The variational formulation of viscoplastic constitutive updates
The variational formulation of viscoplastic constitutive updates
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DOI：
10.1016/s0045-7825(98)00219-9
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发表时间：
1999-04
影响因子：
7.2
通讯作者：
M. Ortiz;L. Stainier
中科院分区：
文献类型：
--
作者：
M. Ortiz;L. Stainier
我们提出了一类一般粘塑性固体的本构更新，包括材料行为的有限弹性和塑性变形，非牛顿粘度，速率敏感性和任意流动和硬化规则等方面。所提出的本构更新的显著特征是，通过构造，相应的增量应力-应变关系来源于伪弹性应变-能量密度。这反过来又赋予了增量边值问题一个变分结构。特别地，增量变形映射遵循最小原则。这种最小原则可以方便地作为误差估计和网格自适应的基础。通过有限变形的米塞斯固体和延性单晶的收敛试验，证明了变分本构更新的准确性和鲁棒性。更新解决后一种应用中出现的滑动活动的复杂模式的能力特别值得注意。
We present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations, non-Newtonian viscosity, rate-sensitivity and arbitrary flow and hardening rules. The distinguishing characteristic of the proposed constitutive updates is that, by construction, the corresponding incremental stress—strain relations derive from a pseudo-elastic strain-energy density. This, in turn, confers the incremental boundary value problem a variational structure. In particular, the incremental deformation mapping follows from a minimum principle. This minimum principle may conveniently be taken as a basis for error estimation and mesh adaption. The accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely-deforming Mises solid and ductile single crystals. The ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy.