Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers

Computational modelling of contact problems raises two basic questions: Which method should be used to enforce the contact conditions and how should this method be discretised? The most popular enforcement methods are the Lagrange multiplier method, the penalty method and combinations of these two. A frequently used discretisation method is the so called node-to-segment approach. However, this approach might lead to problems like jumps in contact forces, loss of convergence or failure to pass the patch test. Thus in the last few years, several segment-to-segment contact algorithms based on the mortar method were proposed.Combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations. On the other hand, a Lagrange multiplier mortar method requires additional unknowns. Hence, condensation of the Lagrange multipliers is desirable to preserve the initial size of the system of equations. This can be achieved by interpolating the Lagrange multipliers with so-called dual shape functions.Discretising two contacting bodies leads to opposed contact surface representations of finite element edges, called slave and master elements, respectively. In current versions of dual Lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element (instead of the entire element) belongs to the contact area. We present a modified definition of the dual shape functions in such slave elements. The basic idea is to construct dual shape functions that fulfill the so-called biorthogonality condition within the contact area. This leads to consistent mortar matrices also in the boundary region. To avoid ill-conditioning of the stiffness matrix, the modified mortar matrices are weighted with appropriate weighting factors. In doing so, the corresponding modified Lagrange multiplier nodal values are of the same order as the unmodified ones. Various examples demonstrate the performance of the modified mortar contact algorithm.     

Correlation between the fracture roughness and fatigue threshold of high-temperature degraded steel

We analyze the influence of degradation of 12Kh1MF heat-resistant steel under in-service and laboratory conditions on the characteristics of surface roughness after fatigue fracture. It is shown that the behavior of the threshold stress intensity factor ΔK _{th cl} characterizing the effect of crack closure is similar to the behavior of the amplitude characteristics of surface roughness in the direction perpendicular to the direction of crack propagation. This enables to make a conclusion that the decisive role in the process of crack closure in the degraded metal is played by longitudinal shear. It is shown that hydrogen absorbed by the degraded metal determines the characteristics of its crack resistance and affects the process of crack closure. We propose a model of crack closure that additionally takes into account the influence of longitudinal shear. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv; Technical University of Wrocław, Poland. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 6, pp. 37–42, November–December, 1999.     

Viability of the Lactobacillus rhamnosus HN001 Probiotic Strain in Swiss‐ and Dutch‐Type Cheese and Cheese‐Like Products

The objective of this study was to determine the viability of the probiotic Lactobacillus rhamnosus HN001 in Swiss‐type and Dutch‐type cheese and cheese‐like products (milk fat is substituted by stearin fraction of palm fat) during manufacture, ripening, and storage. The use of the probiotic L. rhamnosus HN001 in Dutch‐type cheese and cheese‐like products significantly (P = 0.1) changed their chemical composition (protein and fat content) and an insignificant increase (approximately 1.6% in cheese‐like products and approximately 0.3% in cheese) in yield. L. rhamnosus HN001 did not affect the rate of changes in the pH of ripened cheese and cheese‐like products. A minor increase in probiotic counts was observed in initial stages of production and were partially removed with whey. Ripened cheese and cheese‐like products were characterized by high survival rates of probiotic bacteria which exceeded 8 log CFU/g after ripening. An insignificant reduction in the number of viable probiotic cells was noted during storage of Swiss‐type and Dutch‐type cheese, whereas a significant increase in probiotic cell counts was observed in cheese‐like products during storage.     

A New Method for RTS Noise of Semiconductor Devices Identification

In this paper, a new method, called the noise scattering pattern method (NSP method), for random telegraph signal noise identification in the inherent noise of semiconductor devices is described. A block diagram of a noise measurement system based on the NSP method is presented. Examples of patterns of the NSP method are included.     

Natural antioxidants in milk and dairy products

Milk antioxidants, both lipophilic (conjugated linoleic acid, α‐tocopherol, β‐carotene, vitamins A and D₃, coenzyme Q₁₀, phospholipids) and hydrophilic antioxidants (proteins, peptides, vitamins, minerals and trace elements) play a key role in maintaining pro‐oxidant and antioxidant homeostasis in the human body. Lipophilic antioxidants are characterised by high thermal stability and they are active in all dairy products. Lipophilic and hydrophilic antioxidants interact in the process of deactivating reactive oxygen species and the final products of lipid peroxidation. A negative correlation between milk consumption and the incidence of diet‐dependent diseases confirms that the consumption of milk and dairy products delivers health benefits.     

Geoenergy in Poland

This paper presents the current state of geothermal energy production in Poland and its future development prospects. At present, there are four geothermal heating plants in Poland. In addition, warm water is used in seven spa towns in balneology as well as in seven thermal swimming pools for recreational purposes. There has recently been an increase in the number of installed heat pumps in Poland – reaching 10,000 in 2010. In the near future the development of geothermics in Poland is forecast to continue. The first power and heat geothermal plant is being built in Uniejów whilst in more than ten other towns special swimming pool complexes using geothermal warm water are being built or designed. In the coming years heat pumps will be installed in living and office buildings as well as in public use buildings (mostly in newly built ones). Moreover, in Poland it is planned to use heat pumps in order to recover waste heat from factories and power plants.