The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular situation of a solid with inhomogeneities. Description of the fracture processes are based on the theory of material damage. It introduces two independent damage parameters to distinguish between interface and internal cracks. The parameter responsible for interface cracks is defined in a thin adhesive layer of the interface and renders relation between stress and strain quantities in fashion of cohesive zone models.The second parameter is defined inside material domains and it is founded on the theory of phase-field fracture guaranteeing the material damage to occur in a thin material strip introducing a regularised model of internal cracks. Additional property of both interface and phase-field damage is their capability to distinguish between fracture modes which is useful if the structures is subjected to combined loading. The solution methodology is based on a variational approach which allows implementation of non-linear programming optimisation into standard methods of finite-element discretisation and time stepping method.Computational implementation is prepared in MATLAB whose numerical data validate developed formulation for analysis of problems of fracture in multi-domain elements of structures.

翻译：所发展的计算方法能够在准静态条件下，于一般多域结构材料内部及材料界面处起始并扩展裂纹。特别关注含非均质固体的特定情形。断裂过程的描述基于材料损伤理论。引入两个独立损伤参数以区分界面裂纹与内部裂纹。负责界面裂纹的参数定义于界面薄粘合层内，并以内聚区模型的方式建立应力与应变量的关系。第二参数定义于材料域内，基于相场断裂理论，通过正则化的内部裂纹模型确保材料损伤发生在薄材料条带中。界面损伤与相场损伤的另一特性是能够区分断裂模式，当结构承受联合加载时这一特性尤为有用。求解方法基于变分法，可将其非线性规划优化实现集成至标准有限元离散与时间步进法中。计算实现在MATLAB中完成，其数值数据验证了所提公式用于分析结构多域单元断裂问题的有效性。