计及作用于接触斑点上的切向力，通过比较作用于接触斑点上的法向弹性载荷与法向塑性载荷，确定了区分弹性接触与塑性接触区域的临界接触斑点面积。总的粘着摩擦系数被表示为弹性接触区与塑性接触区的粘着摩擦系数的组合。假设屈服压力及局部粘着摩擦系数不依赖于接触斑点且等于塑性接触区中的平均值，则总的粘着摩擦系数可用简单的表达式描述。分形几何参数及归一接触面积对于粘着摩擦系数的效应已通过算例表明，研究中，分别考虑了忽略与计及接触斑点的微粒间的相互作用，两种情况的结果完全不同。

In order to tackle behavior of individual components in concrete cells under shock loading, a multi-part model for concrete is presented, wherein mortar and aggregate are assumed to be in mechanical equilibrium and compressed or released isentropically. Computational simulations of plate shock experiments using the multi-part model for concrete are performed. Computational velocity histories of the free surface of the target are compared with experimental results. Nonlocal response of the multi-part model for concrete to uniform shock loading is presented. The irregular aggregate distribution in actual concrete is replaced by a distribution of single-sized equally separate aggregates and the radius of influence surrounding each aggregate is given. The phenomena accompanied by the passage of a spherical shock wave through the mortar and aggregate are discussed. It is shown that RayleighTaylor instability would cause separation of mortar and aggregate seriously for concrete with porous mortar at low initial density. It is shown that the behavior of the interface between mortar and aggregate under shock loading is captured qualitatively by the multi-part model for a simulated concrete cell. The multi-part model presented in this paper can be expected to numerically simulate shock loading behavior of concrete.

Basing on Gathers's work, a set of general equations for traditional determination of spall strength is given under some assumptions for the planar spall experiment with a low-impedance buffer placed behind the target. In the case of no buffer, the equations become the traditional expression given byNovikov within the acoustic approach. It is revealed that the propagation of wave profile in the spall scab is affected seriouslybythe damage evolution on the spall plane. Therefore, the free surface velocityprofile of target or the stress profile of interface between target and low-impedance buffer depends criticallyon the damage evolution on the spall plane. It is concluded that the traditional determination of spall strength without taking into account the stress relaxation due to the damage evolution on the spall plane could be valid only for the numericallysimulat ed "pullback" bythe simple spall cutoff criterion but not valid for the experimental"pullback"in general.