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首页> 外文期刊>International Journal for Numerical Methods in Engineering >Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme
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Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme

机译：梯度增强的计算均匀化方案对异质材料进行多尺度本构建模

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摘要

A gradient-enhanced computational homogenization procedure, that allows for the modelling of microstructural size effects, is proposed within a general non-linear framework. In this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element (RVE). This enables us to incorporate the microstructural size and to account for non-uniform macroscopic deformation fields within the microstructural cell. Every microstructural constituent is modelled as a classical continuum and the RVE problem is formulated in terms of standard equilibrium and boundary conditions. From the solution of the microstructural boundary value problem, the macroscopic stress tensor and the higher-order stress tensor are derived based on an extension of the Hill-Mandel condition. The automatically delivers the microstructurally based constitutive response of the higher-order macro continuum and deals with the microstructural size in a natural way. Several examples illustrate the approach, particularly the microstructural size effects.
机译：在一般的非线性框架内提出了一种梯度增强的计算均化程序，该程序允许对微观结构尺寸效应进行建模。在这种方法中，宏观变形梯度张量及其梯度被施加到微观结构的代表性体积元素（RVE）上。这使我们能够纳入微观结构的尺寸，并解决微观结构单元内的非均匀宏观变形场。每个微结构成分都被建模为经典连续体，并且RVE问题是根据标准平衡和边界条件来表述的。从微观结构边值问题的解，基于Hill-Mandel条件的扩展，导出了宏观应力张量和高阶应力张量。自动传递高阶宏连续体的基于微观结构的本构响应，并以自然方式处理微观结构的大小。几个例子说明了该方法，特别是微观结构尺寸效应。

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