Local zigzag effects and brittle delamination fracture of n-layered beams using a structural theory with three displacement variables

Abstract

Equivalent single layer theories for layered beams effectively and accurately predict global displacements and internal force and moment resultants using a limited number of displacement variables. However, they cannot reproduce local effects due to material architecture or weak/imperfect bonding of the layers, such as zigzag displacement fields, displacement jumps at the layer interfaces and complex transverse stress fields, nor can they simulate delamination damage growth. In this work we will present some applications and discuss advantages and limitations of a recently formulated zigzag model. The model, through a modification of the equilibrium equations of an equivalent single layer theory, which maintains the same number of variables, reproduces local effects and delamination fracture under mode II dominant conditions. The approach is based on a local enrichment of the displacement field of first order shear deformation theory, the introduction of cohesive interfaces and homogenization.

Computational design of innovative mechanical metafilters via adaptive surrogate-based optimization

“…Further improvements in its convergence rate could be obtained by choosing, as a penalty term, a trade-off between exploration and exploitation [57]. In these respects, benefits are expected in high-dimensional problems characterized by hierarchical beam lattice metamaterials, in which microstructured ligaments are employed [58][59][60].…”

Design of tunable acoustic metamaterials with periodic piezoelectric microstructure

“…The promising results obtained can be positively exploited towards optimal design of tunable acoustic filters, adapt to a changing performance requirement in real-time. Interesting future developments may concern, on the one hand, the study of the acoustic behaviour of tunable metamaterials connected to more sophisticated and even dissipative electrical circuits and, on the other, the design of tunable metamaterials with smart and/or imperfect microstructured interfaces [107][108][109][110].…”

Effective Modeling of Interlaminar Damage in Multilayered Composite Structures Using Zigzag Kinematic Approximations

“…Figure 12 shows predictions of the critical load for crack propagation versus load point displacement in End Notched Flexure and End-Loaded Split specimens. The specimens are made of a graphite-epoxy unidirectionally reinforced laminate, tested in Madhukar and Drzal (1992), and of a cross-ply carbon-epoxy laminate, analyzed using a 2D finite element model in Massabò and Monetto (2020). Predictions using the zigzag theories have been obtained in closed form.…”

“…(b) Critical load for crack propagation versus load point displacement in a ELS specimen. Geometry and properties given in Massabò and Monetto (2020) Fig. 13 Dimensionless diagram of critical load for crack propagation versus crack length in threepoint bend sandwich beams with isotropic layers, H ¼ 3 h. Black curves: homogeneous beam with asymmetric delamination, (2) E/ (1) E ¼ 1; red curves: sandwich beam, (2) E/ (1) E ¼ 1/4.…”