Finite element analysis has been carried out to obtain the interfacial stresses in a single lap joint using a special 6-node isoparametric element for adhesive layer. The analysis results are found to be in good agreement with the closed-form solution of Goland and Reissner. The peak normal and shear stresses found in the adhesive layer at the edges of the joint are due to stress singularity. The bond strength of the single-lap joint is estimated considering one of the stress fracture criteria known as the point stress criterion. Bond strength estimates are found to be reasonably in good agreement with existing test results.Introduction. Adhesive bonding can offer better performance over the mechanical fastening and being used extensively in space, automobiles, construction industries, packaging industries etc. It has the ability to join dissimilar materials and to join efficiently thin sheet materials such as thin-walled composite structures [1]. Single-lap joint [2-7] and double-lap joint [8,9] are simple in geometry and are widely used in characterizing adhesive behavior and structural connections. Failures in an adhesive joint are classified as adhesive and cohesive failure.Adhesive failure occurs at the interface between the adhesive and adherend, whereas, the cohesive failure occurs either in the adhesive or in the adherend. Failure analysis of an adhesive joint requires reliable structural deformation and stresses in the joint for the applied loads. The mechanisms of adhesion are related to chemical and physical properties of the adhesive polymers. The structural deformation and stress states for the bonded joint configuration can be obtained by specifying material properties of the joint configuration, loads and appropriate boundary conditions. Since there is no unique failure criterion for the bonded joints, the designer has to select or establish a suitable criterion to estimate the joint strength [10][11][12][13][14][15][16][17][18][19]. The stress distribution for simple geometries can be obtained from a closed-form solution, which will be useful to validate the finite element models. Finite element analysis (FEA) is essential for analyzing complex geometries and structural materials. Da Silva et al. [20] have reviewed several analytical models. Stress analysis has been carried out for various joint configurations having different adherend and adhesive properties [21][22][23][24][25][26][27][28].Standard finite elements are not well suited for modeling the adhesive layers which are extremely thin as compared to other dimensions of the bonded structure. Reasonably accurate results can be expected from the standard finite elements when the aspect ratio of the width to the height of the element is approximately unity. An element having a large aspect ratio becomes much stiffer in the transverse direction and much weaker in the axial direction. Backer and Hatt [29] have developed a linear element assuming thin adhesive layers which behave elastically as simple tension-compression springs and shear spring...

The elasto-plastic indentation of auxetic and metal foams is investigated using the finite element method. The contributions of yield strain, elastic, and plastic Poisson’s ratio on the indentation hardness are identified. For a given yield strain, when the plastic Poisson’s ratio is reduced from 0.5, the indentation hardness decreases first and then increases. This trend was found to be valid for a wide of yield strains. For yield strains less than 0.08, the hardness of auxetic materials is much larger when compared with materials having positive plastic Poisson’s ratio. As the plastic Poisson’s ratio approaches −1, the elastic deformations dominate over the plastic deformations. The plastic dissipation, when compared with the elastic work, is lower for materials with negative Poisson’s ratio. There is no effect of elastic Poisson’s ratio on the indentation hardness when the plastic Poisson’s ratio is more than −0.8. When the plastic Poisson’s ratio is less than −0.8, the hardness increases with a decrease of elastic Poisson’s ratio. The plastic dissipation per unit strain energy is maximum for materials with vanishing plastic Poisson’s ratio.

Using the finite element method, we investigate the elasto-plastic impact of a rigid sphere on a half-space of auxetic and metal foams. The validity of the Hertz theory for elastic impacts is investigated for both positive and negative Poisson's ratio. For elastic impacts, the results from Hertz theory are accurate within 20 % with the finite element simulations. The plasticity is modeled using the Deshpande-Fleck metal foam yield criterion. This yield criterion allows for plastic compressibility and can also accommodate materials having a negative Poisson's ratio. The elasto-plastic simulations reveal that the coefficient of restitution decreases as the impact velocity is increased. The coefficient of restitution is also least for materials having a zero plastic Poisson's ratio. Our study suggests for maximum energy dissipation the plastic Poisson's ratio should be close to zero.

We investigate the mechanics of the detachment of an inclined micro-pillar adhered to a dissimilar substrate when subjected to a combination of an axial load and end moment. When the micro-pillar has adhered to the substrate, singular stress fields exist at the bi-material corners. The order of singularity is estimated using asymptotic analysis. The first two terms in the asymptotic expansion lead to singular stress fields. The magnitude of the singularity is evaluated in terms of the elastic mismatch between the pillar and substrate and the micro-pillar inclination. The asymptotic stress due to the moment loading is more sensitive to the micro-pillar inclination when compared to that due to the axial loading. They are insensitive to the micro-pillar inclination when the micro-pillar is rigid when compared to the substrate. A short interfacial crack is further assumed to exist at the bi-material corner. This crack is embedded in the corner singularity region and is loaded by the singular fields due to axial and bending loads. A boundary layer analysis is performed on the singular zone to estimate the stress intensity factor when a short crack embedded in it is subjected to the singular fields. The stress intensity factors are also calculated for a long interfacial crack at the bi-material corner, which extends beyond the singular zone. Using the above results, we investigate the detachment of the inclined micro-pillar under the combination of an axial load and end moment.

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