A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities
A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities
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DOI：
10.1016/j.jcp.2011.12.017
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发表时间：
2012-04
期刊：
影响因子：
--
通讯作者：
F. Bobaru;Monchai Duangpanya
中科院分区：
文献类型：
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作者：
F. Bobaru;Monchai Duangpanya
我们介绍了一个多维的瞬态传热的周向列式。该模型不包含空间导数，而是使用材料点周围区域上的积分。通过构造，该公式在视界（一点周围的非局部区域）趋于零的极限收敛于经典热传导方程。然而，新的模型，是适合于建模，例如，在不断发展的不连续性，如增长的绝缘裂纹的机构的热流。我们引入了即使在尖角处或等温线不是光滑表面时也存在的周向热通量。在简单的情况下，近周热通量与经典热通量一致，一般来说，它在近周视界趋于零的极限处收敛于经典热通量。我们解决测试问题，并与经典模型的解析解或其他数值解的结果进行比较。在视界趋于零的极限中可以看到经典解的收敛。然后，我们解决了瞬态热流的问题，在板中的绝缘裂纹生长和相交，从而改变热流模式。我们还模拟了纤维增强复合材料中的热传递，并观察到在高传导性纤维和低传导性基质之间的界面处的瞬态但陡峭的热梯度。这样的热梯度可导致复合材料中由热疲劳引起的分层裂纹。该公式可用于例如评估具有任意形状的绝缘或可渗透的、可能交叉的裂纹的演变分布的物体中的有效热导率。
We introduce a multidimensional peridynamic formulation for transient heat-transfer. The model does not contain spatial derivatives and uses instead an integral over a region around a material point. By construction, the formulation converges to the classical heat transfer equations in the limit of the horizon (the nonlocal region around a point) going to zero. The new model, however, is suitable for modeling, for example, heat flow in bodies with evolving discontinuities such as growing insulated cracks. We introduce the peridynamic heat flux which exists even at sharp corners or when the isotherms are not smooth surfaces. The peridynamic heat flux coincides with the classical one in simple cases and, in general, it converges to it in the limit of the peridynamic horizon going to zero. We solve test problems and compare results with analytical solutions of the classical model or with other numerical solutions. Convergence to the classical solutions is seen in the limit of the horizon going to zero. We then solve the problem of transient heat flow in a plate in which insulated cracks grow and intersect thus changing the heat flow patterns. We also model heat transfer in a fiber-reinforced composite and observe transient but steep thermal gradients at the interfaces between the highly conductive fibers and the low conductivity matrix. Such thermal gradients can lead to delamination cracks in composites from thermal fatigue. The formulation may be used to, for example, evaluate effective thermal conductivities in bodies with an evolving distribution of insulating or permeable, possibly intersecting, cracks of arbitrary shapes.