We analyze in this contribution the propagation of bulk and Rayleigh surface waves in periodic architectured materials undergoing internal damage. An elastic damageable continuum-based model is developed in the framework of the thermodynamics of irreversible processes, whereby the displacement experiences a jump across the faces of the propagating crack. The crack propagation involves an enhancement of the displacement field associated with embedded discontinuities, which remain localized within each (triangular type) finite element. The displacement discontinuity is regulated by the traction separation behavior described by an exponential cohesive model with damage hardening followed by softening. The effective mechanical properties of the overall network are evaluated versus the increasing damage. The phase velocities for the longitudinal and transverse modes are then computed continuously versus the amount of damage, considering successively the situations of symmetrically and unsymmetrically distributed damage occurrence and propagation. Simulation results show that although the crack pattern is different in these two situations, it has no impact on the evolution of the effective moduli versus global damage. The phase velocities computed based on the effective moduli decrease as damage propagates within the network; thus, it is an indicator of the amount of global damage.

我们以这种贡献来分析主体结构和瑞利表面波在遭受内部破坏的周期性建筑材料中的传播。在不可逆过程的热力学框架内建立了基于弹性破坏连续体的模型，由此位移经历了传播裂纹表面的跳跃。裂纹扩展涉及与嵌入的不连续相关的位移场的增强，这些不连续保持在每个（三角形）有限元内。位移不连续性是由牵引分离行为控制的，该行为由指数凝聚力模型描述，先进行破坏硬化再进行软化。评估整个网络的有效机械性能与不断增加的损坏之间的关系。然后，连续计算纵向和横向模态的相速度与损伤量的关系，并依次考虑对称和不对称分布的损伤发生和传播的情况。仿真结果表明，尽管这两种情况下的裂纹模式均不同，但对有效模量与整体损伤的演化没有影响。随着损伤在网络中的传播，基于有效模量计算出的相速度会降低。因此，它是整体损害程度的指标。仿真结果表明，尽管这两种情况下的裂纹模式均不同，但对有效模量与整体损伤的演化没有影响。随着损伤在网络中的传播，基于有效模量计算出的相速度会降低。因此，它是整体损害程度的指标。仿真结果表明，尽管这两种情况下的裂纹模式均不同，但对有效模量与整体损伤的演化没有影响。随着损伤在网络中的传播，基于有效模量计算出的相速度会降低。因此，它是整体损害程度的指标。