Plasticity

Modeling & Computation

verfasst von: Ronaldo I. Borja

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

There have been many excellent books written on the subject of plastic deformation in solids, but rarely can one find a textbook on this subject. “Plasticity Modeling & Computation” is a textbook written specifically for students who want to learn the theoretical, mathematical, and computational aspects of inelastic deformation in solids. It adopts a simple narrative style that is not mathematically overbearing, and has been written to emulate a professor giving a lecture on this subject inside a classroom. Each section is written to provide a balance between the relevant equations and the explanations behind them. Where relevant, sections end with one or more exercises designed to reinforce the understanding of the “lecture.” Color figures enhance the presentation and make the book very pleasant to read. For professors planning to use this textbook for their classes, the contents are sufficient for Parts A and B that can be taught in sequence over a period of two semesters or quarters.

Inhaltsverzeichnis

Frontmatter

Motivations and Scope

Abstract

Natural and manufactured materials generally exhibit an irreversible deformation behavior such that when an applied load is removed only a fraction of deformation is recovered. The extent of reversible deformation is called the elastic range, whereas the extent of irreversible or inelastic deformation, or yield, is the plastic range. The elastic range depends on the properties of a given material: rubber, for example, can experience very large deformation and still stay within the elastic range, whereas steel yields at a much smaller strain. The mechanisms responsible for irreversible deformation also varies from one material to another.

Ronaldo I. Borja

One-Dimensional Problem

Abstract

This chapter presents the basic elements of plasticity theory in the context of a one-dimensional bar problem. The goals are to facilitate an understanding of the basic ideas of plasticity theory without the need for extensive tensor notations, and to provide the reader an opportunity to conduct simple manual calculations that solidify understanding of the important concepts. The chapter introduces the notions of yield function, flow rule, hardening/softening responses, convexity of a function, and the concept of plastic dissipation. To provide a balanced treatment of theory and computation, we introduce at the outset the idea of return mapping for integrating the rate-constitutive equations in one dimension.

Ronaldo I. Borja

J2 Plasticity

Abstract

During his studies on plastic yielding of metals, Tresca (1864) conducted experiments on punching and extrusion through dies of various shapes. He concluded that yielding in metals would occur when the maximum shear stress reaches a certain yield value.

Ronaldo I. Borja

Isotropic Functions

Abstract

Many natural and manufactured materials exhibit plastic deformation behavior that cannot be captured by the J ₂ theory. They include concrete, rock, and metallic glass, which can compact or dilate inelastically and whose yield strength depends on the confining stress. High-porosity rocks compact under shearing due to collapse of the pores (Baud et al. 2004). Dense sands dilate to enable the moving particles to overcome interlocking (Lambe and Whitman 1969, Reynolds 1885).

Ronaldo I. Borja

Finite Deformation

Abstract

Many applications of plasticity theory involve large deformation for which the infinitesimal theory developed in the previous chapters may not be appropriate. Even if the stretching or straining of a material is small, the infinitesimal formulation is insufficient if the domain of interest experiences large rotation. This chapter focuses on the theoretical formulation and finite element implementation of a finite deformation theory of elastoplasticity. Whereas numerous finite deformation theories abound in the literature, we shall focus mainly on a formulation based on a multiplicative decomposition of the deformation gradient, which gives rise to so-called multiplicative plasticity theory.

Ronaldo I. Borja

Cap Models

Abstract

Elastic materials often exhibit a linear stress-strain response, but a nonlinear response does not necessarily imply inelastic behavior. The definition of an elastic material is quite broad: if it stores but does not dissipate energy, and if it returns to its undeformed shape when the loads are removed, then the material is elastic. Nonlinear elastic behavior could be due to the elastic parameters being intrinsically dependent on the state of stress (material nonlinearity), or to the large deformation that developed in the specimen during testing (geometric nonlinearity).

Ronaldo I. Borja

Discontinuities

Abstract

Material failure and damage typically involve some form of discontinuous deformation over a narrow zone. The mechanisms of deformation within this zone can be very complex, and they occur at multiple scales. Consider a geologic fault, as an example, which evolves from shearing across a series of échelon joints forming pockets of highly damaged rock. As shearing progresses, a fault core, or cataclasite zone, develops between surrounding less damaged zones made up of joints and sheared joints. As one moves farther away from the fault core, the rock becomes less and less damaged, until one finds the competent host rock that marks the end of the fault zone (Aydin et al. 2006).

Ronaldo I. Borja

Crystal Plasticity

Abstract

Metals and igneous rocks are most common materials with crystalline microstructures. Their elastoplastic properties are attributed to the existence of slip planes. The face-centered cubic (f.c.c.) structure has slip planes along (111) directions, while body-centered cubic (b.c.c.) crystals have slip planes in the (110) family. Because of their denser packing, materials with a f.c.c. structure, such as aluminum, copper, gold, and silver, tend to be more ductile than materials with a b.c.c. structure, such as iron, chromium, tungsten, and niobium. But packing alone does not determine the absolute ductility of a given material.

Ronaldo I. Borja

Bifurcation

Abstract

Localized deformation in solids occurs in many applications and in different forms. Examples of localized deformation include Lüders bands in metals (Nádai 1931), cracking in concrete (Baz̆ant and Planas 1997), and flow localization in bulk metallic glasses (Flores and Dauskardt 2001). Figure 9.1 shows images of shear bands in steel and bulk metallic glass at different scales. Shear bands have received considerable attention over the years because of their distinctive and intriguing style characterized by significant shear offset within a very narrow zone.

Ronaldo I. Borja

Backmatter

Titel: Plasticity
verfasst von: Ronaldo I. Borja
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-38547-6
Print ISBN: 978-3-642-38546-9
DOI: https://doi.org/10.1007/978-3-642-38547-6