In this work, a new thermo-mechanical formulation for the conventional and localizing gradient damage method is proposed. The proposed formulation is based on the generalized micromorphic theory, which accounts for the underlying fracture processes at the micro-level. The thermal and mechanical effects on the fracture response are incorporated in the formulation through three primary variables. These variables are displacement (u), micro-equivalent strain (ē) and temperature (θ), which are strongly/weakly coupled. In addition to mechanical loading, steady-state and transient heat transfers are considered in the formulation. Several 1D and 2D numerical examples are solved using the formulation to demonstrate its accuracy and effectiveness in simulating thermo-mechanical fracture. In the numerical examples, different types of thermal and mechanical loads are considered to study various effects on the fracture response of the components. Moreover, a detailed description of the formulation and its numerical implementation is presented for a better understanding.

中文翻译：

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一种热机械梯度增强断裂损伤方法

在这项工作中，提出了一种用于传统和局部梯度损伤方法的新热机械公式。所提出的公式基于广义微晶理论，该理论解释了微观层面的潜在断裂过程。对断裂响应的热效应和机械效应通过三个主要变量纳入配方中。这些变量是位移 (u)、微等效应变 (ē) 和温度 (θ)，它们是强/弱耦合的。除了机械载荷外，公式中还考虑了稳态和瞬态传热。使用该公式求解了几个一维和二维数值示例，以证明其在模拟热机械断裂方面的准确性和有效性。在数值例子中，考虑不同类型的热载荷和机械载荷来研究对部件断裂响应的各种影响。此外，还提供了公式及其数值实现的详细描述，以便更好地理解。