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Open system peridynamics
Continuum Mechanics and Thermodynamics ( IF 2.6 ) Pub Date : 2022-05-10 , DOI: 10.1007/s00161-022-01105-8
Emely Schaller , Ali Javili , Paul Steinmann

We propose, for the first time, a thermodynamically consistent formulation for open system (continuum-kinematics-inspired) peridynamics. In contrast to closed system mechanics, in open system mechanics mass can no longer be considered a conservative property. In this contribution, we enhance the balance of mass by a (nonlocal) mass source. To elaborate a thermodynamically consistent formulation, the balances of momentum, energy and entropy need to be reconsidered as they are influenced by the additional mass source. Due to the nonlocal continuum formulation, we distinguish between local and nonlocal balance equations. We obtain the dissipation inequality via a Legendre transformation and derive the structure and constraints of the constitutive expressions based on the Coleman–Noll procedure. For the sake of demonstration, we present an example for a nonlocal mass source that can model the complex process of bone remodelling in peridynamics. In addition, we provide a numerical example to highlight the influence of nonlocality on the material density evolution.



中文翻译:

开放系统近场动力学

我们首次提出了开放系统(受连续运动学启发)近场动力学的热力学一致公式。与封闭系统力学相比,在开放系统力学中,质量不再被视为保守性质。在这项贡献中,我们通过(非本地)质量源增强了质量平衡。为了阐述热力学一致的公式,需要重新考虑动量、能量和熵的平衡,因为它们受到额外质量源的影响。由于非局部连续统公式,我们区分了局部和非局部平衡方程。我们通过勒让德变换获得耗散不​​等式,并根据 Coleman-Noll 过程推导出本构表达式的结构和约束。为了演示,我们提出了一个非局部质量源的例子,它可以模拟近场动力学中骨重塑的复杂过程。此外,我们提供了一个数值例子来强调非定域性对材料密度演化的影响。

更新日期:2022-05-11
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