Wolfgang Mueller

• Dr. rer. nat.
• Chair at Technische Universität Berlin

This study investigates the morphology of a free-falling liquid jet by using a computational approach with an experimental validation. Numerical simulations are developed by means of the Finite Element Method (FEM) for solving the viscous fluid flow and the level set method in order to track the interface between the fluid and air. Experiments are...

The aim of this study is to determine experimentally the higher material parameter of a metamaterial with a triangular substructure and to verify a higher‐gradient elasticity model for beams with internal substructures or microstructures. The investigations of the higher‐gradient elasticity models of Bernoulli‐Euler and Timoshenko beams with a peri...

The additive manufacturing and experimental analysis of a beam with a 2D triangular substructure continues a study based on prior investigations into higher-order elasticity models for Bernoulli-Euler and Timoshenko beams with periodic triangular substructures (Khakalo et al. in Int J Eng Sci 127:33–52 (2018), [1]). The primary objective of this wo...

In this article we present some information about the life and the scientific work of the late Prof. K. P. Herrmann. It contains various details regarding his scientific education, the academic institutions he was affiliated with, the principal direction of his research, his Ph.D. students, and a (hopefully) complete list of his scientific publicat...

In this work we explain the concept of images of physical quantities when switching from the frame of reference of one observer to another. Specifically it will be used to transform the balances of linear momentum and of spin to reveal the various inertial terms. Moreover, the corresponding literature is briefly reviewed and it is explained how the...

This paper is devoted to a review of attempts to interpret Maxwell’s equation from a mechanics point-of-view. Three variants will be presented, discussed, and compared. (a) Early attempts (MacCullagh, Maxwell, Sommerfeld) based on (extended) linear elasticity; (b) The viewpoint of Zhilin, which interprets the æther and electromagnetic waves in term...

In this research, we delve into the intricacies of viscous fluid flow with electric field coupling by employing the Finite Element Method (FEM) in tandem with the level set method. We generate a weak form for satisfying governing equations for electric field and fluid velocity while two phases are tracked by the level set function. The primary focu...

Ever since their appearance in Maxwell’s famous Treatise the way of how to write His equations went through many changes. These changes were not just of cosmetic nature. Rather with every alteration new aspects of their meaning appeared. In this paper we shall pursue and comment on their development.

We present a review of the recent workshop “Micropolar Continua and beyond” which held in March 28–31, 2023, at Technische University of Berlin, Germany.

In this paper, we study the blood flow through blood vessels of various radii (including the case of variable cross section as well as modeling the blood flow through venae and arteries). Two approaches are discussed in order to mimic the dependence of blood viscosity on red blood cells aggregation, which changes with the shear rate and position in...

This paper analyzes the applicability of Eringen’s Generalized Continuum Theories as a model for human blood in the microcirculation. The applied theory considers a fluid with a fully deformable substructure, namely a micromorphic fluid. This analysis is motivated by the fact that blood itself can be considered a suspension of deformable particles,...

Especially at high frequencies, as they occur in 5G or relevant applications, electromagnetism in electronic components plays a significant role in system behavior. Moreover, dissipative effects are triggered by mechanical deformation. Indeed, dissipation is an energy loss and thus the industry tries to minimize this effect by optimizing the design...

In this paper the effect of external magnetic fields on a ferrofluid is studied numerically. The details of the proposed model are presented and compared to the literature. The governing equations are normalized and the order of magnitude of the dimensionless numbers is analyzed for realistic material parameters. Numerical difficulties arising from...

In this work, parallel plate capacitors are numerically simulated by solving weak forms within the framework of the finite element method. Two different domains are studied. We study the infinite parallel plate capacitor problem and verify the implementation by deriving analytical solutions with a single layer and multiple layers between two plates...

This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material....

When an elastoplastic material undergoes large plastic deformations, the elastic law and particularly the stiffness tetrad will evolve. This evolution is strongly dependent on the particular material. In the present paper, we consider a fiber-reinforced composite with fibers in different distinct directions. These directions introduce the anisotrop...

In this paper optimal topologies of isotropic linear elastic strain gradient materials are investigated by means of isogeometric topology optimization. The employment of strain gradient theory allows not only to capture the microstructural effects of materials but also to regularize stress/strain concentration phenomena and to address the so-called...

In this paper a simple particle population homogenization approach is used in order to estimate the magnetic relaxation time of a ferrofluid by means of a microscopic analysis. At a macroscopic level the ferrofluid is modeled as a micropolar fluid with rotational degrees of freedom. The governing equations for these degrees of freedom are the spin...

In this paper, we propose an approach to define thermal conductivity for a purely ballistic transient heat conduction and study its size dependence for two-dimensional structures in circular geometry in order to use this dependence as a purely ballistic regime signature. Then, a review of various experimental techniques by which the thermal conduct...

As part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF),...

A system of rigid permanent magnets of cylindrical shape is studied. In particular their motion due to gravity and their mutual magnetic interaction is investigated. Additionally, if the magnets move inside a copper tube an electric current is induced which in turn leads to another interaction that influences the motion of the magnets. The magnets...

In the present paper, we propose a mechanistic mathematical model describing the process of drug release from a drug delivery system. This model takes various aspects of drug release into account, namely gradual penetration of the surrounding solution into the system, dissolution of solid drug particles embedded within, diffusion of the dissolved d...

A model is proposed for the description of a highly inhomogeneous distribution of hydrogen within a saturated metal specimen (the so-called skin effect due to hydrogen saturation). The model is based on the micropolar continuum approach and results in a nonuniform stress–strain state of a cylindrical metal specimen due to distributed couples or mic...

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determ...

In this work the energy transfer in a one-dimensional harmonic crystal is investigated. In particular, a comparison between the discrete approach presented by Klein, Prigogine, and Hemmer with the continuum approach presented by Krivtsov is made. In the pioneering work of Klein and Prigogine the transfer of thermal energy is considered. In particul...

As there are different computational methods for simulating problems in generalized mechanics, we present simple applications and their closed-form solutions for verifying a numerical implementation. For such a benchmark, we utilize these analytical solutions and examine three-dimensional numerical simulations by the finite element method (FEM) usi...

An analytical model of electromigration and stress affected kinetics of a chemical reaction is investigated based on the notion of the chemical affinity tensor within the small strain approximation. Effects of stresses are accounted for through their influence on the chemical affinity tensor on which the reaction front velocity depends. Electromigr...

Localized stress-affected chemical reactions between solid and diffusive reactants are studied based on the chemical affinity tensor approach. A kinetic equation for the chemical reaction front, such that the interface velocity depends on the normal component of the chemical affinity tensor, is formulated and used for solving coupled boundary value...

In this paper the process of polarization of transversally polarizable matter is investigated based on concepts from micropolar theory. The process is modeled as a structural change of a dielectric material. On the microscale it is assumed that it consists of rigid dipoles subjected to an external electric field, which leads to a certain degree of...

In this paper, the solution to a coupled flow problem for a micropolar medium undergoing structural changes is presented. The structural changes occur because of a grinding of the medium in a funnel-shaped crusher. The standard macroscopic equations for mass and linear momentum are solved in combination with a balance equation for the microinertia...

Strain gradient theory is an accurate model for capturing size effects and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of such theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determin...

The principal relations of the refined Maxwell electromagnetic theory of piezoceramic bodies demonstrating a piezoeffect are presented. The chapter also includes the principal relations of linear electroelasticity theory composed of equations describing a mechanical component of the piezoeffect (the relations being valid for any linear medium, appe...

Various approaches to the solution of linear problems of elasticity and electroelasticity of anisotropic inhomogeneous finite-length cylinders based on discrete–continuous methods and three-dimensional formulations are presented. The advantage of these method consists in the reduction of the partial differential equations of the considered problems...

The axisymmetric and nonaxisymmetric problems of natural and forced vibrations of a hollow sphere made of a functionally gradient piezoelectric material theory are considered based on 3D electroelasticity. The properties of the material vary along the radial coordinate. The external surface of the sphere is free of tractions and is either insulated...

The propagation of axisymmetric and nonaxisymmetric electroelastic waves in hollow inhomogeneous piezoceramic cylinders based on 3D electroelasticity are considered. The elastic and electric properties of the material vary in the radial direction. Two variants of materials are considered: piecewise constant properties of the material (layered struc...

Based on the progress and advances of additive manufacturing technologies, design and production of complex structures became cheaper and therefore rather possible in the recent past. A promising example of such complex structure is a so-called pantographic structure, which can be described as a metamaterial consisting of repeated substructure. In...

In this paper, size effects exhibited by mechanical metamaterials have been studied. When the sizescale of the metamaterials is reduced, stiffening or softening responses are observed in experiments. In order to capture both the stiffening and softening size effects fully, a second-order asymptotic homogenization method based on strain gradient the...

This study is concerned with the modeling of plate buckling induced by a chemical reaction and is inspired by the observation that buckling may be a mechanism of stress relaxation in Si-based anodes in Li-ion batteries. A chemical reaction is localized at a sharp interface and accompanied by transformation strains, which produce internal stresses....

This book presents various dynamic processes in non-uniform piezoceramic cylindrical and spherical bodies based on numerical methods. It discusses different variants of nonhomogeneous structural polarized piezoceramic materials in the shape of cylinders and spheres, and highlights the validation of the reliability of the results obtained by numeric...

This paper is concerned with the analytical modeling of an intermetallic compound formation in a eutectic tin solder joint on copper interconnects subjected to an electrical current. We pro-pose a model that couples mechanical stresses, chemical reaction, diffusion, temperature, and electromigration. The kinetics of the chemical reaction fronts of...

Two-dimensional localized strain wave solutions of the nonlinear equation for shear waves in two-dimensional lattices are studied. The corresponding equation does not possess an invariance in one of the spatial direction while its exact plane traveling wave solution does not reflect that. However, the numerical simulation of a two-dimensional local...

In this paper a rational derivation of Maxwell’s equations is presented in a purely spatial description. On a macroscopic scale this can be done by means of localization of global balance laws. The mathematical tools for the localization in a spatial description are presented. Subsequently the balance laws of electric charge and magnetic flux are d...

Strain gradient continuum damage modelling has been applied to quasistatic brittle fracture within an approach based on a maximum energy-release rate principle. The model was implemented numerically, making use of the FEniCS open-source library. The considered model introduces non-locality by taking into account the strain gradient in the deformati...

In this paper, the growth of intermetallic compound (IMC) layers is considered. After soldering, an IMC layer appears and establishes a mechanical contact between eutectic tin-silver solder bumps and Cu interconnects in microelectronic components. Intermetallics are relatively brittle in comparison with copper and tin. In addition, IMC formation is...

By using modern additive manufacturing techniques, a structure at the millimeter length scale (macroscale) can be produced showing a lattice substructure of micrometer dimensions (microscale). Such a system is called a metamaterial at the macroscale, because its mechanical characteristics deviate from the characteristics at the microscale. Conseque...

For a given elastic stiffness tetrad an algorithm is provided to determine the distance of this particular tetrad to all tetrads of a prescribed symmetry class. If the particular tetrad already belongs to this class then the distance is zero and the presentation of this tetrad with respect to the symmetry axes can be obtained. If the distance turns...

In this paper, a strain gradient continuum model for a metamaterial with a periodic lattice substructure is considered. A second gradient constitutive law is postulated at the macroscopic level. The effective classical and strain gradient stiffness tensors are obtained based on asymptotic homogenization techniques using the equivalence of energy at...

It is shown that angular stiffness in the hexagonal lattice model plays a significant role in the geometrical nonlinear terms in the equations of the continuum limit. A geometrically nonlinear discrete model is formulated for the hexagonal lattice by considering the interaction of two sublattices. An asymptotic procedure is developed in order to ob...

Different numerical implementations have been proposed in the literature for computation in generalized mechanics. A computational benchmark problem is beneficial to highlight the differences or even validate an approach. We briefly present the strain gradient elasticity theory and its weak form. A relatively simple analytic solution in strain grad...

This paper presents a parameter study of the flow of nematic liquid crystals which possess both viscous and elastic properties. The well-known Ericksen–Leslie theory is used. The underlying general equations are stated and subsequently simplified for non-isothermal and steady state conditions. The flow situation of a two-dimensional lid-driven cavi...

In the recent past new experimental techniques have been developed with the objective of linking generalized continuum theories with technology. So-called pantographic structures, which can be characterized as a meta-material, will be presented and investigated experimentally: Samples of different materials and dimensions are subjected to large def...

In this document, it will be attempted to summarize the currently available experimental evidence for the need of higher gradient continuum theories. They allow to capture size effects, e.g., within the elastic behavior of materials with an internal substructure, which gives rise to additional length scale parameters. These are not available in ela...

Fifty years have passed since Truesdell's seminal paper on the origin and status of the balance for the moment of momentum was published in ZAMM. It is time to take stock: Important new developments in the theory of generalized continua with internal degrees of freedom and some fascinating fundamental applications need to be pointed out. Is there n...

The representation of rotations and of the corresponding angular velocity commonly used in rigid body dynamics are revisited using an abstract tensorial approach. In order to do so, Rodrigues’ formula is recalled and the related angular velocity vector is derived. This paper focuses on the analysis of successive rotations and especially a proof of...

This book commemorates the 75th birthday of Prof. George Jaiani – Georgia’s leading expert on shell theory. He is also well known outside Georgia for his individual approach to shell theory research and as an organizer of meetings, conferences and schools in the field. The collection of papers presented includes articles by scientists from various...

In order to model the flow of nematic crystals, the theoretical framework according to Ericksen and Leslie is applied. The essentials of the theory are compiled and then specialized to Couette flow. The profiles for linear velocity and orientation angle will be computed and, in particular, we shall also study the rise in temperature due to viscous...

The American mathematician Robert Jackson Adcock (1826-1895) is an obscure figure, hitherto associated with the history of regression analysis and least-squares, whose identity and life is described in Part II of this work. In 1872, he self-published a pamphlet, Gravitation to the sphere and the two ellipsoids of revolution: ratio of the axes of a...

Between 1870 and 1896, the American mathematician Robert Jackson Adcock (1826-1895) contributed a number of short articles to early mathematical journals such as The Analyst. His biography is given here for the first time: An obscure figure hitherto associated with the history of regression analysis and least-squares he has, on occasion, been confu...

A completely algebraic algorithm is given to determin the distance of an elastic stiffness tensor to any of the symmetry classes.

From Maxwell’s equations balance laws for the electromagnetic linearmomentum, angular momentum, and energy can be found after recasting and usingseveral identities of vector calculus. Therefore, the obtained equations are not “newresults” but rather identities having the form of a balance law. However, there is some degree of freedom, (a) during co...

Especially in metal forming, large plastic deformation occurs in thin plates. The problem of compressing dies is analyzed to evaluate the spreading of a thin layer in between. The velocity of dies is a given function in time so that the kinematics of the process is known. This problem can be considered as a generalization of the classical Prandtl p...

We consider a silicon nanopowder based anode for a lithium ion battery cell. We present the design of the battery cell ready for in situ Raman and X-ray experiments and a technical procedure for the cell manufacturing. From the continuum mechanics point of view, this type of anode can be represented by a spherical nanoparticle surrounded by viscoel...

This paper presents a new aspect in generalized continuum theory, namely micropolar media showing structural change. Initially, the necessary theoretical framework for a micropolar continuum is presented. To this end, the standard macroscopic equations for mass and linear and angular momentum are complemented by a recently proposed kinetic equation...

In this paper foundations are laid for a future solution of a fully coupled flow problem for the micropolar medium undergoing structural change in a funnel-shaped crusher. Initially the fundamental equations of micropolar media are revisited and the problem of structural changes of micropolar media moving in a crusher is explained. Then a review of...

Marine organisms possess a vast range of properties, which portray a lot of their appropriate biomedical application potentials either directly, modified or as templates for biomimicking. It is and will remain a humble and smart move to learn from nature and try to copy faithfully the vital components so as to develop implantable biomaterials to mi...

The current need for new medicines with reduced toxicity, enhanced bioavailability as well as improved drug efficacy and patient compliance is more pressing than ever before. Clinical active agents can now be reformulated with the help of nanotechnology into “nanopharmaceuticals” with superior pharmacokinetics for site-specific delivery. With the a...

In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be so...

Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the macroscale as the mechanical characteristics deviate from the characteristics at the microscale. As a remedy, metamater...

This paper solves the problem of a sliding ladder for the cases with and without friction at the wall and at the floor. Solutions for arbitrary initial conditions are obtained by strict application of the fundamental principles of mechanics. The validity of these solutions is discussed in context with the loss of contact of the ladder with the wall...

Following up on a previous paper in which planar and spherical geometries were discussed we now present a similar analysis of the influence of stress on the diffusion induced velocity of chemical reaction fronts in cylindrical objects. The essential equations of mechanochemistry and stationary diffusion are briefly revisited. Various models for the...

Knowledge about the release behavior of drugs into the human body is essential for correct long-term medication. This paper complements a previous work by providing details of the numerical methods that were used before. Therefore, we shortly explain the experimental setup and state the governing equations. For the numerical solution, two different...

Post-operative infection often occurs following orthopedic and dental implant placement requiring systemic administered antibiotics. However, this does not provide long-term protection. Over the last few decades, alternative methods involving slow drug delivery systems based on biodegradable poly-lactic acid and antibiotic loaded hydroxyapatite mic...

This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial t...

The success of medical therapy depends on the correct amount and the appropriate delivery of the required drugs for treatment. By using biodegradable polymers a drug delivery over a time span of weeks or even months is made possible. This opens up a variety of strategies for better medication. The drug is embedded in a biodegradable polymer (the “c...

At present information about viscous properties of the eye's sclera is scarce, the main reason being that direct measurements cause technical problems. Nevertheless, coefficients of the sclera viscosity are of paramount interest for biomechanics and ophthalmologists. This paper investigates a method for determining the shear viscosity of the sclera...

Due to the latest advancements in 3D printing technology and rapid prototyping techniques, the production of materials with complex geometries has become more affordable than ever. Pantographic structures, because of their attractive features, both in dynamics and statics and both in elastic and inelastic deformation regimes, deserve to be thorough...

While one of the major clinical and scientific challenges in the management of implant-related infections and post-operative complications after surgery is the application of new techniques, a new approach is pertinent in the design of medical implants to reduce bacterial infections. We have designed and tested antibiotic-containing biocomposite th...

This paper is concerned with a materials model within the framework of an extended theory of micropolar media. The extension affects the balance for the tensor field of micro-inertia which, in contrast to the common theory, will now contain a production term. As a consequence the tensor of the moment of inertia becomes an independent field varying...

This book discusses recent findings and advanced theories presented at two workshops at TU Berlin in 2017 and 2018. It underlines several advantages of generalized continuum models compared to the classical Cauchy continuum, which although widely used in engineering practice, has a number of limitations, such as: • The structural size is very small...