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 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

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

Elasto-Plastic and Damage Analysis of Plates and Shells

Shells and plates are critical structures in numerous engineering applications. Analysis and design of these structures is of continuing interest to the scienti c and engineering communities. Accurate and conservative assessments of the maximum load carried by a structure, as well as the equilibrium path in both the elastic and inelastic range, are of paramount importance to the engineer. The elastic behavior of shells has been closely investigated, mostly by means of the nite element method. Inelastic analysis however, especially accounting for damage effects, has received much less attention from researchers. In this book, we present a computational model for nite element, elasto-plastic, and damage analysis of thin and thick shells. Formulation of the model proceeds in several stages. First, we develop a theory for thick spherical shells, providing a set of shell constitutive equations. These equations incorporate the effects of transverse shear deformation, initial curvature, and radial stresses. The proposed shell equations are conveniently used in nite element analysis. 0 AsimpleC quadrilateral, doubly curved shell element is developed. By means of a quasi-conforming technique, shear and membrane locking are prevented. The element stiffness matrix is given explicitly, making the formulation computationally ef cient. We represent the elasto-plastic behavior of thick shells and plates by means of the non-layered model, using an Updated Lagrangian method to describe a small-strain geometric non-linearity. For the treatment of material non-linearities, we adopt an Iliushin\u27s yield function expressed in terms of stress resultants, with isotropic and kinematic hardening rules.https://repository.lsu.edu/facultybooks/1421/thumbnail.jp

Mechanics of Composite Materials with MATLAB

This is a book for people who love mechanics of composite materials and ? MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing the numerical calculations needed in mechanics of c- posite materials. In particular, the steps of the mechanical calculations will be emphasized in this book. The reader will not ?nd ready-made MATLAB programs for use as black boxes. Instead step-by-step solutions of composite material mechanics problems are examined in detail using MATLAB. All the problems in the book assume linear elastic behavior in structural mechanics. The emphasis is not on mass computations or programming, but rather on learning the composite material mechanics computations and understanding of the underlying concepts. The basic aspects of the mechanics of ?ber-reinforced composite materials are covered in this book. This includes lamina analysis in both the local and global coordinate systems, laminate analysis, and failure theories of a lamina.https://repository.lsu.edu/facultybooks/1589/thumbnail.jp

Side Effects in Plasticity: From Macro to Nano

Size Effects in Plasticity: From Macro to Nano provides concise explanations of all available methods in this area, from atomistic simulation, to non-local continuum models to capture size effects. It then compares their applicability to a wide range of research scenarios. This essential guide addresses basic principles, numerical issues and computation, applications and provides code which readers can use in their own modeling projects. Researchers in the fields of computational mechanics, materials science and engineering will find this to be an ideal resource when they address the size effects observed in deformation mechanisms and strengths of various materials.https://repository.lsu.edu/facultybooks/1069/thumbnail.jp