1-D Insertion

The 1-D cohesive insertion concept is illustrated in Figure 2.7 for the case of two adjacent two-node volumetric elements. Cohesive elements are represented as two node halves connected by a non-linear spring satisfying the chosen cohesive traction-separation law. In order to satisfy the conservation of mass, each of the node halves receives a mass contribution of its connected volumetric elements. As a result, if the element on the right of the cohesive node is more massive, the right half will have a larger mass than the left. In order to conserve the linear momentum of the system, the newly formed right node gets a copy of all pertinent information (displacement, velocity and acceleration) from the left node. Additionally, the volumetric elements on the left and right side must have their nodal connectivity information updated to take the new node into account. The various node and element data and connectivity are stored as arrays in the code and these arrays will grow with any duplication and should be adjusted as necessary throughout the simulation.

Figure 2.7: (a) Standard 1-D mesh. (b) 1-D mesh with inserted cohesive node.