General non-linear finite element analysis of thick plates and shells

AbstractA non-linear finite element analysis is presented, for the elasto-plastic behavior of thick shells and plates including the effect of large rotations. The shell constitutive equations developed previously by the authors [Voyiadjis, G.Z., Woelke, P., 2004. A refined theory for thick spherical shells. Int. J. Solids Struct. 41, 3747–3769] are adopted here as a base for the formulation. A simple C0 quadrilateral, doubly curved shell element developed in the authors’ previous paper [Woelke, P., Voyiadjis, G.Z., submitted for publication. Shell element based on the refined theory for thick spherical shells] is extended here to account for geometric and material non-linearities. The small strain geometric non-linearities are taken into account by means of the updated Lagrangian method. In the treatment of material non-linearities the authors adopt: (i) a non-layered approach and a plastic node method [Ueda, Y., Yao, T., 1982. The plastic node method of plastic analysis. Comput. Methods Appl. Mech. Eng. 34, 1089–1104], (ii) an Iliushin’s yield function expressed in terms of stress resultants and stress couples [Iliushin, A.A., 1956. Plastichnost’. Gostekhizdat, Moscow], modified to investigate the development of plastic deformations across the thickness, as well as the influence of the transverse shear forces on plastic behaviour of plates and shells, (iii) isotropic and kinematic hardening rules with the latter derived on the basis of the Armstrong and Frederick evolution equation of backstress [Armstrong, P.J., Frederick, C.O., 1966. A mathematical representation of the multiaxial Bauschinger effect. (CEGB Report RD/B/N/731). Berkeley Laboratories. R&D Department, California.], and reproducing the Bauschinger effect. By means of a quasi-conforming technique, shear and membrane locking are prevented and the tangent stiffness matrix is given explicitly, i.e., no numerical integration is employed. This makes the current formulation not only mathematically consistent and accurate for a variety of applications, but also computationally extremely efficient and attractive

A Two-Dimensional Finite Element Model Of The Grain Boundary Based On Thermo-Mechanical Strain Gradient Plasticity

In this work, a two-dimensional finite element model for the grain boundary flow rule is developed based on the thermo-mechanical gradient-enhanced plasticity theory. The proposed model is temperature-dependent. A special attention is given to physical and micromechanical nature of dislocation interactions in combination with thermal activation on stored and dissipated energy. Thermodynamic conjugate microforces are decomposed into energetic and dissipative components. Correspondingly, two different grain boundary material length scales are present in the proposed model. Finally, numerical examples are solved in order to explore characteristics of the proposed grain boundary flow rule

A physically based constitutive model for dynamic strain aging in Inconel 718 alloy at a wide range of temperatures and strain rates

Dynamic strain aging has a huge effect on the microstructural mechanical behavior of Inconel 718 high-performance alloy when activated. In a number of experimental researches, significant additional hardening due to the dynamic strain aging phenomenon was reported. A constitutive model without considering dynamic strain aging is insufficient to accurately predict the material behavior. In this paper, a new constitutive model for Inconel 718 high-performance alloy is proposed to capture the additional hardening, which is caused by dynamic strain aging, by means of the Weibull distribution probability density function. The derivation of the proposed constitutive relation for the dynamic strain aging-induced flow stress, the athermal flow stress and the thermal flow stress is physically motivated. The developed model is applied to Inconel 718 high-performance alloy to demonstrate its ability to capture the dynamic strain aging behavior, which was observed in the literature across a wide range of temperatures (300–1200 K) and strain rates from quasi-static loading (0.001/s) to dynamic loading (1100/s)

Effect of element wall thickness on the homogeneity and isotropy of hardness in SLM IN718 using nanoindentation

In this paper the homogeneity and isotropy of the mechanical hardness of thin-walled Inconel 718 (IN718) alloy samples manufactured by Selective Laser Melting (SLM) were examined using nanoindentation testing. SLM-produced honeycombed samples with wall thicknesses of 0.8, 0.6 and 0.4 mm respectively were studied by measuring the hardness across the wall thickness, and on the planes parallel and perpendicular to the build direction over the range of depths of 10-2000 nm. The average hardness values close to the edges were 4.0-6.5% lower than the areas away from the them. Interestingly the average hardness dropped by 15.2% with reduction in the cell wall thickness from 0.8 mm to 0.4 mm. Average hardness values were reported to be higher on the plane perpendicular to the build direction compared to the parallel plane. A variable material length scale was proposed in this work to describe the size effects of the microstructure. It was evaluated using the nanoindentation hardness test results and a computational model developed in previous studies by the first author and his co-workers.Polish National Agency for Academic Exchange (NAWA, PPI/APM/2018/1/00045/U/001

Effect of Reinforcement Ratio on Damage in Reinforced Concrete Beams- A Damage Mechanics Approach

The principles of damage mechanics are used to study the effect of reinforcement ratio on the total damage of reinforced concrete beams. The definition of the damage variable in terms of the damaged and effective crosssectional areas is adopted. A consistent and simple mathematical derivation is presented to find the exact relation between the total damage and the damage of concrete in a reinforced concrete beam. It is shown that the reinforcement ratio has a clear but small effect on the total damage variable of the reinforced concrete beam. As the reinforcement ratio increases, the total damage in the beam decreases. Although this effect is small, it becomes more pronounced at higher levels of damage in the beam

Damage Mechanics in a Uniaxially - Loaded Elastic Tapered Bar

The principles of damage mechanics are used to predict the displacements and stresses in a uniaxially-loaded one-dimensional elastic tapered bar. The variation of the damage variable along the length of the bar is studied. A random distribution of the damage variable along the length of the bar is also considered. It is shown how the displacements and stresses are obtained in closed-form solutions whenever possible. Otherwise, finite element analysis is employed to solve the resulting problem. The computer algebra system MAPLE is used to write a symbolic finite element program specifically for this problem with the random distribution of the damage variable for which there is no closed form solution

3D FEA modelling of laminated composites in bending and their failure mechanisms

keywords: 3D keywords: 3D keywords: 3D keywords: 3D keywords: 3DAbstract This paper developed three-dimensional (3D) Finite Element Analysis (FEA) to investigate the effect of fibre lay-up on the initiation of failure of laminated composites in bending. Tsai-Hill failure criterion was applied to identify the critical areas of failure in composite laminates. In accordance with the 3D FEA, unidirectional ([0]16), cross-ply ([0/90]4s) and angle-ply ([±45]4s) laminates made up of pre-preg Carbon Fibre Reinforced Plastics (CFRP) composites were manufactured and tested under three-point bending. The basic principles of Classical Laminate Theory (CLT) were extended to three-dimension, and the analytical solution was critically compared with the FEA results. The 3D FEA results revealed significant transverse normal stresses in the cross-ply laminate and in-plane shear stress in the angle-ply laminate near free edge regions which are overlooked by conventional laminate model. The microscopic images showed that these free edge effects were the main reason for stiffness reduction observed in the bending tests. The study illustrated the significant effects of fibre lay-up on the flexural failure mechanisms in composite laminates which lead to some suggestions to improve the design of composite laminates

Evaluating the Performance of Geosynthetic Reinforced Soil-Integrated Bridge System (GRS-IBS) under Working Stress Condition

This paper evaluates the performance of geosynthetic reinforced soil-Integrated Bridge System (GRS-IBS) in terms of lateral facing deformation and strain distribution along geosynthetics. Simulations were conducted using 2D PLAXIS program. The hardening model proposed by Schanz et al. [1] was used to simulate the behavior of backfill material; the backfill-reinforcement interface was simulated using Mohr-Coulomb model, and the reinforcement and facing block were simulated using linear elastic models. The numerical model was verified using the results of a case study conducted at Maree Michel GRS-IBS, Louisiana. Parametric study was carried out to investigate the effects of span length, reinforcement spacing, and reinforcement stiffness on the performance of GRS-IBS. The results indicate that span length have significant impact on strain distribution along geosynthetics and lateral facing deformation. The reinforcement stiffness has significant impact on the GRS-IBS behavior up to a certain point, beyond which the effect tends to decrease contradictory to reinforcement spacing that has a consistent relationship between the GRS-IBS behavior and reinforcement spacing. The results also indicate that reinforcement spacing has higher influence on the lateral facing deformation than the reinforcement stiffness for the same reinforcement strength/spacing ratio (Tf/Sv) due to the composite behavior of closely reinforcement spacing

A physically based gradient plasticity theory’,

Abstract The intent of this work is to derive a physically motivated mathematical form for the gradient plasticity that can be used to interpret the size effects observed experimentally. The step of translating from the dislocation-based mechanics to a continuum formulation is explored. This paper addresses a possible, yet simple, link between the TaylorÕs model of dislocation hardening and the strain gradient plasticity. Evolution equations for the densities of statistically stored dislocations and geometrically necessary dislocations are used to establish this linkage. The dislocation processes of generation, motion, immobilization, recovery, and annihilation are considered in which the geometric obstacles contribute to the storage of statistical dislocations. As a result, a physically sound relation for the material length scale parameter is obtained as a function of the course of plastic deformation, grain size, and a set of macroscopic and microscopic physical parameters. Comparisons are made of this theory with experiments on micro-torsion, micro-bending, and micro-indentation size effects