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Axial compression behavior of foam materials can be explained by two ideal deformation scenarios: discrete crush band process and progressive collapse. In this paper, a perfectly new model for strength assessment and quantitative/qualitative description of one-dimensional progressive collapse of aluminum foams under impulsive loadings is presented and its capability to split this way of crushing into two distinct regimes of shock wave and elastic- plasic wave propagation is highlighted. Then, using conservation relations and the new introduced model, the analytical solution of dynamic deformation of aluminum foams in the two mentioned regimes is developed. Regime 2 considers the case when the crushing front velocity is lower than the linear sound velocity of the foam; but remains higher than the effective sound velocity for a perturbation in which the amplitude lies in the so-called “plateau region’ of the static stress-strain diagram. The physical difference between this regime and the fiest one entails not only the creation a shock front associated with the collapsing foam, but also an acoustic precursor in the case of second regime.Finite element simulation is also performed to validate the analytical procedure. The numerical prediction is found to be in very good agreement with the analytical results.

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In this paper we developed and modeled elastic - plastic contact theories for soft spherical nano - bacteria to be applied in manipulation of various micro/nanobio particles based on atomic force microscopy. First, we simulated elastic contact for three types of nano - bacteria: S. epidermidis, S. salivarius and S. aureus, using Hertz contact model and finite element. Comparing simulation results of elastic contact with experimental data showed that considering elastic contact for simulating the contact of nano - bio particles is not appropriate and will yield incorrect results. Therefore, in this research, we tried to develop and simulate Chang elastic - plastic contact theory to be applied in simulation of contact mechanics for application in simulating manipulation. Comparing simulation of Chang contact theory with available experimental data and the results from contact simulation of Chen et al showed that Chang’s complete elastic - plastic theory yields desirable results. Comparing the diagram of contact radius in terms of indentation in Hertz and Chang theories showed that the created contact radius in elastic - plastic state is larger than contact radius in elastic state.

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In this paper, elastic-plastic symmetrical buckling of a thin solid circular plate of variable thickness, under uniform edge pressure, is investigated, based on both Incremental Theory (IT) and Deformation Theory (DT). Two kinds of simply supported and clamped boundary conditions have been considered. A power-law function was assumed for thickness variation. To minimize the integral uniqueness criterion, based on Rayleigh-Ritz method, transversal displacement was approximated by a test function which includes some unknown coefficients and satisfies geometric boundary conditions. Substituting the test function in the stability criterion and minimizing with respect to the unknown coefficients results in a homogeneous algebraic set of equations in terms of unknown coefficients. For non-trivial solution, the determinant of coefficient matrix should be equated to zero. Using this equation, critical buckling load is determined. The results of present study were compared with existing analytical solutions for circular plate of constant thickness and a good agreement was observed. This clearly shows the validity of presented analysis. Then the effect of thickness variation and boundary conditions type on the critical buckling load was investigated, for commercial aluminum and steel 1403 materials. The results show that when the thickness of circular plate center is 10% greater than its edge thickness the buckling load may increase up to 40% comparing with the circular plate for which the center thickness is 10% less than its edge thickness.

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Abstract Nowadays, polymeric materials are used in most industrial and engineering applications. In many of the applications, crack is initiated in mixed mode loading conditions. As a result, investigation of these materials at different loading angles is essential for safe design of structures. In this paper the mixed-mode elastic-plastic fracture behavior of ABS material based on J-integral key parameter was studied and the modified Arcan fixture was employed to investigate fracture behavior of this material under pure mode I (opening mode), pure mode II (shearing mode) and in plane mixed mode loading conditions. This work has been carried out experimentally by J–integral method named multi-specimen and normalization techniques. Finally, by fitting linear and power functions based on ASTM E813-81 and E813-87 test procedures respectively, the fracture toughness of this polymeric material was obtained in plane strain condition. The (J-R) curve comparison showed good agreement between the two methods. The minimum difference between the two methods obtained in a shear mode by ASTM E813-81 was about 1.37% and the maximum difference observed in tensile mode by ASTM E813-87 was about 30.7%.

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In this paper, elastic-plastic buckling of a thick rectangular plate has been investigated based on both Incremental (IT) and Deformation (DT) plasticity theories. Uniform biaxial edge traction was assumed as the plate loading while simply supported as the boundary conditions. Integral uniqueness criterion has been minimized to determine the critical buckling traction. Based on Rayleigh-Ritz method, a linear combination of polynomial base functions, which satisfy the geometrical boundary conditions, has been used as the trial functions for rotations and transverse deflection. To validate the analysis, the results for the Mindlin plate theory have been compared with the previously published results and a very close agreement has been observed. Then the effects of thickness ratio, aspect ratio and also different biaxial traction ratios on the buckling traction have been investigated. The results show that for the problem considered here, very close critical buckling traction is predicted by the both Mindlin and sinusoidal plate theories. This implies that Mindlin plate theory is sufficiently accurate to predict critical buckling traction in this problem. Moreover when the loading is gradually changed from biaxial into uniaxial compression or when the thickness-ratio is increased, the difference between the two theories is also increased. Also for compression-tension loading case, the critical buckling traction predicted by deformation theory is much less than the incremental theory.

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For ductile fracture, the toughness can be measured as a single parameter value or in a resistance curve format (J-R curve) and is often characterized by the J-integral for elastic-plastic materials. Because of their effectiveness in measuring toughness, the J-integral and J-R curve have become the most important material parameters in elastic-plastic fracture mechanics, and have been applied widely in practical engineering. Polymeric materials are widely being used for load-bearing structural applications and, therefore, understanding of their fracture properties is becoming more important. In this study, mixed-mode I/II stable crack growth experiments were carried out on a widely used polymeric material, polypropylene, using recently modified fixture. Multi-specimen R-curve method were used for obtaining J-R curves of different states of mixed-mode loading conditions from pure mode-I to pure mode-II by varying the loading angle by 15° steps accordance with the standard ASTM-D6068 and then the resulting R-curves have been evaluated to determine the values of initiation toughness, JIC, following the schemes of the E813 and E1820 standard procedures. Finite-element analyses were done by ABAQUS and mode-I and mode-II non-dimensional stress intensity factors and geometric work factors of elastic-plastic fracture were obtained for different conditions. Results show that for this material the value of JIC is much more than the value obtained for the JIIC. This material also exhibited a greater resistance to ductile crack growth in mode-I.