The minimum determinant of Minkowski-reduced quinary quadratic forms

The aim of this work is to determine what free energy functionals are expressible as quadratic forms of the state functional \(I^t\) which is discussed in earlier papers. The single integral form is shown to include the functional \(\psi _F\) proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a new systematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to uncover new free energy functionals. However, while, in principle, the same method should apply to free energies which can be given by quadratic forms in terms of \(I^t\), it emerges that this requirement is very restrictive; indeed, only the minimum free energy can be expressed in such a manner.

Energy-stable boundary conditions based on a quadratic form: Applications to outflow/open-boundary problems in incompressible flows

A peridynamic approach to computation of elastic and entropic interactions of inclusions on a lipid membrane

The analysis of linear elastic structures having cable-like members, that is members which can take tension but not compression, is formulated as one in quadratic programming. The objective function is the total complementary energy function, a quadratic form in terms of the variables which are forces and force resultants, and the constraints are the equations of equilibrium of forces at the joints. A technique is indicated to reduce the size of the quadratic program obtained so that the number of variables in the reduced program is approximately the larger of the degree of indeterminacy and the number of the cable-like members. The formulation is performed entirely for a truss.

This report describes a general yield function for anisotropic elastoplastic materials written in a quadratic form in terms of the stress components. The function contains 28 independent coefficients that must be determined experimentally. A set of inequality constraint conditions imposed on these coefficients is derived from the convexity requirement for all yield functions. A number of previously derived yield functions are recognized here as special cases of the general quadratic yield function, and the convexity condition for each of them is also provided. These inequality conditions should aid experimental projects for material identification.

We consider two quadratic forms on a class of manifolds conformally equivalent to the euclidean space. We give necessary and sufficient conditions for the equivalence of these quadratic forms in terms of a weighted Hardy inequality.

Representations by some quinary quadratic forms of level 8

2-universal positive definite integral quinary quadratic forms

The reduction of positive definite quinary quadratic forms

An expansion for certain symmetric determinants