Green elastic materials

Craine, R.E., Green, A.E., Naghdi, P.M. A mixture of viscous elastic materials with different constituent temperatures. Q. J. Mech. Appl. Math. 23(2), 171-184 (1970)... 

The Cauchy stress tensor cr and Green Lagrange strain tensor Cgl are of second order and may be connected for a general anisotropic linear elastic material via a fourth-order tensor. The originally 81 constants of such an elasticity tensor reduce to 36 due to the symmetry of the stress and strain tensor, and may be represented by a square matrix of dimension six. Because of the potential property of elastic materials, such a matrix is symmetric and thus the number of independent components is further reduced to 21. For small displacements, the mechanical constitutive relation with the stiffness matrix C or with the compliance matrix S reads... 

The simplest (and weakest ) definition of an elastic material is one for which the stress depends only on the current strain these materials are termed Cauchy elastic. A subset of these materials is occupied by those for which the strain energy depends only on the current strain. These are termed Green elastic or hyperelastic and for these the strain energy is a function of the current strain only, and fully defines the material behaviour. For Cauchy... 

Butter, and other unctuous materials, may be qualitatively described by a modified Bingham body (Elliott and Ganz, 1971 Elliott and Green, 1972), which consists of viscous, plastic and elastic elements in series. The stress-strain behavior for the model proposed by Elliot and Ganz (1971) is shown in Figure 7.12B. Diener and Heldman (1968) proposed a more complex model to describe how butter behaves when a low level of strain is applied. The model consists of plastic and viscous elements in parallel, coupled in series with a viscous element in parallel with a combination of a viscous and an elastic element. Figure 7.12C shows the stress-strain curve for... 

At this voliime fraction, the viscosity diverges because the shear stress is now given by the particle-particle contact in the tightly packed structure. As a result, we obtain a fluid with visco-elastic properties similar to polymeric solids. In ceramic processing, we extrude and press these pastes into green shapes. As a result, the rheology of ceramic pastes is of importance. The rheology of very concentrated suspensions is not particularly well developed, with the exception of model systems of monodisperse spheres. This section first discusses visco-elastic fluids and second the visco-elastic properties of ceramic pastes of monodisperse spheres. The material on visco-elastic fluids draws heavily from the book Colloidal Dispersions by Russel, Saville, and Schowalter [31]. 

Table 10.2. Coefficients of variation for mechanical properties of clearwood and kiln-dried visually graded lumber compared to those of competitive structural materials. Clearwood values are based on tests of approximately 50 species (USDA, 1999) and lumber properties are from Green and Evans (1989). MOR is modulus of rupture, MOE is modulus of elasticity.

From the standpoint of the continuum simulation of processes in the mechanics of materials, modeling ultimately boils down to the solution of boundary value problems. What this means in particular is the search for solutions of the equations of continuum dynamics in conjunction with some constitutive model and boundary conditions of relevance to the problem at hand. In this section after setting down some of the key theoretical tools used in continuum modeling, we set ourselves the task of striking a balance between the analytic and numerical tools that have been set forth for solving boundary value problems. In particular, we will examine Green function techniques in the setting of linear elasticity as well as the use of the finite element method as the basis for numerical solutions. 

New materials can hardly compete with existing ones if they merely copy their properties without being distinctly cheaper. Instead it is necessary to use novel, hitherto unavailable combinations of properties in the case of the PAni developed by us, for example, its metal-like conductivity combined with transparency in the red and violet parts of the spectrum, its elasticity and ease of processing even for complicated shapes, its chemical and electronic interactions with light, and its extremely high surface tension. The material can also be reversibly reduced and oxidised, changing its colour in the process (dispersed PAni is normally green the reduced form is yellow, the oxidised form blue). Both an acid state and a base state exist. 

Green, A. E. and Zerna, W. (1954) Theoretical Elasticity, Oxford Clarendon Press. McClintock, F. A. and Argon, A. S. (1966) Mechanical Behavior of Materials, Reading, MA Addison Wesley. 

Fig. 12.11 The height density distribution (

Surimi is the Japanese term for an intermediate food product prepared by washing mechanically deboned fish mince (Okada, 1985). The process removes water-soluble proteins, enzymes, blood and metal ions. The removal of these nutrients for microbial growth leads to its greater stability (Green and Lanier, 1985). A representation of the process is shown in Figure 2.1. Surimi is an off-white, odourless material with a bland flavour. The proteins myosin and actin are the major components and these salt-soluble fish proteins have the ability to form a strong, highly elastic gel at relatively low temperatures c, 40°C) (Niwa, 1985). After preparation it is mixed with cryoprotectants and then frozen. 

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