simulation based on classical damage model exsitsbigger difference by three different grid size model of damage distribution in area andsize, which verifies the classical damage model dependence meshence. The gradientdamage model is simulated at different grid sizes, and the results remove eliminateclassic damage model meshence dependence. The first ladder damage models ofdifferent materials inside dimension value are analysed.