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The purpose of this paper is to test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor.

For ceteris paribus, the constitutive relations of the resistor and inductor have been reformulated by following the novel constitutive relation of capacitor. The responses of RL, RC, LC and RLC circuits defined on the fractal set described by these definitions have been derived by means of the fractal calculus and fractal Laplace transformation. A comparative Hamiltonian formalism-based analysis has been performed where the circuits described by the conventional and the formerly proposed revisited constitutive relations have also been considered.

This study has found that the novel constitutive relations give unreasonable results unlike the conventional ones. Like such previous revisited constitutive relations, an odd Hamiltonian has been obtained. On the other hand, the conventional constitutive relations give a reasonable Hamiltonian.

To the best of the author’s knowledge, for the first time, the analysis of fractal set defined electrical circuits by means of unconventional constitutive relations has been performed where the deficiency of the tested capacitive constitutive relation has been pointed out.

Liquefaction phenomenon and its catastrophic nature can be analysed as a particular material behaviour of granular media under certain loading paths. Proposes a definition of liquefaction and its modelling by constitutive relations. Discusses this modelling in relation to the questions of stability and uniqueness. Considers the signs of three scalar quantities: the work of second order, the determinant of the symmetric part of the tangent constitutive tensor and the determinant of the tensor itself. Concludes that the liquefaction path is situated inside a potentially unstable domain and that in some cases this path reaches some states of loss of uniqueness, which are essentially bifurcation points.

Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide the applied strain increment into subincrements using an estimate of the local error and attempt to control the global integration error in the stresses. For a given scheme, the number of substeps used is a function of the error tolerance specified, the magnitude of the imposed strain increment, and the non‐linearity of the constitutive relations. The algorithms build on the work of Sloan in 1987 but include a number of important enhancements. The steps required to implement the integration schemes are described in detail and results are presented for a rigid footing resting on a layer of Tresca, Mohr‐Coulomb, modified Cam clay and generalised Cam clay soil. Explicit methods with automatic substepping and error control are shown to be reliable and efficient for these models. Moreover, for a given load path, they are able to control the global integration error in the stresses to lie near a specified tolerance. The methods described can be used for exceedingly complex constitutive laws, including those with a non‐linear elastic response inside the yield surface. This is because most of the code required to program them is independent of the precise form of the stress‐strain relations. In contrast, most of the implicit methods, such as the backward Euler return scheme, are difficult to implement for all but the simplest soil models.

The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive relationship, and (ii) the tangent softening model based on the incremental stress‐strain relationship. The models are implemented using a new softening initiation criterion proposed for application in multi‐dimensional finite element analysis. Parametric analyses on plain concrete beams, tested experimentally by other researchers, have been carried out to investigate the required numerical efforts, the mesh objectivity, and the energy dissipation characteristics of the structures. The stiffness degrading model is very stable even when applied with relatively coarse finite element meshes. However, the computational demand of this model is relatively high. The combination of a total stress‐strain constitutive relationship to compute the element responses, and an incremental relationship to formulate the stiffness matrix, appears to be computationally efficient and stable, provided that adequately refined finite element mesh is used to model the structure.

The purpose of this paper is to perform experimental investigation and constitutive modeling of the viscoelastic and viscoplastic behavior of metallocene catalyzed polypropylene (mPP) with application to lifetime assessment under conditions of creep rupture.

Three series of experiments are conducted where the mechanical response of mPP is analyzed in tensile tests with various strain rates, relaxation tests with various strains, and creep tests with various stresses at room temperature. A constitutive model is derived for semicrystalline polymers under an arbitrary three‐dimensional deformation with small strains, and its parameters are found fitting the observations.

Crystalline structure and molecular architecture of polypropylene strongly affect its time‐ and rate‐dependent behavior. In particular, time‐to‐failure of metallocene catalyzed polypropylene under tensile creep noticeably exceeds that of isotactic polypropylene produced by the conventional Ziegler‐Natta catalysis.

Novel stress‐strain relations are developed in viscoelastoplasticity of semi‐crystalline polymers and applied to predict their mechanical behavior in long‐term creep tests.

The purpose of this paper is to develop a constitutive model in cyclic viscoplasticity of perfluoroelastomers that accounts for the Mullins effect and to determine adjustable parameters in the stress‐strain relations by fitting observations in mechanical tests.

A perfluoroelastomer with a complicated internal structure is modeled as an equivalent incompressible, permanent, non‐affine network of chains with constrained mobility. Its viscoplastic response at finite strains is treated as sliding of junctions between chains with respect to their reference positions. Damage accumulation is associated with acceleration of plastic flow of junctions driven by growth of free volume. Stress‐strain relations are derived by using the Clausius‐Duhem inequality.

Constitutive equations are developed that correctly describe the mechanical behavior of perfluoroelastomers under cyclic loading with stress‐ and strain‐controlled deformation programs and arbitrary numbers of cycles. Adjustable parameters in the stress‐strain relations are found by matching experimental data in uniaxial tensile tests. Numerical simulation demonstrates that the model adequately predicts characteristic features of the Mullins effect.

A constitutive model is derived that can be applied for description of the viscoplastic response in perfluoroelastomers at cyclic loading with complicated deformation programs and prediction of their time to failure under fatigue conditions.

The purpose of this paper is to compare mechanical response of polypropylene in multi‐cycle tensile tests with strain‐controlled and mixed deformation programs and to develop constitutive equations that describe quantitatively the experimental data.

Multi‐cycle tensile tests are performed on isotactic polypropylene with strain‐controlled (oscillations between fixed maximum and minimum strains) and mixed (oscillations between a fixed maximum strain and the zero minimum stress) programs. A constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and its parameters are found by fitting observations. The effect of damage accumulation of material parameters is analyzed numerically.

The model predicts accurately mechanical behavior of polypropylene in tests with numbers of cycles strongly exceeding those used to determine its parameters. In the regime of developed damage, material constants in the stress‐strain relations are independent of deformation program.

A novel constitutive model is derived in cyclic viscoelastoplasticity of semicrystalline polymers and comparison of its adjustable parameters is performed for different deformation programs.

Understanding the differences in the Islamic and Christian view of interest requires coming to terms not with the acts constitutive of the practice but the meaning of the practice in two different views of what an economy produces and delivers. The difference in the norms that govern interest transactions differ because the metaphysical foundations about what the practice means differ. The Islamic norms are broader via public accountability for the good produced by an economy as a social good than the normative regulation of interest transactions in Christian cultures that focuses on the goods delivered by an economy to more or less independent individuals participating in an economy. However, some reconciliation of the Christian and Islamic view is possible when we recognize that the ethical accountability of interest rests on a view of economic justice as increasing the degree of economic participation in an economy as an economic and social good. When this view is taken, we see that the range of potentially illicit practices in Christian economies is larger than is actually the case in the actual regulation of interest transactions.