By John G. Collier, John R. Thome
Large advances in laptop applied sciences and strategies have triggered an exceptional call for for refinements within the constitutive types of plasticity. Such refinements comprise the improvement of a version that might account for cloth anisotropy and produces effects that evaluate good with experimental facts. Key to constructing such models-and to assembly many different demanding situations within the box- is an organization seize of the foundations of continuum mechanics and the way they follow to the formula of plasticity concept. additionally serious is knowing the experimental points of plasticity and fabric anisotropy. Integrating the characteristically separate topics of continuum mechanics and plasticity, this publication builds figuring out in all of these components. half I presents systematic, accomplished insurance of continuum mechanics, from a evaluate of Carteisian tensors to the correct conservation legislation and constitutive equation. half II bargains an exhaustive presentation of the continuum concept of plasticity. This encompasses a designated therapy of the experimental facets of plasticity, covers anisotropic plasticity, and comprises contemporary study effects regarding the endochronic concept of plasticity acquired by way of the writer and his colleagues. by means of bringing all of those jointly in a single booklet, Continuum Mechanics and Plasticity enables the educational of reliable mechanics. Its readers might be organized for pursuing both examine regarding the mechanical habit of engineering fabrics or developmental paintings in engineering research and layout.
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Extra resources for Continuum Mechanics and Plasticity
7 The Isotropic Tensors A tensor is isotropic if it has the same components with respect to a Cartesian coordinate system of any orientation. Isotropic tensors of various ranks are given below: Scalar: Every scalar is an isotropic tensor, because the scalar does not have a direction. Vector: There is no nontrivial isotropic vector. 122) where λ is a constant. 124) where α, β, and γ are constants. 129) and we see that the independent constants are now reduced to α and β. 7 Show that there are no nontrivial isotropic vectors.
These are intensity of forces (force per unit area) along the coordinate directions. They vary with the location in the body and their magnitudes and speciﬁc characteristics depend on the geometrical shape of the body and the loading condition (surface traction). To determine the distribution of stress in the body, we need to solve a boundary-value problem, by specifying the boundary conditions. However, this problem will not be discussed in this chapter. Instead, we concentrate on understanding the nature of stress at a given point, and consider the stress at a point.
153) where ds is the length of dxi . 155) Cartesian Tensors 39 Note that ni ui is negative at A and positive at B. 158) is valid for the inﬁnitesimal cylinder considered. 150). We remark that the theorem of Gauss is still valid for multiply connected region. In that case, we have to make branch cuts to prove the theorem. Some special cases of the theorem are listed below: 1. 7 Contour and surface. 151). 152) by ekij . 2. 165) In the two-dimensional case, the theorem changes the surface integral into the line integral and vice versa.
Continuum Mechanics and Plasticity by John G. Collier, John R. Thome