Download Numerical Continuum Mechanics by Vladimir N Kukudzhanov; Alexei Zhurov PDF

By Vladimir N Kukudzhanov; Alexei Zhurov

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Extra resources for Numerical Continuum Mechanics

Example text

1 General form of constitutive equations. 43). Although thermodynamic laws do not allow one to obtain a closed system of equations, these impose certain restriction on the constitutive equations of the medium. In order to close the system of equations of continuum mechanics, one requires equations that would determine thermomechanical properties of the medium and link the quantities U , s, q, and , appearing in the conservation laws, to kinematic and thermal characteristics determining the deformation " and temperature T of the medium as well as g D grad T .

63) p and the condition of active loading ij "Pij > 0 holds. 63) is a condition of plasticity with translationally isotropic hardening. In the stress space ij , the yield surface is displaced as a rigid body relative to the origin of coordinates. This displacement characterizes translational hardening of the material and is determined by the coordinates ijc . In addition, the surface radius increases with Wp , resulting in isotropic hardening of the plastic material. 4. 4. Transformation of the yield surface in translationally isotropic hardening in the space of ij .

In this case, for stationary problems of elasticity, one can formulate a principle of statically admissible stress fields. 106), after multiplying it by ui and integrating over the volume V , that Z Z Z Z ı ij;j ui d V D ı ij nj ui dS C ı ij nj ui dS ı ij "ij d V D 0; V S Su V where ui are prescribed displacements on the part Su of the body surface. 108) expresses Castigliano’s variational principle, which can be formulates as: the true stress field delivers a stationary value to the Castigliano functional.

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