热力耦合系统的有限元模型：非线性应变限制热弹性体
A finite element model for a coupled thermo-mechanical system: nonlinear strain-limiting thermoelastic body
摘要：
本文研究了一个特殊的有限元模型，在非线性应变限制本构关系的背景下研究了弹性体的热弹性行为。作为隐式关系的一个特殊子类，我们感兴趣的热弹性响应是这样的，应力可以是任意大的，但应变仍然很小，特别是在附近的裂纹尖端。因此，所提出的模型可以在本质上与小应变理论的假设是一致的。在本通讯中，我们考虑一个二维耦合系统-线性和拟线性偏微分方程的温度和位移，分别。边界条件考虑两种不同的Dirichlet型温度分布，采用连续Galerkin的标准有限元法求解场变量的数值解。对于一个域的边缘裂纹，我们发现，我们的模型的近端应变增长是远远低于应力的增长，这是显着的特点相比，经典的线性化描述的弹性体的不一致的结果。目前的研究可以提供一个理论和计算框架，以开发物理上有意义的模型，并检查其他耦合的多物理，如复杂的网络裂纹的演化引起的热冲击。
英文摘要：
We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic response of our interest is such that stresses can be arbitrarily large, but strains remain small, especially in the neighborhood of crack-tips. Thus, the proposed model can be inherently consistent with the assumption of the small strain theory. In the present communication, we consider a two-dimensional coupled system-linear and quasilinear partial differential equations for temperature and displacements, respectively. Two distinct temperature distributions of the Dirichlet type are considered for boundary condition, and a standard finite element method of continuous Galerkin is employed to obtain the numerical solutions for the field variables. For a domain with an edge-crack, we find that the near-tip strain growth of our model is much slower than the growth of stress, which is the salient feature compared to the inconsistent results of the classical linearized description of the elastic body. Current study can provide a theoretical and computational framework to develop physically meaningful models and examine other coupled multi-physics such as an evolution of complex network of cracks induced by thermal shocks.
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