强非局部连续介质的热力学框架
A thermomechanical framework for strongly nonlocal continua
- Donald P. Shiley School of Engr., Univ. of Portland（波特兰大学唐纳德·P·夏利工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一个强非局部连续介质的热力学框架，涵盖非局部动量平衡、守恒定律和本构结构，并通过拉伸弹塑性杆示例展示非局部性赋予变形模式特征尺寸。
AI中文摘要：
本文提出了一个适用于强非局部连续介质的自洽热力学框架。强非局部连续介质是一种广义介质，其中材料在某一点处的响应取决于其邻域内的变形和温度梯度。这种依赖性导致了具有内在尺寸的局部化现象，而非局部建模也可作为一种实用的正则化工具，以防止网格依赖性。非局部性属于积分类型，使用一个核函数来表示邻域内各点对中心点的相对影响。本文发展了三种非局部性来源：（1）非局部动量平衡方程；（2）非局部守恒定律（包括热力学第一定律和第二定律）；（3）材料的非局部本构结构。平衡方程是利用虚功率原理推导的，允许非光滑的力场和位移场以及法向方向不明确的非光滑边界表面。这些平衡方程不同于经典局部连续介质的平衡方程。守恒定律也不同于局部连续介质的守恒定律，其中某一点处的机械功率和加热量是在其邻域内平均的。这些定律是针对足够缓慢的过程而发展的，以最小化由于内部湍流而产生的额外细观尺度动能。应力、熵和耗散力被获得为自由能函数分别对应变、温度和内部变量的平均导数。文中给出了一个带有小缺陷的拉伸弹塑性杆的示例，并表明非局部性赋予了变形模式一个特征尺寸。
英文摘要：
The paper presents a consistent thermomechanical framework for strongly nonlocal continua, a type of generalized media in which a material's response at a point depends on deformation and temperature gradients within its neighborhood. Such dependence is responsible for localization phenomena having an intrinsic size, and nonlocal modeling also serves as a practical regularization tool to prevent mesh dependence. Nonlocality is of the integral type, using a kernel function that gives the relative influence of neighboring points on a central point. The paper develops three sources of nonlocality: (1) nonlocal momentum balance equations; (2) nonlocal conservation laws (including the first and second laws of thermodynamics); and (3) a material's nonlocal constitutive structure. Balance equations are derived using the principle of virtual power, permitting non-smooth force and displacement fields and non-smooth boundary surfaces with indistinct normal directions. The balance equations differ from those of classical local continua. Conservation laws also differ from those of local continua, with the mechanical power and heating at a point being averaged over its neighborhood. These laws are developed for processes that are sufficiently slow to minimize additional meso-scale kinetic energy due to internal turbulence. Stress, entropy, and dissipative forces are obtained as averaged derivatives of the free energy function with respect to strain, temperature, and internal variables. An example is presented of a stretched elastoplastic bar with a small defect, and nonlocality is shown to impart a characteristic size to the deformation pattern.
