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In this study, a promising model is presented to describe the flow stress curves with acceptable accuracy as well as generality. In this model, peak strain, peak stress, steady-state stress and hardening and softening constants are uncoupled and expressed as either bi-linearly interpolated or closed-form functions of temperature and strain rate. A practical method to obtain material constants is developed to render the model applicable in practice, which is based on optimization scheme. The flow stress curves of four materials are obtained using the new model and compared with experiments or the other models at some specific temperatures and strain rates. The comparison has revealed that the new model is feasible and general to describe the flow stress curves of various metals and alloys at different temperatures and strain rates with acceptable accuracy. Keywords: Flow stress model, Closed-form function, Bi-linear interpolation, Softening, Hardening

The data contained within this article relate to experimental data on mechanical behavior of an in-house cast hyperelastic Polydimethysiloxane (PDMS) based membrane (SilasticⓇ T-4, Dow Corning) for cell culture, which was used as a tool for applying tensile stress on cells and tissues. With the experimentally obtained material constants, tensile stress distribution over the membrane surface was numerically assessed using a finite element analysis (FEA). The membrane area having a uniform tensile stress distribution under different strain loading conditions of 1–20% was suggested for cell culture.

The permeability evolution of rock during the progressive failure process is described. In combination with the strength degradation index, the degradation formulas of s and a, which are dependent on the plastic confining strain component, the material constants of Hoek–Brown failure criterion are presented, and a modified elemental scale elastic–brittle–plastic constitutive model of rock is established. The relationship between volumetric strain and permeability through tri-axial compression is investigated. Based on the above, a permeability evolution model is established. The model incorporates confining pressure-dependent degradation of strength, dilatancy and corresponding permeability evolution. The model is implemented in FLAC by the FISH function method. The permeability evolution behavior of rock is investigated during the progressive failure process in a numerical case. The results show that the model is capable of reproducing, and allowing visualization of a range of hydro-mechanical responses of rock. The effects of confining pressure on degradation of strength, dilatancy and permeability evolution are also reflected. Keywords: Hoek–Brown failure criterion, Dilatancy, Permeability evolution, Confining pressure, Degradation of strength

Chapter 19 deals with the myth that dust explosion parameters are fundamental material properties. The reality is that dust explosion parameters such as the size-normalized maximum rate of pressure rise, K St , are strongly dependent on material characteristics such as particle size and experimental conditions such as turbulence intensity. Therefore, they are not intrinsic or fundamental material constants. Standardized equipment and test methodologies are available for determining these parameters; these must be followed to generate test data for use with the measures identified in dust explosion prevention and mitigation standards.

Publisher Summary This chapter discusses the strain-based multiaxial fatigue analysis. Strain tensor components can be used as damage parameters for multiaxial fatigue analysis. To capture physical features of the cracking behavior of the materials, the strain terms are often used in conjunction with stress terms to account for mean stresses or hydrostatic stresses. Strain-based damage parameters can be used for high-, mid-, and low-cycle fatigue life regimes with the proper selection of damage parameter. Fatigue life estimates for proportional multiaxial loading can be obtained with equivalent strain equations based on a yield criterion. For damage parameters that include stress terms, an accurate calculation of the stress tensor history from the strain tensor history requires sophisticated multiaxial material models and material constants. These material constants and damage parameter material constants can be challenging to obtain for an absolute fatigue life prediction, although comparative analysis can be conducted to examine general trends in fatigue life using multiple damage parameters.

The mathematical modelling of superplastic sheet forming processes is based on knowledge of the membrane theory and the flow rule to correlate the stresses to the strains in the plastic range. The modelling is limited usually to two special cases concerning bulge forming from a circular sheet and bulge forming from a rectangular sheet. In this chapter, mainly the free forming processes will be emphasized. Moreover, at the end of the chapter, some techniques will be suggested in order to determine the constants of the material from tests of inflation.

This paper describes a novel modelling process for creep crack growth prediction of a 316 stainless steel using continuum damage mechanics, in conjunction with finite element (FE) analysis. A damage material behaviour model, proposed by Liu and Murakami [1], was used which is believed to have advantages in modelling components with cracks. The methods used to obtain the material properties in the multiaxial form of the creep damage and creep strain equations are described, based on uniaxial creep and creep crack growth test data obtained at 600 °C. Most of the material constants were obtained from uniaxial creep test data. However, a novel procedure was developed to determine the tri-axial stress state parameter in the damage model by use of creep crack growth data obtained from testing of compact tension (CT) specimens. The full set of material properties derived were then used to model the creep crack growth for a set of thumbnail crack specimen creep tests which were also tested at 600 °C. Excellent predictions have been achieved when comparing the predicted surface profiles to those obtained from experiments. The results obtained clearly show the validity and capability of the continuum damage modelling approach, which has been established, in modelling the creep crack growth for components with complex initial crack shapes.

Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m = 2 – 5 in metals and m = 10 – 50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review.

Service life prediction is the key concept to assess environmental load of materials. Polymeric materials are degradated outdoors by solar UV irradiation, heat and water. Introducing chemical reaction theories, degradation phenomena can be expressed as a mathematical model consiting of a function of degradation factors and elapsed time. The author has developed a personal computer software system which determines degradation material constants in the model and predicts property change over time by the degradation simulation.

A simple technique is proposed for the prediction of the increase of pore-pressure of saturated granular soils subjected to random earthquake-type cyclic loads. The model involves the determination of two material constants from a single liquefaction test. The predicted rise in pore-pressure is in fairly good agreement with that observed by other researchers.

Review of theoretical results and experimental data on the spontaneous and induced polarization of liquid crystals is given. Dielectric properties and the linear field effects in chiral smectics and flexoelectric nematics are described. Fundamental material constants of ferroelectric smectics are estimated.

The S-N curves of steels are very useful for design purposes. However, it is usually a very difficult job to obtain such a curve or a family of curves from experiments, if we use the conventional smooth specimens (i.e. specimens not pre-cracked). The experimental data are so scattered that one has to be satisfied by obtaining a low bound envelope of the multitude of experimental points as an S-N curve on the safe side. The initiation life of materials are dependent upon the material constants such as C and m in Paris' equation: da/dN = C(δK) m , and the sizes of micro-defects in the materials. The latter depends on the quality of steel, and is different for each specimen. They are unknown to the experimenter. For this reason it is impossible to determine the material constants from the data of the experiments with smooth specimens. Moreover, for each smooth specimen, the initiation life varies from around 10 5 cycles to 10 9 cycles according to the amplitude of the applied load. For each load level at least three to five specimens are needed so it would take very long time to carry out the tests, usually it would exhaust the life of the testing machines themselves.

Summary Internal continuum damage of solids is modelled by an arrangement of oriented cracks. The observed overall mechanical response of directionally damaged materials is anisotropic. Differences in elastic, plastic and failure anisotropics are illustrated for a homogenized damaged material and uniaxial stress experiments were performed on continuously damaged alumium alloy sheets. The stress principal directions varied with respect to those of the introduced damage tensor. Experimentally obtained values of material constants for an orthotropic homogenized solid are given. The preliminary tests allow an approach to mathematical modelling of anisotropic continuous-damage mechanical response within the tensor functions theory for two independent tensor variables.

The constitutive model developed recently by Faruque and Chang (1986) is extended to predict deformation behavior of concrete and rocks under three-dimensional (3-D) loading. The failure and yield surfaces are described by compatible functionals defined by the same material constants. An optimization technique is employed to evaluate the associated material constants.

This chapter presents diagrams of dimensionless equations determining two basic working regimes of Peltier heat pump. The chapter also outlines that in practical selection of material approximately equal specific conductivities of both legs must be chosen to obtain uniform current distribution in both parts. It is also highlighted that the present calculation technique in frequently repeated projects of thermoelectric devices is comparatively laborious, and does not give rapid information on concrete changes of states under simultaneous changes of physical parameters of semiconductor materials. The problem has been solved by the use of dimensionless equations valid for Peltier heat pump system, that were numerically computed for a wide range of temperatures (hot junction temperature) and (cold junction temperature) and for the “effective figure of merit” of material. The results reveal that graphical expression of dimensionless equations solving a Peltier refrigerating element permits a rapid calculation of thermoelectric devices generally with physical parameters of any description. It does away with a laborious numerical calculation for the changing temperature conditions, or for various material constants of semi-conductors.