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A matter of fact is that extremal principles have been introduced in mechanics in more (Euler, Lagrange) or less (Hamilton) than 200 years ago. One may also observe an impact of thermodynamic extremal principles based on maximum dissipation due to all the entropy production expressed in several disciplines. According fields are theory of communication, statistical mechanics and later physics of earth since already 70 years. The current paper offers some (historical) overview on several applications. "Ziegler's principle" is an implementation of the maximum entropy production going out to the dissipation and yielding a maximum dissipation. The goal of this paper is now the implementation of this extremal principle performed along an algebraic concept. Such a concept can be extended to a system with several internal variables as outlined by Coleman and Gurtin in context with the Gibbs (free) energy. [ABSTRACT FROM AUTHOR]

Thermodynamic modeling of the development of non-spherical inclusions as precipitates in alloys is an important topic in computational materials science. The precipitates may have markedly different properties compared to the matrix. Both the elastic contrast and the misfit eigenstrain may yield a remarkable generation of elastic strain energy which immediately influences the kinetics of the developing precipitates. The relevant thermodynamic framework has been mostly based on spherical precipitates. However, the shapes of actual particles are often not spherical. The energetics of such precipitates can be met by adapting the spherical energy terms with shape factors. The well-established Eshelby framework is used to evaluate the elastic strain energy of inclusions with ellipsoidal shapes (described by the axes a, b, and c) that are subjected to a volumetric transformation strain. The outcome of the study is two shape factors, one for the elastic strain energy and the other for the interface energy. Both quantities are provided in the form of easy-to-use diagrams. Furthermore, threshold elastic contrasts yielding strain energy shape factors with the value 1.0 for any ellipsoidal shape are studied. [ABSTRACT FROM AUTHOR]

The growth of living tissue is known to be modulated by mechanical as well as biochemical signals. We study a simple numerical model where the tissue growth rate depends on a chemical potential describing biochemical and mechanical driving forces in the material. In addition, the growing tissue is able to adhere to a three-dimensional surface and is subjected to surface tension where not adhering. We first show that this model belongs to a wider class of models describing particle growth during phase separation. We then analyse the predicted tissue shapes growing on a solid support corresponding to a cut hollow cylinder, which could be imagined as an idealized description of a broken long bone. We demonstrate the appearance of complex shapes described by Delauney surfaces and reminiscent of the shapes of callus appearing during bone healing. This complexity of shapes arises despite the extreme simplicity of the growth model, as a consequence of the three-dimensional boundary conditions imposed by the solid support. [ABSTRACT FROM AUTHOR]

The ensemble of interstitial atoms as C attracted to a dislocation is well established as “Cottrell cloud” phenomenon. The deposition of the interstitial atoms in octahedral or tetrahedral positions in a bcc lattice may yield a remarkable internal stress state according to their anisotropic misfit eigenstrains. The stress fields of the atoms may then lead to a significant change in the stress field, e.g., around a dislocation. In such a case, the interstitial atoms are situated near the dislocation core in cylindrical volume elements along the dislocation line. As the occupancy of the sites in each cylinder by interstitial atoms can be considered as constant, also the eigenstrain state tensor is constant in the cylinder. A complete set of analytical expressions for the eigenstress state inside and outside of the cylinder is presented. The resultant stress field is then given by superposition, which allows also the determination of the interaction energy between the Cottrell cloud and the dislocation. [ABSTRACT FROM AUTHOR]

Grain refinement can be described by the classical kinetic equation using a negative value of the specific grain boundary Gibbs energy. A respective overview is offered reporting according observations and simulations, particularly linked to grain boundary segregation. Classical grain growth model is used in the treatment of evolution of the distribution function during refinement. The adapted model requires defining nucleation rate of new grains, which significantly influences the kinetics of the system of grains. Moreover, a jump in the distribution function is allowed at a certain value of the grain radiusRJ, which separates old grains from newly nucleated ones. Evolution equation for both the critical radiusRcand separation radiusRJ(jump position) as well as for the dimension-free distribution (shape) function are derived. Illustrative examples for the evolution of the system parameters under various nucleation rates of newly generated grains are presented. [ABSTRACT FROM PUBLISHER]

The phase field method is frequently employed to simulate evolution of rather complex microstructures. In order to accurately describe the real kinetics of a specific material system, the phase field parameters must be calibrated to standard thermodynamic quantities such as interface mobilities or interface energies. This letter presents a convenient method, based on thermodynamic modelling of shrinking of a single grain embedded in single crystal (matrix), how to calibrate the phase field parameters. It also shows, how the required thermodynamic quantities can be met by proper rescaling of a phase field simulation carried out for given phase field parameters. [ABSTRACT FROM AUTHOR]

In this contribution, the local stress field very close to the free edges of bilayered compounds is reconsidered. Special emphasis is laid on the fulfilment of the boundary conditions. The bilayer character is represented by two areas in a homogeneous strip, where one of these areas is loaded by a homogeneous eigenstrain. Bilayered compounds are important components in several kinds of electronics and mechanical engineering applications. Positions of the intersection of the interface with free edges are prone to crack initiation. An easy-to-handle semi-analytical concept is presented, which allows estimating the maximum shear stress in the interface and its rapid dropping down very near to the free edges. The stress distributions in the immediate vicinity of the intersection of the interface with the free edges for generalized plane strain situations (as appearing along the side edges of a bilayered strip, sufficiently far away from the strip end), for plane stress situations (as appearing at the end of a bilayered beam), and in an axisymmetric setting (as appearing at the edge of a bilayered circular disc) are investigated. Already published approaches and results for these stress states are reviewed critically. [ABSTRACT FROM AUTHOR]

As outlined in the previous paper, an eigenstrain state due to an interstitial atom, acting as misfitting inclusion in the crystal lattice, may interact with a load stress state and/or a stress state due to a defect. Since the interstitial atoms can be assembled in a cylinder, as in the established case of a so-called Cottrell cloud, the according stress state can be investigated by a cylindrical inclusion with a general eigenstrain state. Both eigenstrain components belonging to the antiplane shear, however, were not dealt with in the past. According stress and deformation equations are now offered in analytical form in this addendum. [ABSTRACT FROM AUTHOR]

The hysteresis of ball-milled Fe-doped YCo5 powder has been optimized by controlling the temperature and time for rapid annealing under vacuum and argon. The crystallite size is only 25 nm; yet, it has been possible to field align Y(Co,Fe) powder with a 5-20 μm grain size in a 5 T field to obtain a remanence ratio of 0.65, due to texture in the ball-milled powder. The nominal energy product of the powder is 140 kJ/m³. A pressed magnet with 78% of theoretical density has an energy product of 65 kJ/m³. This magnet could fill the gap between oriented ferrite (34 kJ/m³) and oriented Nd-Fe-B (350 kJ/m³). [ABSTRACT FROM AUTHOR]

The hysteresis of ball-milled Fe-doped YCo5 powder has been optimized by controlling the temperature and time for rapid annealing under vacuum and argon. The crystallite size is only 25 nm; yet, it has been possible to field align Y(Co,Fe) powder with a 5-20 μm grain size in a 5 T field to obtain a remanence ratio of 0.65, due to texture in the ball-milled powder. The nominal energy product of the powder is 140 kJ/m³. A pressed magnet with 78% of theoretical density has an energy product of 65 kJ/m³. This magnet could fill the gap between oriented ferrite (34 kJ/m³) and oriented Nd-Fe-B (350 kJ/m³). [ABSTRACT FROM AUTHOR]

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The present work focuses on changes of mechanical properties in pyrolysed spruce wood as a function of temperature up to 2400°C. Nanoindentation tests are used for the determination of mechanical properties at the scale of single wood cell walls. Hardness, indentation modulus and elasto-plastic/brittle behaviour of the carbonaceous residues are derived as function of pyrolysis temperature. Hardness values increase continuously by more than one order of magnitude to 4.5?GPa at 700°C. The indentation modulus shows complex changes with a minimum of 5?GPa around 400°C and a maximum of 40?GPa around 1000°C. The deformation induced by the indenter is largely visco-plastic in native wood, but it is almost purely elastic in the carbonaceous residue, with particular low values of the indentation ductility index around 700°C. A low density and a strongly cross-linked carbon structure may explain the mechanical behaviour at these intermediate temperatures. A final decrease of the modulus and a slight decrease of ductility for temperatures above 2000°C can be attributed to a continuous structural transition of the material towards graphite-like stacking of carbon sheets and to preferred carbon orientation along the wood cell axis. [ABSTRACT FROM AUTHOR]