Divergence measure fields and Cauchy’s stress theorem
On Cauchy's stress theorem
In this work a new proof of the theorem of Cauchy on the existence of the stress tensor is given which does not use the tetrahedron argument.
On semiconvexity properties of rotationally invariant functions in two dimensions
Let be a function defined on the set of all by matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function can be represented as a function of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of in terms of its representation
Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity
The integral constitutive equations of a multipolar viscoelastic material are analyzed from the thermodynamic point of view. They are shown to be approximated by those of the differential-type viscous materials when the processes are slow. As a consequence of the thermodynamic compatibility of the viscoelastic model, the coefficients of viscosity of the approximate viscous model are shown to have an Onsager-type symmetry. This symmetry was employed earlier in the proof of the existence of solutions...
Actions with the conservation property
The paper deals with the theory of actions on thermodynamical systems. It is proved that if an action has the conservation property at least at one state then it has the conservation property at every state and admits an everywhere defined continuous potential. An analogous result for semi-systems is also proved.
Rank 1 convex hulls of isotropic functions in dimension 2 by 2
Let be a rotationally invariant (with respect to the proper orthogonal group) function defined on the set of all by matrices. Based on conditions for the rank 1 convexity of in terms of signed invariants of (to be defined below), an iterative procedure is given for calculating the rank 1 convex hull of a rotationally invariant function. A special case in which the procedure terminates after the second step is determined and examples of the actual calculations are given.
Invariant line integrals in the theory of defective crystals
In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.
Global solution to the ideal compressible heat conductive multipolar fluid
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