Matrix Description of Non-Linear Properties of Materials or Structural Components—Idea and Application Examples

Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

A psychology from among, ahead

Held (2020a) does critical psychologists a service in exposing a problematic relativism underlying Teo’s proposal for a less epistemically violent psychology, one sustained by a set of false dualisms and a priori commitments. This commentary can be understood as a logical progression within the author’s larger intellectual journey, reflecting longstanding concerns about threats to objective truth. One take-home lesson is the perils of taking language too literally as a constitutive matrix in deploying counter concepts, as opposed to the empirical realities of how those concepts function (and get wielded) in the world. Importantly, this includes debates over who counts as “oppressed” and who gets to claim this status. As one alternative to Teo’s unsustainable dichotomies, I offer a metaphorical “psychology from ahead” whose concepts and interpretive findings anticipate unfamiliar experiences and challenges evolving in real time, and where emergency and crisis serve as the lens for combating injustices, epistemic and otherwise.

New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

In this paper, a new constitutive matrix Mτ for thermal conduction, for tetrahedral meshes, in a steady state thermal regime is developed through a new algebraic methodology, using the Cell Method as a computational method, which is included in the finite formulation. The constitutive matrix defines the behavior of solids when they are under a thermal potential. The results are compared with those obtained for the same problem by means of the constitutive matrix Mλ developed previously, taking in both cases with a 2D axisymmetric model as reference, calculated with the finite element method. The errors obtained with the new matrix Mτ are of the order of 0.0025%, much lower than those obtained with the matrix Mλ.

Thermal Analysis of a Magnetic Brake Using Infrared Techniques and 3D Cell Method with a New Convective Constitutive Matrix

In this work we analyse the temperature distribution in a conductor disk in transitory regime. The disk is in motion in a stationary magnetic field generated by a permanent magnet and so, the electric currents induced inside it generate heat. The system acts as a magnetic brake and is analysed using infrared sensor techniques. In addition, for the simulation and analysis of the magnetic brake, a new thermal convective matrix for the 3D Cell Method (CM) is proposed. The results of the simulation have been verified by comparing the numerical results with those obtained by the Finite Element Method (FEM) and with experimental data obtained by infrared technology. The difference between the experimental results obtained by infrared sensors and those obtained in the simulations is less than 0.0459%.

Quantification of degraded constitutive coefficients of composites in the presence of distributed defects

Effect of distributed defects on effective material properties of composites is required for the progressive failure models. Although the degradation of the effective material properties due to the presence of the lower scale damages is well investigated, how each material coefficient should be compromised in a progressive failure model is still a dilemma. Percentage of defects, the shape of the defects and their stochastic distribution may affect the individual material coefficients in a unique way and may not be uniform across the constitutive matrix. Hence, to find how the individual material coefficients in a constitutive matrix changes due to the presence of the voids and fiber breakage, all material coefficients in a constitutive matrix were studied herein. Representative volume element of a unidirectional fiber-matrix composite was studied with appropriate boundary conditions and respective material coefficients were calculated. It was found that the local gradients of the degradation curve obtained for each material coefficient are not linear with the increasing percentage of degradation and not uniform for all material coefficients. The shape and different locations of the defects with constant defect percentage were found to be inert towards affecting the material coefficients.

Algebraic Formulation for Moderately Thick Elastic Frames, Beams, Trusses, and Grillages within Timoshenko Theory

The paper is dedicated to the algebraic formulation of elastic frame equations. The obtained set of equations describe deformations of moderately thick frames made of both compressible and incompressible bars, grillages of rigid or pin-joined connections, and trusses. Plane as well as space structures are presented. The paper is an extension of the article of T. Lewiński written in 2001 related to thin bars. Algebraic equations with diagonal constitutive matrix are original and suitable for various engineering applications and for educational purposes.

Transient thermal regime trough the constitutive matrix applied to asynchronous electrical machine using the cell method

In this paper, a new constitutive matrix for thermal conduction in transient thermal regime is developed and tested. We use cell method as a numerical method that is included in finite formulation methodology. The constitutive matrix defines through the cell method the behavior of solids when they are under a thermal potential. We have demonstrated that this matrix is equivalent to the electrical conduction constitutive matrix in steady state. We have applied this constitutive matrix to thermal analysis of asynchronous electric machines in transient regime. This constitutive matrix has been validated with comparisons based on finite element method. In finite formulation, the physical laws governing the electromagnetic fields and the physical thermal phenomena are expressed in integral formulation. The final algebraic equation system is tailored directly without discretizing of the differential equations. This is an important advantage because we omit a complex differential formulation and the discretization of the respective equations.

New Constitutive Matrix in the 3D Cell Method to Obtain a Lorentz Electric Field in a Magnetic Brake

In this work, we have obtained a new constitutive matrix to calculate the induced Lorentz electric current of in a conductive disk in movement within a magnetic field using the cell method in 3D. This disk and a permanent magnet act as a magnetic brake. The results obtained are compared with those obtained with the finite element method (FEM) using the computer applications Getdp and femm. The error observed is less than 0.1173%. Likewise, a second verification has been made in the laboratory using Hall sensors to measure the magnetic field in the proximity of the magnetic brake.

A 149 Line Homogenization Code for Three-Dimensional Cellular Materials Written in matlab

Cellular architectures are promising in a variety of engineering applications due to attractive material properties. Additive manufacturing has reduced the difficulty in the fabrication of three-dimensional (3D) cellular materials. In this paper, the numerical homogenization method for 3D cellular materials is provided based on a short, self-contained matlab code. It is an educational description that shows how the homogenized constitutive matrix is computed by a voxel model with one material to be void and another material to be solid. A voxel generation algorithm is proposed to generate the voxel model easily by the wireframe scripts of unit cell topologies. The format of the wireframe script is defined so that the topology can be customized. The homogenization code is then extended to multimaterial cellular structures and thermal conductivity problems. The result of the numerical homogenization shows that different topologies exhibit anisotropic elastic properties to a different extent. It is also found that the anisotropy of cellular materials can be controlled by adjusting the combination of materials.