Modeling nonlinearities, including damage, in the boundary element method (BEM) is usually carried out in implicit way, or in other words via applying initial stresses or strains over a discretized domain part. Such initial values have no physical meaning. They are only used to compensate the stress level due to the occurred nonlinearity. In this paper explicit implementation of nonlocal damage is proposed. The damaged points inside the domain is physically weakened by decreasing their modulus of elasticity. With the help of Eshelby's equivalent inclusion theory, this idea is developed and implemented in this work. Load control solution algorithm is used. Both average strain and average damage nonlocal models are considered. Numerical examples are presented to verify the developed formulation. Factors that affect the solution accuracy are studied in details.

边界元法 (BEM) 中的非线性建模（包括损坏）通常以隐式方式进行，换句话说，通过在离散域部分上施加初始应力或应变来进行。这样的初始值没有物理意义。它们仅用于补偿由于出现的非线性而引起的应力水平。在本文中，提出了非局部损伤的显式实现。域内的损坏点通过降低其弹性模量而被物理削弱。在 Eshelby 的等效包含理论的帮助下，这个想法在这项工作中得到发展和实施。使用负载控制求解算法。平均应变和平均损伤非局部模型都被考虑。给出了数值例子来验证开发的配方。