Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses at nanoscale. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface stresses are a result of the geometric nonlinearities, even when strains are infinitesimal. They make multiple contributions to the Ginzburg-Landau equation for damage evolution, both in the deformed and undeformed configurations. Important connections between material parameters are obtained using an analytical solution for two separating surfaces, as well as an analysis of the stress-strain curves for homogeneous tension for different degradation and interpolation functions. A complete system of equations is presented in the deformed and undeformed configurations. All the nanoscale phase field parameters are obtained utilizing the existing first principle simulations for the uniaxial tension of Si crystal in the [100] and [111] directions.

断裂相场理论是在大应变下发展起来的，重点是在纳米尺度上正确引入表面应力。这是通过将内聚能和梯度能量乘以变形和未变形配置中裂纹表面积的局部比率以及在参考配置中的有序参数梯度方面的梯度能量来实现的。这导致与尖锐表面方法一致的表面应力表达式。即，柯西表面应力的结构部分表示各向同性的双轴张力，每单位长度的力的大小等于表面能。表面应力是几何非线性的结果，即使应变是无穷小的。他们对 Ginzburg-Landau 方程的损伤演化做出了多重贡献，无论是在变形的还是未变形的配置中。使用两个分离表面的解析解，以及针对不同退化和插值函数的均匀张力的应力-应变曲线分析，获得了材料参数之间的重要联系。一个完整的方程系统以变形和未变形配置呈现。所有纳米级相场参数都是利用现有的第一原理模拟获得的，用于 Si 晶体在 [100] 和 [111] 方向上的单轴张力。以及针对不同退化和插值函数的均匀张力的应力-应变曲线分析。一个完整的方程系统以变形和未变形配置呈现。所有纳米级相场参数都是利用现有的第一原理模拟获得的，用于 Si 晶体在 [100] 和 [111] 方向上的单轴张力。以及针对不同退化和插值函数的均匀张力的应力-应变曲线分析。一个完整的方程系统以变形和未变形配置呈现。所有纳米级相场参数都是利用现有的第一原理模拟获得的，用于 Si 晶体在 [100] 和 [111] 方向上的单轴张力。