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首页> 美国卫生研究院文献>Proceedings. Mathematical Physical and Engineering Sciences >Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity viscoplasticity and damage
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Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity viscoplasticity and damage

机译：非线性正则化算子它源自对梯度弹性粘塑性和损伤的微形态方法

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The construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable.
机译：这项工作中提出的正则化算子的构造是基于将应变矢量或损伤微晶自由度以及位移矢量以及它们的梯度引入本构材料模型的亥姆霍兹自由能函数中的。用于广义应力的新平衡方程和微形本构方程的组合生成正则化算子。在小应变框架内，选择二次势w.r.t.梯度项提供了广泛使用的Helmholtz算子，其正则化性质众所周知：硬化材料中界面和边界层处的不连续性平滑，软化材料中的有限宽度局部化带。目的是从两方面回顾和提出微晶和应变/损伤梯度模型的非线性扩展：第一个引入广义应力与应变之间的非线性关系。第二个设想了几类有限变形模型公式。通用方法适用于包括弹性等温和多物理场耦合在内的一大类弹性粘塑性和损伤模型。将经典本构定律扩展到大应变的两种标准过程与微晶方法相结合：某些拉格朗日应变测度的加法分解或局部目标旋转框架的选择。最后使用变形梯度的乘法分解得出三个不同的算符。一个新功能是，仅依赖于中间等斜构型中定义的变量的自由能函数会导致存在由标量微形态变量的梯度引起的附加运动学硬化。

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