Sami Holopainen

Representations of m-linear functions on tensor spaces: Duals and transpositions with applications in continuum mechanics

The main goal of the present paper is to introduce certain duals and transpositions of a high-order tensor playing an important role in continuum mechanics. Emphasis is also placed on the comparison of the duals and the transpositions. In contrast to the duals, the transpositions depend on a metric of an underlying metric space. A high-order tensor is itself a representation of a multilinear function on a tensor space, obtained by means of the multilinear extension. The duals and the transpositions of a high-order tensor are identified as multilinear maps defined by the generalized scalar and the inner product, respectively. Consequently, the duals and the transpositions distinguish and define symmetries and symmetry-preserving transformation rules of a co-, contra- and mixed-variant tensor, respectively. As an application in continuum mechanics, the duals and the transpositions of a usual fourth-order tensor are defined and are employed to the determination of symmetries involved.

Modeling, Simulation, and Experimentation of Fatigue Behavior in Amorphous Solids

Amorphous solids, such as certain polymers, alloys, and polymer-based composites,are increasingly used materials in engineering components and thus, their fatigue behavioris of utmost importance. The article presents a unified approach suitable for modeling bothisothermal high cycle and low cycle fatigue behavior. The emphasis is placed on the ductilefatigue in which fatigue damage represents the material degeneration during the creation ofmicro-cracks governing majority of the total fatigue life (up to 95%). The model’s capability fortechnologically important polycarbonate (PC) polymer is addressed. The results, in accordancewith experimental observations, favor ductile fatigue behavior, i.e. damage fields remain smallfor most of the fatigue life and do not cause the macroscopic stress reduction. Due to thisproperty, fatigue life of an entire structural element can be evaluated by exploiting singlelocations at which the fatigue damage decisively emerges.

Improving performance in public services: Tools and implications of multiple criteria staff scheduling and ranking

Given the pressure on improving performance of labor-intensive services in the public sector, systematic decision support approaches for work planning within a field of a pertinent process and operations management have met with increasing success. However, due to a complex work pattern and multiple conflicting attributes, the issue has proven difficult to solve. In the face of those complications, we propose a holistic decision support approach comprising fundamental elements of staff scheduling, optimization, and operations management-concepts. For daily scheduling, monitoring, and developing organizational efficiency on continuous manner, an automated system comprising a functional interface and on-line database tools is also developed. The system tool is applied to a case organization in the public administration and the results from tangible examples are evaluated by comparing with observed data.