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Fused deposition modeling (FDM) is an extensively used additive manufacturing method with the capacity to build complex functional components. Due to the machinery and environmental factors during manufacturing, the FDM parts inevitably demonstrated uncertainty in properties and performance. This study aims to identify the stochastic constitutive behaviors of FDM-fabricated polylactic acid (PLA) tensile specimens induced by the manufacturing process.

By conducting the tensile test, the effects of the printing machine selection and three major manufacturing parameters (i.e., printing speed S, nozzle temperature T and layer thickness t) on the stochastic constitutive behaviors were investigated. The influence of the loading rate was also explained. In addition, the data-driven models were established to quantify and optimize the uncertain mechanical behaviors of FDM-based tensile specimens under various printing parameters.

As indicated by the results, the uncertain behaviors of the stiffness and strength of the PLA tensile specimens were dominated by the printing speed and nozzle temperature, respectively. The manufacturing-induced stochastic constitutive behaviors could be accurately captured by the developed data-driven model with the R² over 0.98 on the testing dataset. The optimal parameters obtained from the data-driven framework were T = 231.3595 °C, S = 40.3179 mm/min and t = 0.2343 mm, which were in good agreement with the experiments.

The developed data-driven models can also be integrated into the design and characterization of parts fabricated by extrusion and other additive manufacturing technologies.

Stochastic behaviors of additively manufactured products were revealed by considering extensive manufacturing factors. The data-driven models were proposed to facilitate the description and optimization of the FDM products and control their quality.

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.

Several constitutive models are available in the literature to describe the mechanical behaviour of cement stabilized soils. However, difficulties in implementing such models within commercial finite element programs have hindered their application to solve related boundary value problems. Therefore, the aim of this study is to implement a constitutive model, which has the capability to simulate cement stabilized soil behaviour, into the finite element program ABAQUS through the user material subroutine UMAT.

After a detailed review of existing constitutive models for cement stabilized soils, a model based on the elasto‐plastic theory and the extended critical state concept with an associated flow rule is selected for the finite element implementation. A semi‐implicit integration method (cutting plane algorithm) with a continuum elasto‐plastic modulus and path dependent stress prediction strategy has been used in the implementation. The performance of the new finite element formulation of the constitutive model is verified by simulating triaxial test data using the finite element program with the new implementation and predictions from constitutive equations as well as experimental data.

The paper provides the implementation procedure of the constitutive model into ABAQUS but this method is useful for the implementation of any other constitutive model into ABAQUS or any other finite element program. Simulated results for the volumetric deformation of cement stabilized soils show that the cement stabilized soils do not obey the associated flow rule at high confining pressures. The parametric study shows that the influence of cementation increases the brittle nature and the bearing capacity of treated clay. In addition the results show that proposed finite element implementation has the ability to illustrate key features of the cement stabilized clay.

This paper presents an implementation of an elasto‐plastic constitutive model, based on the extended critical state concept, for cement stabilized soils into a finite element programme, which has been identified as an important and challenging topic in computational geomechanics. This implementation is useful in solving boundary value problems in geomechanics involving cement stabilized soils, incorporating key characteristics of these soils.

In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.

In this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.

The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.

The study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

The purpose of this paper is to propose a set of constitutive functions for dried bodies for accurate prediction of the entire deformation process of ceramic products during firing and to present relevant methods for determining their coefficients from a series of respective thermo-mechanical analysis (TMA) tests.

The function forms of the sintering-induced strain rate, viscoplastic multiplier and elastic modulus are formulated in order with reference to empirical data of relative densities. Separate TMA tests are conducted to identify their coefficients, while a stairway thermal cycle test is carried out to identify the parameters in the densification rate. Then, various finite element analyses (FEA) are performed for accuracy confirmation.

The performances of the present constitutive functions along with the identified material parameters were validated in comparison with the relevant test results. It has then been confirmed that these functions enable us to some extent to accurately estimate the non-mechanical and mechanical deformations of dried bodies during firing. Also, by performing FEA of an actual sanitary ware product, the applicability and capability of the proposed set of constitutive functions could be demonstrated.

The present methodology with the proposed constitutive functions is a simple, but reliable and practical approach for simulating the deformation process of arbitrary ceramic products subjected to firing and applicable for practical applications in various engineering fields.

The constitutive functions of the viscoplastic multiplier and elastic modulus, which enable us to properly characterize the mechanical behavior of dried bodies subjected to firing, are originally formulated in analogy with that of the sintering-induced strain.

The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element calculations. These problems, however, are not documented in previous literature. In this paper an amendment to the Koiter formulation of the constitutive matrices for stress points located on discontinuities is proposed.

First, a review of existing methods of handling yield surface discontinuities is given. Examples of the numerical problems of the methods are presented. Next, an augmentation of the existing methods is proposed and its robustness is demonstrated through footing bearing capacity calculations that are usually considered “hard”.

Previous studies documented in the literature all present “easy” calculation examples, e.g. low friction angles and few elements. The amendments presented in this paper result in robust elasto-plastic computations, making the solution of “hard” problems possible without introducing approximations in the yield surfaces. Examples of “hard” problems are highly frictional soils and/or three-dimensional geometries.

The proposed method makes finite element calculations using yield criteria with corners and apices, e.g. Mohr-Coulomb and Hoek-Brown, much more robust and stable.

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.

This study examines the effect of temperature-dependent material models for normal-strength (NSC) and high-strength concrete (HSC) on the thermal analysis of reinforced concrete (RC) walls.

The study performs an one-at-a-time (OAT) sensitivity analysis to assess the impact of variables defining the constitutive and parametric fire models on the wall's thermal response. Moreover, it extends the sensitivity analysis to a variance-based analysis to assess the effect of constitutive model type, fire model type and constitutive model uncertainty on the RC wall's thermal response variance. The study determines the wall’s thermal behaviour reliability considering the different constitutive models and their uncertainty.

It is found that the impact of the variability in concrete’s conductivity is determined by its temperature-dependent model, which differs for NSC and HSC. Therefore, more testing and improving material modelling are needed. Furthermore, the heating rate of the fire scenario is the dominant factor in deciding fire-resistance performance because it is a causal factor for spalling in HSC walls. And finally the reliability of wall's performance decreased sharply for HSC walls due to the expected spalling of the concrete and loss of cross-section integrity.

Limited studies in the current open literature quantified the impact of constitutive models on the behaviour of RC walls. No studies have examined the effect of material models' uncertainty on wall’s response reliability under fire. Furthermore, the study's results contribute to the ongoing attempts to shape performance-based structural fire engineering.

Relationships are socially constructed by companies in interaction. This study explains the dynamic character of business-to-business relationships with the aid of rules theory, a theory borrowed from the communications field. Two forms of rules are identified: constitutive rules guide the interpretation of the other's acts, and regulative rules guide the appropriate response to the interpreted act. Rules theory asserts that companies act as if applying these rules. Relationships provide not only the context in which the parties’ acts are performed but are also the result of such acts. Thus, relationships are potentially reshaped each time one party performs an act and the other party gives meaning to that act and reacts.

With the discussion on the linear relationship of determined material parameters, this study aims to propose a new method to analyze the deformation mechanism.

A modified constitutive model based on the hyperbolic sine Arrhenius equation has been established, which is applied to describe the flow behavior of Ti-6Al-4V alloy during the superplastic forming (SPF).

The modified constitutive model in this work has a good ability to describe the flow behavior for Ti-6Al-4V in SPF. Besides, a deformation map of titanium material is obtained based on the parameters. As the supplement, finite element models of high-temperature tensile tests are carried out as the application of the constitutive model.

The relationship between constitutive model parameters and forming mechanism is established, which is a new angle in rheological behavior research and constitutive model analysis.