This contribution presents a homogenization approach for the computationally efficient modeling of two-dimensional solid bodies that interact through structured surfaces. Instead of resolving the detailed microscale geometry, the method introduces a finite-thickness surrogate layer that captures the essential mechanical response of the structured contact zone. The proposed formulation is based on the description of microscale quantities, such as (normal) gap and relative sliding velocity, which are transferred to the macroscale using internal volumetric variables. The elastic behavior of the surrogate layer is identified through a mean-field homogenization approach that accounts for the non-linear dependency of stress response on the relative slip. As a result, the anisotropic and history-dependent behavior of the interface can be captured within the model. The proposed method is validated using two benchmark problems: a vertical stack of two structured blocks and a knurled interference fit. In both cases, the finite-thickness layer accurately reproduces the mechanical response of the fully resolved model, i.e., stick–slip transitions, hysteresis, and partial interface separation. The good agreement with the reference solutions, combined with a significant reduction in computational cost, demonstrates the potential of the method for efficient multi-scale interface modeling.

We propose a novel mixed finite-element formulation for geometrically exact (Simo–Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous approximation of rotations, which is key to a simple and efficient discretization framework. The concept of discrete curvature provides a mathematically consistent treatment of rotation discontinuities. For linear constitutive laws, the mixed form is derived via a Legendre transform of the curvature-related strain energy. Objectivity is retained at the discrete level by interpolating relative rotations through a multiplicative split of the rotation field; path-independence is inherent to the total Lagrangian setting and verified numerically. Several benchmarks demonstrate optimal rates of convergence and accuracy, irrespective of the beam's slenderness and order of approximation. Notably, the lowest-order element entirely avoids rotation interpolation by employing element-constant rotations only.

Paper-based printed impedance sensors offer a mechanically compliant and sustainable solution for embedded sensing in wood-based structures. In this work, a multifunctional use of such sensors embedded in laminated timber is investigated, covering both adhesive curing characterization and subsequent strain monitoring. In a first step, a simulation-based approach is presented to estimate the electrical properties of a wood adhesive during curing. A reduced two-dimensional finite element model of the glue curing experiment is combined with a least-squares fitting procedure to identify the time-dependent evolution of electrical conductivity and permittivity from impedance measurements. The estimated parameters exhibit smooth and physically consistent trends over curing time, demonstrating the suitability of the proposed modeling and identification framework.Building on this foundation, the paper-based sensor is subsequently repurposed as a deformation-sensing element after completion of the curing process. An experimental study is conducted on laminated timber specimens with embedded sensors subjected to displacement-controlled cyclic bending. The sensor signals show clear and reproducible correlations with independently measured force, displacement, and strain data.The results demonstrate that paper-based impedance sensors can be successfully integrated into laminated timber structures and used throughout different stages of their lifecycle, from adhesive curing characterization to strain monitoring during service. This multifunctional sensing concept provides a promising basis for low-cost and sustainable structural health monitoring of timber components.

In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or completely filled. Finite element simulations of such setups are highly challenging. A brute force discretization of structural as well as volumetric parts using well-shaped three-dimensional elements may be accurate, but leads to problems of enormous computational complexity even for simple models. One desired alternative is the use of shell elements for thin-walled parts, as such a discretization greatly alleviates size restrictions on the underlying finite element mesh. However, the coupling of different formulations within a single framework is often not straightforward and may lead to locking if not done carefully. Neunteufel and Schöberl proposed a mixed shell element where, apart from displacements of the center surface, bending moments are used as independent unknowns. These elements were not only shown to be locking free and highly accurate in large-deformation regime, but also do not require differentiability of the shell surface. They can directly be coupled to classical volume elements of arbitrary order by sharing displacement degrees of freedom at the center surface, thus achieving the desired coupled discretization. As the elements can be used on unstructured meshes, adaptive mesh refinement based on local stress and bending moments can be used. We present computational results that confirm exceptional accuracy for problems where thin-walled structures are embedded as reinforcements within soft matrix material.

Shaft-hub connections are an important feature of many machines, with knurled interference fits (KIFs) being a novel connection method. While conventional shaft-hub connections use either friction or form closure, KIFs represent a combination offering the advantages of both concepts. To investigate the behavior of such a connection, a computational model of a knurled interference fit is developed. Assuming rotational symmetry, modeling a periodic unit cell of the setup is sufficient. This assumption does not only greatly alleviate the demands on computing power, but also allows to analyze the hysteretic behavior of the connection in a phenomenological way. Parameter studies indicate changes in the transmissible loads and stiffness of the connection when varying geometric dimensions such as tooth height and angle, material and contact characteristics or applied loads. Notably, the hysteresis behavior of KIFs differs significantly from conventional connections like interference fits with smooth shaft-hub interfaces, particularly due to coupling between the radial and circumferential directions due to the tooth angle. Moreover, the simulations demonstrate that a certain stick-slip behavior may also occur in frictionless settings as a result of the geometry.

The finite element simulation of thin viscoelastic membranes is a challenging problem. On the one hand, geometric dimensions of the membrane are adverse to classical finite element formulations, which require the thickness of the structure to be resolved. On the other hand, both material and geometric nonlinearities need to be considered in the large-strain regime. In the present paper, a Kirchhoff–Love shell formulation including thickness deformation is deduced for incompressible viscoelastic membranes at finite strain. For this formulation, a mixed shell element with low regularity is proposed to discretize a viscoelastic shell formulation based on a multiplicative split of the deformation gradient. The formulation is tested against full three-dimensional formulations in a variety of examples. Excellent accordance of results in quasi-static as well as dynamic simulations is observed.

The modeling and simulation of thin dielectric viscoelastic structures experiencing large deformations presents significant challenges. In this work, we introduce a shell formulation that captures the essential kinematic and constitutive features of these structures under transient electric loading. The formulation includes elastic and viscous membrane strains, curvature, as well as thickness deformation and the variation of the electric field through the thickness. A thermodynamically consistent model is developed and discretized using low-regularity shell elements within a variational framework. The proposed method is validated through several computational examples. The results demonstrate a high level of accuracy in capturing the transient large-strain behavior of dielectric elastomer shells even for very coarse discretizations.

Silicone-based polymers are recognized for their exceptional damping properties and ability to undergo large deformations. Their mechanical behavior can be characterized through a variety of experimental setups. Small-strain measurements at various frequencies and temperatures, as conducted in a dynamic thermo-mechanical analysis, provide storage and loss moduli. Tensile tests at large strain determine the elastic response, while experiments such as the ball-drop test characterize damping through the rebound resilience. Combining these different perspectives into a comprehensive material model for silicone-based polymers remains a challenging task and often requires numerical approaches to complement physical experiments. In this context, we present a finite element formulation specifically designed to simulate the ball-drop experiment, incorporating experimentally identified viscoelastic parameters into a nonlinear large-strain material model. Prony parameters obtained from small-strain dynamic thermo-mechanical analysis serve as the basis for our study. Large strains are captured via a multiplicative decomposition of the deformation gradient. The matrix exponential is used to consistently incorporate logarithmic viscous strains into the constitutive model. The model is thermodynamically consistent and rooted in the Clausius-Duhem inequality. A distinctive feature of our formulation is the spatial discretization of the internal viscous strains using tensor-valued finite elements, which allows the evolution laws to be expressed in weak form. Through numerical studies, we analyze the sensitivity of the rebound behavior to imperfections and geometric variations. We identify potential sources of discrepancies with respect to previously reported experimental observations, including frictional contact and three-dimensional effects such as eccentric impacts, which break the assumption of axisymmetric deformation.

The present article is concerned with modeling the viscoelastic behavior of Polydimethylsiloxane (PDMS) in large-strain regime. Starting from the basic principles of thermodynamics, an incremental variational formulation is derived. Within this model, the free energy density and dissipation function determine elastic and viscous properties of the solid. The main contribution of this paper is the estimation of the parameters in the proposed phenomenological model from measurements conducted on Sylgard184 samples. This non-linear material model simplifies to a Prony-series representation in frequency domain in case of small deformations. The coefficients of this Prony-series are detected from dynamical temperature mechanical analysis measurements. Time-temperature superposition allows to combine measurements at different temperatures, such that a sufficiently large frequency range is available for subsequent fitting of Prony-parameters. A set of material parameters is thus provided. The incremental variational formulation directly lends itself to finite element discretization, where an efficient and stable choice of elements is proposed for radially symmetric problems. This formulation allows to verify the proposed model against experimental data gained in ball-drop experiments.

So-called electro-active polymers are not only capable of undergoing very large deformations, but they also exhibit different electromechanical coupling effects due to their dielectric or electrostrictive characteristics. In the present paper the sub-class of dielectric elastomers is studied; in particular, we focus on thin dielectric elastomer shells, which undergo large deformations under an applied electric field. We develop a framework for the modeling and subsequent efficient simulation of thin structures made from incompressible dielectric elastomers. A thermodynamically consistent phenomenological continuum model based on the free energy density is adapted imposing the kinematic assumptions of Kirchhoff-Love shells in combination with including the thickness deformation and the electric field as independent unknown fields. To make the formulation accessible to finite element simulations, existing non-linear elastic shell mixed finite elements are extended to the present hyperelastic electromechanically coupled formulation for dielectric elastomer shells. Computational results of the shell theory are compared to three-dimensional results validating the proposed modeling and numerical simulation methodology, and showing high accuracy already for coarse finite element discretizations of the shell.

We discuss nonlinear modeling of ferroelectric plates as electro-elastic material surfaces assuming the plate as a two-dimensional continuum with five mechanical degrees of freedom for each material point.Constitutive coupling by means of electrostriction, ferroelectric hysteresis and piezoelectricity are accounted for.For that sake, the augmented free energy is additively decomposed into an elastic part, a dielectric part and an augmentation energy.The elastic part involves an additive decomposition of the plate strain measures into elastic and electrical parts.Here, the electrical parts account for electrostriction and piezoelectricity, where electrostriction is assumed to depend quadratically on the polarization.For the dielectric part, we introduce the internal energy as a function of the polarization and an internal polarization, which allows us to accurately capture nonlinearities, such as saturation.Then, we compute the free energy applying a Legendre transformation, such that the voltage enters the formulation.The augmentation energy accounts for the contribution from vacuum.Finally, we introduce a so-called dissipation function, by means of which irreversible polarization due to domain switching is accounted for.Numerical results computed with the plate model are compared to results using a three-dimensional formulation.

Ferroic materials are characterized by the presence of electric/magnetic dipoles that can be irreversibly re-oriented under sufficiently strong loading.Upon poling, an initially random distribution of dipoles on the microscopic domain scale results in a non-vanishing state of remanent polarization/magnetization on the macroscopic level.The remanent switching of dipoles constitutes the "smartness" in materials and their usage both as sensors and as actuators.Once being poled, material properties are typically assumed to be constant and uni-directional in engineering problems.To extend the operational range of ferroic transducers and open perspectives for novel applications, we seek for an accurate understanding of the evolution of the polarization/magnetization, which requires both physical and geometric non-linearities to be included in the modeling.To describe irreversible changes of the remanent state, we transfer phenomenological concepts and algorithms of associative elasto-plasticity to the field of electro-magneto-mechanics. To describe the dissipative response in a thermodynamically consistent manner, the principle of maximum dissipation is adopted.As in elasto-plasticity, constitutive equations for dissipative internal forces that drive the evolution of the remanent polarization/magnetization then follow as associated flow rules.To simplify the algorithmic treatment, we introduce the notion of dissipation functions, by which the constrained optimization problem is converted into an unconstrained problem, which can be efficiently solved by standard means.The vectors of remanent polarization/magnetization enter the model as additional internal variables.The constitutive response is governed by thermodynamic potentials, i.e., the free energy and dissipation functions.We derive a (mixed) variational formulation, identify appropriate function spaces for the dependent fields involved, and introduce a finite-element discretization.Representative numerical examples demonstrate the efficacy of the framework in electro-magneto-mechanically coupled problems.

The present paper is concerned with static shape control of sub-domains of material bodies. Eigenstrains or their corresponding actuation stresses are used as the actuation applied only in the sub-domain. Two problems are of particular interest, strain tracking and displacement tracking of the sub-domain. Exact solutions for the two tracking problems are derived and numerical results computed with the Finite Element method are presented for a plane stress problem for validation.

The present contribution is devoted to a special equivalence problem concerning the linear dynamic theories of elasticity and viscoelasticity. We seek for distributions of eigenstrain-induced actuation stresses acting upon a force loaded linear elastic body, such that the resulting displacements are equal to the displacements of a viscoelastic body that is loaded by the same set of forces, but in the absence of actuating stresses. Special emphasis is given to the presence of propagating singular waves. A three-dimensional solution for this equivalence problem is presented first. The presented special solution yields equivalence of stresses in both problems, so that a complete analogy is obtained. The solution then is exemplified for the one-dimensional case of a uni-axial shock wave propagating in a semi-infinite half-space made of a viscoelastic material of the Maxwell-type.

The present article, provides a novel mixed finite element formulation for elastoplasticity which is suitable for the discretization of thin‐walled structures using highly anisotropic volume elements. We present a thermodynamically consistent framework for the modeling of elastoplastic stress response, where dissipative effects are considered through a dissipation function instead of explicit flow rules. Along these lines, a mixed incremental principle, in which stresses are included as independent unknowns, is derived. We propose to employ tangential‐displacement normal‐normal‐stress (TDNNS) elements for a Galerkin discretization of the underlying variational problem. These elements were originally developed for linear elasticity, where it could be shown that they do not suffer from shear locking if the element's aspect ratio deteriorates. Excellent computational performance and accuracy of the proposed method are demonstrated in several benchmark problems.