Continuum Mechanics and Theory of Materials by Peter Haupt

By Peter Haupt

This treatise makes an attempt to painting the tips and basic rules of the speculation of fabrics in the framework of phenomenological continuum mechanics. it's a well-written mathematical creation to classical continuum mechanics and offers with ideas comparable to elasticity, plasticity, viscoelasticity and viscoplasticity in nonlinear fabrics. the purpose of a basic idea of fabric behaviour is to supply a labeled variety of chances from which a consumer can opt for the constitutive version that applies top. The booklet may be worthy to graduate scholars of fabrics technology in engineering and in physics. the hot version contains extra analytical tools within the classical concept of viscoelasticity. This results in a brand new conception of finite linear viscoelasticity of incompressible isotropic fabrics. Anisotropic viscoplasticity is totally reformulated and prolonged to a normal constitutive thought that covers crystal plasticity as a distinct case.

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It is also intended to form the basis of the thermomechanical theory of materials in this treatise. 9 6 Introduction consideration. The presentation of classical continuum mechanics in combination with more recent developments in the formulation and application of constitutive models is intended to encourage the reader to develop a comprehensive understanding of the terminological content of the constitutive theory. This, in turn, will lead to a realistic assessment of its possible achievements and present limitations.

XR(X ds + sGL , t)1 s= 0 ' (4 F(X, t)GL = --;;'XR(X, t) = XRi (X\ X 2, X 3, t))9. ax ax ~ t he components P kL k a X k(X1X2X3) ax = 9·k FGL = ax ' , ,t = ax L R L or the component representation F a~ = P kL 9 k ® GL = ax L L 9k ® G . e. its determinant is always different from zero: k 8x ) ~ det ( 8X L o. 22). Accordingly, it always holds that detF ~ o. It is generally assumed that detF> o. 7 Cf. LEIGH [1968], pp. 102; MARSDEN & HUGHES [1983], p. 47. 50) 25 1. 48) refer to a mixed base of tensors, namely the system {9 k ® GL} (k, L == 1, 2, 3), consisting of tangent and gradient vectors of the current and reference configuration respectively.

1 Material Bodies All statements in continuum mechanics relate to material bodies which continuously fill parts of space with matter. Matter is the actual scene of physical occurrences: a material body can be identified with different parts of space at different moments in time and is simultaneously the carrier of the physical processes. The concept that matter is continuously distributed in space is presented by the term configuration: Definition 1. lJ] C IR3 ~ ~ X(~) = (xl, x2 , x3 ) <=> ~ = X-I (xl, x2, x3) .

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