Mixed finite element for modelling interfaces

Computation of mode I strain energy release rate of symmetrical and asymmetrical sandwich structures using mixed finite element

“…The element is a quadrilateral mixed finite element with 7 nodes and 14 degrees of freedom [17]. The final configuration of the element, in a natural (ξ, η) plane, was obtained after the three following stages [18]: (i) construction of the parent element by adding a displacement node (node 5); (ii) delocalization of some variables inside the element and displacement of static nodal unknown of the corners towards the side itself; (iii) static condensation of the internal unknown variables to obtain the final form of the present mixed finite element. The obtained element has three of its sides compatible with linear traditional elements and presents a displacement node at each corner.…”

“…On the fourth side, in addition to its two displacement nodes of corner (node 1 and node 2), There are three additional nodes: a median node (node 5) and two intermediate nodes in the medium on each half-side (nodes 6 and 7), introducing the components of the stress vector along the interface. The formulation and the validation of the element have been presented by Bouziane et al [18]. The element displacement component is approximated by:…”

“…It should be noted that nodes 8, 9, 10 and 11 are inside the element, and which are eliminated by the static condensation technique [18].…”

Mixed Finite Element Computation of Energy Release Rate in Anisotropic Materials Based on Virtual Crack Closure-Integral Method

“…1.c), with a static condensation procedure, that merges the internal degrees of freedom by reducing the size of equations per elimination of a certain number of variables. Bouziane et al [35] introduced the design of the finite element in a natural (ξ, η) plane. The RMQ11 itself is gotten from the parent element RMQ5 by re-localization of certain variables and by displacement of the static nodal unknown of the corners toward the side itself.…”

“…This element was, at first, created by Bouzerd [34] with a setup in a physical (x, y) plane. Bouziane et al [35] redevelop the element beginning from the parent element in a natural (ξ, η) plane. That added a rationalization of the calculations and a huge benefit of modeling distinctive types of cracks with different orientations.…”