The advent of additive manufacturing allows the design of increasingly intricate mechanical metamaterial lattices for enhanced engineering performance. In structural systems that absorb energy and shield a more valuable structure, mechanical properties with a quasi-zero stiffness (QZS) immediately after exhibiting a high initial stiffness, can ensure that a desired amount of energy may be absorbed within a limited displacement. This limits the stress transfer to the valuable structure while the absorption system has a considerably reduced structural volume compared to conventional systems. Presently, a mechanical model, comprising rigid-links and springs, is formulated that generates a system of nonlinear algebraic equations with the aim of simulating the elastic deformation of a series of deforming cells of the lattice structure. Under loading, the structure switches deliberately between conventional material behaviour (with a positive Poisson's ratio) to that exhibiting auxetic behaviour (with a negative Poisson’s ratio) through a sequence of snap-through instabilities within individual lattice cells. The equations are solved using numerical continuation techniques and the resulting sequence of instabilities may be controlled to maintain the load in the QZS zone while the necessary energy quantity is absorbed and elasticity is maintained. This is a departure from the usual paradigm where such structures tend to be sacrificial and introduces the feasibility of such structural elements being redeployable and reusable that were previously single-use, which could be advantageous in quite diverse applications within different branches of engineering.

This paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi-Pasta-Ulam nonlinear lattice) with p=2 nonlinear interactions (nonlinear direct and second-neighbouring interactions). The static response of this n-degree-of-freedom nonlinear system under pure tension loading is theoretically and numerically investigated. The mathematical problem is equivalent to a nonlinear fourth-order difference eigenvalue problem. The bifurcation parameters are calculated from the exact resolution of the fourth-order linearized difference eigenvalue problem. It is shown that the bifurcation diagram of the generalized softening FPU system depends on the stiffness ratio of both the linear and the nonlinear parts of the nonlinear lattice, which accounts for both short range and long range interactions. This system possesses both a saddle node bifurcation (limit point) and some unstable bifurcation branches for the parameters of interest. We show that for some range of structural parameters, the bifurcations in (n-1) unstable bifurcation branches prevail before the limit point. In the complementary domain of the structural parameters, the bifurcations in (n-1) unstable bifurcation branches prevail after the limit point, which means that the system becomes unstable first, at the limit point. At the border between both domains in the space of structural parameters, the bifurcation in (n-1) unstable bifurcation branches coincide with the limit point, with an addition unstable fundamental branch. This case is the hill-top bifurcation, already analysed by Challamel et al. (2023) in the case p=1 interaction. The paper also discusses the capability of continuous gradient elastic systems to capture the bifurcation parameters of the discrete system.

References:

Challamel N., Ferretti M. and Luongo A., Multi-degenerate hill-top bifurcation of Fermi-Pasta-Ulam softening chains: exact and asymptotic solutions, Int. J. Non-linear Mech., 156, 104509, 1-11, 2023.

Lateral-torsional instability characterizes beams subjected to bending about the major axis that unstably shifts into a combination of bi-axial bending and twist. Opposed to the buckling and wrinkling of sandwich structures, which were extensively investigated in the past three decades, the lateral-torsional instability of sandwich beams and the resulting evolution of interfacial phenomena typical to such layered configuration were not. In that context, the lateral instability of such sandwich beams and the interfacial mechanisms it involves define open questions that are addressed here.

The study explores the evolution of interfacial phenomena under lateral-torsional instability of soft-core sandwich beams. Due to the layered structure of the sandwich beam and the significant differences in thickness and elastic moduli of the layers, the transfer of tractions across the core's interfaces is essential to this unique structural form. The lateral-torsional instability, which drives the sandwich beam into a completely new, un-designed, and off-optimal regime, immediately impacts all aspects of the response, including the interfacial response. The sudden instability is expected to be involved with significant amplification of the interfacial shear and out-of-plane normal tractions, potential degradation of the bond, or even delamination and failure of the composite beam. The quantification of such mechanisms is at the focus of the current investigation.

The investigation of this aspect of lateral-torsional instability adopts an analytical methodology and combines geometrically nonlinear analysis with a high-order torsional sandwich beam theory. The latter integrates the rich stress and deformation fields in the compliant core into the analysis. Numerical results obtained by the analytical model look at the interfacial tractions before, at, and after the point of instability and into their effect on the composite structure. The presentation will look into these effects, aiming to assess the impact of lateral instability on the performance of soft-core sandwich beams.

This research investigates the stability of orthodontic bracket structures and the integrated bracket-adhesive-tooth structural system. In particular, the investigation focuses on the stability structural debonding failure of such orthodontic brackets. In that context, it applies structural concepts of geometrical nonlinearity and interfacial instabilities to investigate a fundamental problem in orthodontic therapeutic treatment.

Orthodontic braces are a common treatment addressing both medical and aesthetic needs. The orthodontic system consists of brackets that are bonded to the teeth with a layer of adhesive and a wire that connects them. Like any layered structure, the Tooth-Adhesive-Bracket (TAB) system is exposed to instability in the form of delamination, detachment, or separation failure. Such failure impairs the effectiveness of the therapeutic process and requires the attention of both the patient and the physician. The available body of knowledge found in the literature with regard to debonding failure is mostly based on experiments and models that focus on the stability strength of the system. Models that address the structural stability of the system and the potentially unstable evolution of the failure are missing. This research relies on an analytical approach and formulates a 2D nonlinear structural model that describes and tracks the stability of the debonding failure in orthodontic brackets. The model combines a high-order theory for the representation of the compliant layer of adhesive and cohesive interfaces that introduce the spontaneous evolution of interfacial failure. Quantitative results obtained through numerical solution of the nonlinear governing equations demonstrate the capabilities of the model and highlight the unstable nature of the failure mechanism. The study establishes an analytical foundation for the quantitative analysis of the instability, gains insight into the nature of the detachment failure, and mechanistically explains the driving forces in the failure mechanism.

This contribution presents a novel exact solution for the buckling load of an asymmetrically supported 3D column. The equations that form the basis for our exact solution are taken from the pioneering work of J. C. Simo (1985). In the first part, we present the axioms and basic equations of the 3D beam model, which are then linearized around the primary equilibrium configuration. In the second part, we explain the solution procedure and finally present an illustrative example. In the illustrative example, we focus on a straight column with a constant cross-sectional area. We show how different boundary conditions and their spatial orientation with respect to the cross-sectional plane affect the buckling load of such a column. This means that we can determine the buckling load of a column which is not supported symmetrically in the directions of its principal axes. The presented solution is useful when we want to evaluate the bearing capacity of a column that cannot be designed based on the minimum buckling load due to technical, spatial or other constraints.

Fabricated I-profiles – especially those that fall outside the range of more common catalogued sections – can exhibit behavior that is poorly accounted for by existing design methods. This observation is particularly common in hybrid profiles, where the web and flange are made of different grades or types of steel. To fill some of the gaps in existing experimental literature, compression tests were conducted on twenty stub columns. The tests include hybrid and homogeneous sections with stainless-steel and carbon steel covering a wide range of values for sectional slenderness. Strength predictions from the effective width method, direct strength method (DSM), and continuous strength method (CSM) are then compared. As found in past investigations, the general form of the DSM provides overly conservative estimations of the compressive strength when the cross-section exhibits substantial post web local buckling reserve leading to yielding in the flanges, with little flange deformation. In this case, a modified form of the direct strength method was recently proposed to expand the applicability of the technique to a greater subset of fabricated I-profiles. With these tests added to the available experimental evidence, the recently proposed modifications to design methods are evaluated. This theoretical and experimental work advances understanding of which design methods are most appropriate to employ for fabricated and hybrid sections under pure compression.