弹塑性固体中水力压裂的变分极小化公式
A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids
AI总结：
本文提出一种弹塑性固体水力压裂的变分极小化框架，结合相场断裂、Drucker-Prager塑性准则和Darcy-Biot流体公式，并采用H(div)协调有限元与增强假定应变方法，通过数值算例验证其鲁棒性。
摘要：
本文建立了一个用于弹塑性固体水力压裂的变分建模框架。所建立的变分结构提供了一个全局极小化问题。裂缝扩展通过相场断裂方法建模，塑性效应则采用Drucker-Prager型屈服准则函数加以考虑。该屈服准则函数控制着流固混合物的塑性演化。流体储存与输运由Darcy-Biot型公式描述。其中，流体储存被分解为由弹性变形引起的贡献和由塑性变形引起的贡献。采用局部返回映射格式更新塑性量。全局极小化结构要求采用H(div)协调的有限元公式。此外，该公式与增强假定应变公式相结合，以克服塑性变形引起的锁定现象。所提出框架的鲁棒性和能力将通过一系列数值算例加以展示。
英文摘要：
A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is modeled by means of a phase-field approach to fracture, plastic effects are taken into account by using a Drucker-Prager-type yield-criterion function. This yield-criterion function governs the plastic evolution of the fluid-solid mixture. Fluid storage and transport are described by a Darcy-Biot-type formulation. Thereby the fluid storage is decomposed into a contribution due to the elastic deformations and one due to the plastic deformations. A local return mapping scheme is used for the update of the plastic quantities. The global minimization structure demands a $H($div$)$-conforming finite-element formulation. Furthermore this is combined with an enhanced-assumed-strain formulation in order to overcome locking phenomena arising from the plastic deformations. The robustness and capabilities of the presented framework will be shown in a sequence of numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
