Ductile fracture of aluminum 2024-T351 under proportional and non-proportional multi-axial loading: Bao–Wierzbicki results revisited

Strain gradient plasticity under non-proportional loading

A critical examination is made of two classes of strain gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quantities expressed in terms of increments of strains and their gradients, whereas the other class employs incremental relationships between all stress quantities and the increments of strains and their g...

The super-replication theorem under proportional transaction costs revisited

We consider a financial market with one riskless and one risky asset. The super-replication theorem states that there is no duality gap in the problem of super-replicating a contingent claim under transaction costs and the associated dual problem. We give two versions of this theorem. The first theorem relates a numéraire-based admissibility condition in the primal problem to the notion of a lo...

Ordinal regression modelling between proportional odds and non-proportional odds

Multi-Attribute Proportional Representation

We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should have. We look for a set that fits as much as possible the desired distributions on all attributes. Examples of applications include choosing members of a rep...

Non-proportional Shrinkage Compensation

Shrinkage and warpage is a leading fact in casting. It is common to compensate shrinkage by scaling the tool by a certain percentage. The transformed 3D CAD model of a final product is used for tool generation. The transformations of CAD model include 3D scaling or external surface offset. Both methods are proportional and uniform in all three axes, and they are already included in a vast varie...