We propose a novel variational framework to regularize softening plasticity problems. Specifically, we modify the plastic dissipation potential term by adding a contribution depending on the cumulative plastic strain-rate gradient. We formulate the evolution of the so-obtained strain-rate gradient plasticity model with an incremental variational principle. The time-discretized evolution equations are deduced from the corresponding first-order optimality conditions. To investigate the model, the problem of a bar in traction is studied. Analytical solutions are explicitly derived, and characterized by exponential localization profiles. Contrary to other regularization strategies, no spurious spreading of the plastic localization band is observed. A first numerical implementation in 1D and 2D plane strain conditions is proposed based on conic programming solvers and validated against the analytical predictions. Numerical results on plane strain von Mises plasticity show that the proposed framework leads to mesh-independent results and efficient control of plastic localization bands.

中文翻译：

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软化塑性随累积塑性应变率梯度的正则化


我们提出了一种新的变分框架来正则化软化塑性问题。具体来说，我们通过根据累积塑性应变率梯度添加贡献来修改塑性耗散电位项。我们用增量变分原理构建了所获得的应变率梯度塑性模型的演变。时间离散的演化方程是从相应的一阶最优性条件推导出来的。为了研究该模型，研究了牵引杆的问题。解析解是显式推导的，并以指数定位剖面为特征。与其他正则化策略相反，没有观察到塑性定位带的虚假扩散。基于圆锥规划求解器，提出了 1D 和 2D 平面应变条件下的第一个数值实现，并根据解析预测进行了验证。平面应变 von Mises 塑性的数值结果表明，所提出的框架导致了独立于网格的结果和塑性定位带的有效控制。