基于介观力学信息的颗粒材料损伤-愈合与塑性宏观表征

摘要

本文在二阶计算均匀化框架下提出了颗粒材料损伤--愈合与塑性的多尺度表征方法.颗粒材料结构在宏观尺度模型化为梯度Cosserat连续体,在其有限元网格的每个积分点处定义具有离散颗粒介观结构的表征元.建立了表征元离散颗粒系统的非线性增量本构关系.表征元周边介质作用于表征元边界颗粒的增量力与增量力偶矩以表征元边界颗粒的增量线位移与增量转动角位移、当前变形状态下表征元离散介观结构弹性刚度、以及凝聚到表征元边界颗粒的增量耗散摩擦力表示.基于平均场理论与Hill定理,导出了基于介观力学信息的梯度Cosserat连续体增量非线性本构关系.在等温热动力学框架下定义了表征颗粒材料各向异性损伤--愈合和塑性的损伤、愈合张量因子与综合损伤、愈合效应的净损伤张量因子和塑性应变.此外,定义了损伤和塑性耗散能密度与愈合能密度,以定量比较材料损伤、愈合、塑性对材料失效的效应.应变局部化数值例题结果显示了所建议的颗粒材料损伤--愈合--塑性表征方法的有效性.%The multiscale characterization of coupled damage-healing and plasticity for granular materials is presented in the frame of second-order computation homogenization. The structure composed of granular materials is modeled as Cosserat continuum at the macroscale. The representation volume element(RVE)possessing the meso-structure of dis-crete particle assembly is assigned at each of the integration points of the finite element mesh generated in the macroscopic continuum.The incremental non-linear constitutive relation for the discrete particle assembly of RVE is established.The incremental forces and couple moments applied to the peripheral particles on the boundary of the RVE from the medium outside the RVE are expressed in terms of the incremental translational and rotational displacements of peripheral par-ticles of the RVE, the elastic stiffness of the current deformed meso-structural RVE, and the incremental dissipative frictional forces condensed to the peripheral particles of the RVE.Based on the average field theory and the Hill's lemma,meso-mechanically informed macroscopic incremental nonlinear constitutive relation is derived for the gradient-enhanced Cosserat continuum. The tensorial damage,healing factors,and the tensorial net damage factor combining the effects of both the damage and the healing and the plastic strain to characterize anisotropic damage-healing and plasticity of granular materials are defined in the isothermal thermodynamic framework.In addition,densities of damage and plastic dissipative energies,the density of healing energy are defined so that the damage,the healing and the plastic effects on the failure of granular material are quantitatively comparable.The results of the example problem of strain localization demonstrate validity of the proposed method for characterizing the damage-healing-plasticity occurring in granular materials.