Influence of the intermediate material on the singular stress field in tri-material junctions

According to the mathematical formalism of the eigenfunction expansion method, the problem of stress-singularities arising from multi-material junctions is addressed. The wedges are composed of isotropic homogeneous materials and are in a condition of plane stress or strain. The order of the stress-singularity is provided for tri-material junctions, paying special attention to the role played by Mode-I and Mode-II deformation. The effect of cracks inside either the softer or the stiffer material is also investigated. Numerical results can be profitably used for establishing optimum material configurations

Theoretical and numerical investigation on internal instability phenomena in composite materials

Instability phenomena occurring in the microstructure of composite materials are investigated. To this aim, a complete description of the mechanical behavior of bi-material interfaces in composite materials requires the definition of both a cohesive law involving damage for the debonding stage, and a contact model during the closure of the interface. Both formulations are herein presented and implemented in the FE code FEAP. Numerical examples showing the transition from a snap-back instability to a stable mechanical response are presented

Static-kinematic duality in beams, plates, shells and its central role in the finite element method

AbstractStatic and kinematic matrix operator equations are revisited for one-, two-, and three-dimensional deformable bodies. In particular, the elastic problem is formulated in the details in the case of arches, cylinders, circular plates, thin domes, and, through an induction process, shells of revolution. It is emphasized how the static and kinematic matrix operators are one the adjoint of the other, and then demonstrated through the definition of stiffness matrix and the application of virtual work principle. From the matrix operator formulation it clearly emerges the identity of the usual Finite Element Method definition of elastic stiffness matrix and the classical definition of Ritz-Galerkin matrix

Scaling and fractality in fatigue crack growth: Implications to Paris' law and Wöhler's curve

Abstract Size effects on crack growth are of paramount importance on the fatigue problem. Paris' and Wohler's fatigue curves exhibit scale effects, which can be explained in the framework of incomplete self-similarity and fractal geometry concepts. In particular, scaling laws are found for the main fatigue parameters, that is, the fatigue threshold ΔKth and the fatigue limit Δσfl. The fatigue threshold increases with the crack length, whereas the fatigue limit decreases with the specimen size. Eventually, the proposed models are positively compared to experimental data available in the literature

Funicularity in elastic domes: Coupled effects of shape and thickness

Abstract An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the ad-joint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without 'exural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one