By E. A. de Souza Neto, D. Peric, D. R. J. Owen
The topic of computational plasticity encapsulates the numerical equipment used for the finite aspect simulation of the behaviour of a variety of engineering fabrics thought of to be plastic – i.e. those who suffer an everlasting swap of form in line with an utilized strength. Computational tools for Plasticity: concept and Applications describes the idea of the linked numerical equipment for the simulation of a variety of plastic engineering fabrics; from the best infinitesimal plasticity conception to extra advanced harm mechanics and finite pressure crystal plasticity versions. it truly is cut up into 3 elements - simple suggestions, small traces and massive traces. starting with user-friendly thought and progressing to complex, advanced concept and machine implementation, it truly is compatible to be used at either introductory and complicated degrees. The book:
- Offers a self-contained textual content that enables the reader to profit computational plasticity idea and its implementation from one volume.
- Includes many numerical examples that illustrate the appliance of the methodologies described.
- Provides introductory fabric on comparable disciplines and approaches comparable to tensor research, continuum mechanics and finite parts for non-linear sturdy mechanics.
- Is observed by way of purpose-developed finite point software program that illustrates the various options mentioned within the textual content, downloadable from the book’s significant other website.
This accomplished textual content will entice postgraduate and graduate scholars of civil, mechanical, aerospace and fabrics engineering in addition to utilized arithmetic and classes with computational mechanics parts. it's going to even be of curiosity to investigate engineers, scientists and software program builders operating within the box of computational strong mechanics.
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Additional resources for Computational Methods for Plasticity: Theory and Applications
The material has been organised into sixteen chapters and four appendices. These will now be brieﬂy described. The remainder of Chapter 1 discusses the general scheme of notation adopted in the book. Chapter 2 contains an introduction to elementary tensor analysis. In particular, the material is presented mainly in intrinsic (or compact) tensor notation – which is heavily relied upon thoughout the book. Chapter 3 provides an introdution to the mechanics and thermodynamics of continuous media. The material presented here covers the kinematics of deformation, balance laws and constitutive theory.
In this section we introduce some basic deﬁnitions and operations involving higher-order tensors. 53). The alternating tensor is a linear operator that maps vectors into skew symmetric tensors. 81) for arbitrary vectors a, b, c and d. The multiplication of the alternating tensor by a vector v yields the second-order tensor v = ijk vk ei ⊗ ej . 52) can be equivalently written in compact form as w = ( v) u. 1. FOURTH-ORDER TENSORS Fourth-order tensors are of particular relevance in continuum mechanics.
DIRECTIONAL DERIVATIVE Let X and Y be ﬁnite-dimensional normed vector spaces and let a function Y be deﬁned as Y : D ⊂ X → Y, where the domain D of Y is an open subset of X. e. lim U→0 o(U ) = 0. 112) If the linear map DY(X 0 ) exists, it is unique and is called the derivative of Y at X 0 . 113) =0 for each U ∈ X. For a given U , the term DY(X 0 ) [U ] is called the directional derivative of Y (at X 0 ) in the direction of U . 2. 114) is the called the linearisation of Y about X 0 , that is, it is the linear approximation to Y at X 0 .