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首页> 外文期刊>International journal of non-linear mechanics >Modeling of materials capable of solid-solid phase transformation. Application to the analytical solution of the semi-infinite mode Ⅲ crack problem in a phase-changing solid
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Modeling of materials capable of solid-solid phase transformation. Application to the analytical solution of the semi-infinite mode Ⅲ crack problem in a phase-changing solid

机译：能够进行固-固相变的材料建模。在相变固体中半无限Ⅲ型裂纹问题的解析解中的应用

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The paper proposes two frameworks for the derivation of constitutive models for solids undergoing phase transformations. Two distinct approaches are considered: the first is based on the assumption that solid phases within the material are finely mixed whereas the second considers the material as a heterogeneous solution of different phase fragments and uses the homogenization theory to derive constitutive relations at the macroscale. For both approaches, the mathematical representation of the material behavior is intentionally kept simple and the derivations are fully developed for ease of future modification and use by the readership. It is shown that in the case of reversible phase transformation, the energy of the material can be obtained by convexifiying the energy functions of the constituent phases. It is further shown that for dissipative phase transformation the material behavior can be made stable by deriving the evolution equations of the state variables from adequately chosen dissipation potentials. Some new results of existence and uniqueness of the solution of boundary value problems of structures undergoing phase change are also given. As an application, a schematic model is derived and used to obtain analytical solutions for the problem of semi-infinite mode Ⅲ crack in a solid capable of phase transformation.
机译：本文为推导经历相变的本构模型提出了两个框架。考虑了两种不同的方法：第一种方法基于以下假设：材料中的固相被精细混合，而第二种方法则将材料视为不同相碎片的异质溶液，并使用均质化理论得出宏观尺度的本构关系。对于这两种方法，有意使材料行为的数学表示保持简单，并充分开发了派生类，以方便读者将来修改和使用。结果表明，在可逆相变的情况下，可以通过凸现组成相的能量函数来获得材料的能量。进一步表明，对于耗散相变，可以通过从适当选择的耗散势中导出状态变量的演化方程来使材料性能稳定。给出了相变结构边值问题解的存在性和唯一性的一些新结果。作为一种应用，推导了一个示意性模型，并用于获得能够相变的固体中的半无限Ⅲ型裂纹问题的解析解。

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