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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.

An extension of the concept of error on constitutive relation is proposed to the case of Mindlin plate finite element computations. The error of the performed analysis is estimated from the incompatibility in relation with the constitutive equation of admissible fields calculated from the finite element results. In a first stage, loads and moments densities leading to the equilibrium of each element are computed on the element edges as the sums of densities derived from the finite element solution and of densities with a resultant equal to zero on each element edge. Then strictly statically admissible stress resultants are calculated within each element. Both of the two stages allow an optimization for the statically admissible field in order to get a more accurate error. The calculations are local which is very interesting especially in case of complex structure analyses with a large number of degrees of freedom for which adaptivity is an important feature. A set of examples shows the efficiency of the proposed estimator and the good adaptation of the error on constitutive law method to Mindlin plate analysis.

Different axiomatizations of network theory are considered. Kirchhoff networks are regarded with priority. Multipole and multiport networks are introduced as alternative variants. Additionally, Minty and Paynter networks, which are always dualizable are discussed briefly. The latter are special cases of Kirchhoff as well as of multiport networks. This paper seeks to discuss these issues.

The paper develops network theory inside of set theory, i.e. networks, multipoles, etc. are defined as objects of set theory. As such objects we use preferably ordered pairs, ordered triples, etc. The objects of network theory are then separated from the class of all these set theoretical objects by means of some defining conditions. These conditions are the axioms of our approaches to network theory.

It is shown that all presented variants of axiomatizations can be developed on the basis of a uniform representation for the time functions for voltages and currents. All these variants allow interdisciplinary applications of network theory and they can be generalized to multidimensional networks. An interesting byproduct is the relationship between multiport networks, networks in Belevitch normal form, Paynter networks, and bond graphs.

For applications it is essential that Kirchhoff and multipole networks are with respect to their modeling capability of equal value. But from the foundational point of view the multipole terminology has a number of crucial disadvantages compared with that based on Kirchhoff networks. This fact is important both for the conception of circuit simulation software packages and for the development of basic circuit theory curricula.

This paper aims to critically reflect on the growing systems orientation in marketing research and the approaches used to understand marketing systems. In response, the paper offers an integrative metatheory built on the ontic necessity and subsequently constitutive and causal efficacy of relations.

This conceptual paper is built on a logic of critique, identifying the generative absences that produce problems in the frameworks in use and attempting to rectify these problems by offering an alternative meta-theoretical structure. This paper draws from critical realism, systems thinking and relational sociology.

This paper advocates for an emergentist ontology for marketing systems built on the value of both substance and relation as co-principles of existence and the subsequent irreducible stratification derived from this. This position suggests the following propositions: the ontological premise of being is reliant on relations; the social world is constructed of stratified levels of organisation in which entities, their properties and powers emerge by virtue of these relations; these entities operate in complex and mutually modifying interrelations; stability and change is the result of this complex interplay of temporally/spatially stratified relations; and time and space are properties and potential powers of organisation.

This paper considers a number of inconsistencies in current approaches to the study of marketing systems arguing these arise based on the absence of a view of relations that supports an effective theory of emergence. In response, the paper develops a set of ontological presuppositions regarding the nature of marketing systems and a subsequent set of epistemic conditions as an integrative metatheoretical position, through which these systems are better understood and analysed. The paper argues that these improve our ability to theorise about the multi-dimensionality of these systems.

The purpose of this paper is to propose a computational approach in order to help establish the effect of various self-piercing rivet (SPR) process and material parameters on the quality and the mechanical performance of the resulting SPR joints.

Toward that end, a sequence of three distinct computational analyses is developed. These analyses include: (a) finite-element modeling and simulations of the SPR process; (b) determination of the mechanical properties of the resulting SPR joints through the use of three-dimensional, continuum finite-element-based numerical simulations of various mechanical tests performed on the SPR joints; and (c) determination, parameterization and validation of the constitutive relations for the simplified SPR connectors, using the results obtained in (b) and the available experimental results. The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash or even in simulations of vehicle component manufacturing, e.g. car-body electro-coat paint-baking process. In such simulations, explicit three-dimensional representation of all SPR joints is associated with a prohibitive computational cost.

It is found that the approach developed in the present work can be used, within an engineering optimization procedure, to adjust the SPR process and material parameters (design variables) in order to obtain a desired combination of the SPR-joint mechanical properties (objective function).

To the authors’ knowledge, the present work is the first public-domain report of the comprehensive modeling and simulations including: self-piercing process; virtual mechanical testing of the SPR joints; and derivation of the constitutive relations for the SPR connector elements.

A concrete material model is presented. The model is based on non‐associated plasticity for the pre‐failure and ductile post‐failure regimes and fracture (smeared crack approach) for the brittle post‐failure regime. The implementation of the constitutive model in the 2‐D elements of a general purpose non‐linear incremental finite element code is discussed. Some important numerical features of the implementation are the implicit integration of the stress/strain relation and the use of an efficient symmetric stiffness formulation for the equilibrium iterations.

Discusses an alternative formulation for the incremental determination of stresses in strain measures that can be used to replace the stress rates currently employed. The formulation is based on Doyle‐Hill generalized definition of strain, the corresponding conjugate stresses and an isotropic hyperelastic constitutive equation. When used to analyze the simple shear deformation, the proposed formulation avoids the pathologies usually observed (oscillations, pressure build up, path dependence). The origin and importance of these pathologies is then discussed in relation to different materials behavior. It is shown that the incremental procedure used together with the logarithmic definition of strain is the most convenient, but that other approximations may be used in well defined particular situations. The numerical algorithms proposed are detailed in an Appendix.

In this paper, we focus on the quality of a 2D elastic finite element analysis.

Our objective is to control the discretization parameters in order to achieve a prescribed local quality level over a dimensioning zone. The method is based on the concept of constitutive relation error.

The method is illustrated through 2D test examples and shows clearly that in terms of cost, this technique provides an additional benefit compared to previous methods.

The saving would be even more significant if this mesh adaptation technique were applied in three dimensions. Indeed, in 3D problems, the computing cost is vital and, in general, it is this cost that sets the limits.

This tool is directly usable in the design stage.

The new tool developed guarantees a local quality level prescribed by the user.

The numerical simulation of metal forming processes follows a highly non‐linear analysis where general aspects such as elastoplasticity, finite deformation and contact mechanics are combined. Approximated solutions obtained by finite element techniques require strong computational effort, that contradicts the need of interactive industrial applications. The first part of the work deals with the description of the main elements of the formulation, with attention to mathematical modelling and the approximating algorithms in the incremental iterative frame of non‐linear analysis, ending with the results obtained in hot rolling simulation. The second part is dedicated to computational efficiency analysis and the presentation of the related methods and results obtained in this work.