动态损伤与相场断裂模型及其各种时间离散化
Models of dynamic damage and phase-field fracture, and their various time discretisations
AI总结：
本文研究Kelvin-Voigt粘弹性连续介质中的动态损伤模型，采用Galerkin方法分析，特别关注相场断裂近似，并提出多种时间离散化方案，同时扩展到复杂流变学和大应变情形。
摘要：
本文提出并分析了Kelvin-Voigt流变学下小应变粘弹性连续介质中损伤模型的几种变体，并利用Galerkin方法进行了分析。特别地，详细讨论了被称为裂纹相场断裂近似的特殊情况。所有这些模型都是动态的（即涉及惯性以模拟快速损伤/断裂过程中可能发射的振动或波，或由快速变化的强迫引起的振动或波），并考虑了同样可损伤的粘性。随后，设计了各种时间离散化选项。最后，简要介绍了向更复杂流变学的扩展或对大应变的修改。
英文摘要：
Several variants of models of damage in viscoelastic continua under small strains in the Kelvin-Voigt rheology are presented and analyzed by using the Galerkin method. The particular case, known as a phase-field fracture approximation of cracks, is discussed in detail. All these models are dynamic (i.e. involve inertia to model vibrations or waves possibly emitted during fast damage/fracture or induced by fast varying forcing) and consider viscosity which is also damageable. Then various options for time discretisation are devised. Eventually, extensions to more complex rheologies or a modification for large strains are briefly exposed, too.
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