arXiv subjects

Martin Horák

Publications and source records attributed to Martin Horák.

17 recordsLinked to original sources

arXiv2026

Technology-Enhanced Tabletop Exercises for Cybersecurity Education: Lessons Learned

This innovative practice full paper examines the integration of technology-enhanced tabletop exercises (TTXs) into computing education, focusing on cybersecurity curricula. The motivation is to better prepare students for complex, collaborative problem solving typical of incident response and IT governance, where coordination, communication, and timely decision-making are essential. Although TTXs are well-established in professional practice, they remain underused in universities. We address this gap by augmenting TTX delivery and evaluation through the INJECT Exercise Platform (IXP), a web-based environment that automates scenario flow and enables data-driven assessment. Our practice implements IXP to automatically deliver scenario updates, facilitate team discussions, and collect interaction data to support automated assessment. This combination enhances realism, reduces instructor workload, and provides actionable insight into student learning. From 2024 to 2026, we ran 25 exercises with 743 participants in multiple university courses and extracurricular events. We observed increased engagement and collaboration among students, and clearer visibility for instructors into how teams navigate complex scenarios. This paper shares 24 lessons learned from these exercises. Instructors and curriculum designers may benefit from concrete guidance for integrating technology-enhanced TTXs. We demonstrate that digital TTXs provide a scalable and replicable model for cybersecurity courses and others requiring team-based problem-solving.

cs.CY↗

arXiv2026

Frame-indifferent discretization in nonlinear thermoviscoelasticity: Analysis and numerical simulations

We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. We refine the discretization schemes in [Badal-Friedrich-Kružík '23, Mielke-Roub\'ıček '20] by imposing frame indifference already at a time-discrete level. This is justified both analytically and numerically.

math.AP↗

arXiv2026

Deformation gradient averaging regularization for third medium contact

The third medium contact method has recently come into popularity as an alternative to traditional contact methods in contexts where search for contact boundaries is problematic, i.e. topology optimization. To enforce the contact constraints, it relies on a fictitious compliant material occupying the void space. In finite strain setting, this necessitates regularization techniques to improve the behavior of the third medium material. A number of existing models rely on penalization of locally computed second gradients of displacements, either through direct calculation on second-order elements or through additional degrees of freedom. Here we propose an alternative approach using element-wise deformation gradient averaging to effectively penalize spatial variations of the deformation gradient, together with a linear elastic term enforcing constant third medium stiffness. Our approach enables the use of first-order finite element formulations without any additional degrees of freedom and is therefore easy to implement. We demonstrate the robustness of the proposed method on several well-established benchmarks.

cs.CE↗

arXiv2026

Incremental equations in curvature-dependent surface elasticity

We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we derive compact governing equations expressed in a coordinate-free Lagrangian setting that remain valid for arbitrary geometries. Linearization about an arbitrarily large finite deformation yields incremental bulk and surface balance laws that closely resemble the classical small-on-large theory, but are now extended to include surface-curvatureinduced stresses. The applicability of the general theory is demonstrated by analyzing the onset of periodic beading in a soft cylindrical substrate coated with a surface layer exhibiting stretching- or curvature-dependent behavior, illustrating how surface stretching and bending effects influence instability thresholds for both compressible and incompressible bulk. This unified formulation thus provides a foundation for studying stability phenomena in elasto-capillary systems where surface curvature plays a critical mechanical role.

math-ph↗

arXiv2025

Surface-Polyconvex Models for Soft Elastic Solids

Soft solids with surface energy exhibit complex mechanical behavior, necessitating advanced constitutive models to capture the interplay between bulk and surface mechanics. This interplay has profound implications for material design and emerging technologies. In this work, we set up variational models for bulk-surface elasticity and explore a novel class of surface-polyconvex constitutive models that account for surface energy while ensuring the existence of minimizers. These models are implemented within a finite element framework and validated through benchmark problems and applications, including, e.g., the liquid bridge problem and the Rayleigh-Plateau instability, for which the surface energy plays the dominant role. The results demonstrate the ability of surface-polyconvex models to accurately capture surface-driven phenomena, establishing them as a powerful tool for advancing the mechanics of soft materials in both engineering and biological applications.

math-ph↗

arXiv2025

Finite-strain constitutive model for shape memory alloys formulated in the logarithmic strain space

This work presents a finite-strain version of an established three-dimensional constitutive model for polycrystalline shape memory alloys (SMA) that is able to account for the large deformations and rotations that SMA components may undergo. The model is constructed by applying the logarithmic strain space approach to the original small-strain model, which was formulated within the Generalized Standard Materials framework and features a refined dissipation (rate) function. Additionally, the free energy function is augmented to be more versatile in capturing the transformation kinetics. The model is implemented into finite element software. To demonstrate the model performance and validate the implementation, material parameters are fitted to the experimental data of two SMA, and two computational simulations of SMA components are conducted. The applied approach is highly flexible from the perspective of the future incorporation of other phenomena, e.g., irreversibility associated with plasticity, into the model.

cond-mat.mtrl-sci↗

arXiv2025

Towards active stiffness control in pattern-forming pneumatic metamaterials

Pattern-forming metamaterials feature microstructures specifically designed to change the material's macroscopic properties due to internal instabilities. These can be triggered either by mechanical deformation or, in the case of active materials, by other external stimuli, such as pneumatic actuation. We study a two-dimensional rectangular lattice microstructure which is pneumatically actuated by non-uniform pressure patterns in its voids, and demonstrate that this actuation may lead toifferent instability patterns. The patterns are associated with a significant reduction in the macroscopic stiffness of the material. The magnitude of this reduction can be controlled by different arrangements of the pressure actuation, thus choosing the precise buckled shape of the microstructure. We develop an analytical model and complement it with computational tests on a two-dimensional plane-strain finite element model. We explain the phenomenon and discuss ways of further developing the concept to actively control the stiffness of materials and structures.

physics.app-ph↗

arXiv2024

Integral Micromorphic Model Reproducing Dispersion in 1D Continuum

The paper develops a new integral micromorphic elastic continuum model, which can describe dispersion properties of band-gap metamaterials, i.e., metamaterials that inhibit propagation of waves in a certain frequency range. The enrichment consists in nonlocal averaging of three terms in the expression for the potential energy density of the standard micromorphic continuum. After proper calibration, such a formulation can exactly reproduce two given branches of the dispersion curve (acoustic and optical), even in cases with a band gap. The calibration process exploits Fourier images of the unknown weight functions, which are analytically deduced from the dispersion relation of the material of interest. The weight functions are then reconstructed in the spatial domain by numerical evaluation of the inverse Fourier transform. The presented approach is validated on several examples, including a discrete mass-spring chain with two alternating masses, for which the dispersion relation has an explicit analytical form and the optical and acoustic branches are separated by a band gap.

physics.app-ph↗

arXiv2024

Third Medium Finite Element Contact Formulation for Pneumatically Actuated Systems

Mechanical metamaterials are artificially engineered microstructures that exhibit novel mechanical behavior on the macroscopic scale. Active metamaterials can be externally controlled. Pneumatically actuated metamaterials can change their mechanical, acoustic, or other types of effective behavior in response to applied pressure with possible applications ranging from soft robotic actuators to phononic crystals. To facilitate the design of such pneumatically actuated metamaterials and structures by topology optimization, a robust way of their computational modeling, capturing both pneumatic actuation of internal voids and internal contact, is needed. Since voids in topology optimization are often modeled using a soft material model, the third medium contact formulation lends itself as a suitable stepping stone. We propose a single hyperelastic material model capable of maintaining a prescribed hydrostatic Cauchy stress within a void in the pre-contact phase while simultaneously acting as a third medium to enforce frictionless contact, contrasting existing third medium approaches focused solely on contact. We split the overall third-medium energy density into contact, regularization, and pneumatic pressure contributions, all of which can be individually controlled and tuned. To prevent distortions of the compliant third medium, we include curvature penalization in our model. This improves on existing formulations in terms of compliant third medium behavior, leading ultimately to better numerical stability of the solution. Since our formulation is energetically consistent, we are able to employ more advanced finite element solvers, such as the modified Cholesky algorithm to detect instabilities. We demonstrate the behavior of the proposed formulation on several examples of traditional contact benchmarks, including a standard patch test, and validate it with experimental measurement.

cs.CE↗

arXiv2024

From Paper to Platform: Evolution of a Novel Learning Environment for Tabletop Exercises

For undergraduate students of computing, learning to solve complex practical problems in a team is an essential skill for their future careers. This skill is needed in various fields, such as in cybersecurity and IT governance. Tabletop exercises are an innovative teaching method used in practice for training teams in incident response and evaluation of contingency plans. However, tabletop exercises are not yet widely established in university education. This paper presents data and teaching experience from a cybersecurity course that introduces tabletop exercises in classrooms using a novel technology: INJECT Exercise Platform (IXP), a web-based learning environment for delivering and evaluating the exercises. This technology substantially improves the prior practice, since tabletop exercises worldwide have usually been conducted using pen and paper. Unlike in traditional tabletop exercises, which are difficult to evaluate manually, IXP provides insights into students' behavior and learning based on automated analysis of interaction data. We demonstrate IXP's capabilities and evolution by comparing exercise sessions hosted throughout three years at different stages of the platform's readiness. The analysis of student data is supplemented by the discussion of the lessons learned from employing IXP in computing education contexts. The data analytics enabled a detailed comparison of the teams' performance and behavior. Instructors who consider innovating their classes with tabletop exercises may use IXP and benefit from the insights in this paper.

cs.CY↗

arXiv2024

Research and Practice of Delivering Tabletop Exercises

Tabletop exercises are used to train personnel in the efficient mitigation and resolution of incidents. They are applied in practice to support the preparedness of organizations and to highlight inefficient processes. Since tabletop exercises train competencies required in the workplace, they have been introduced into computing courses at universities as an innovation, especially within cybersecurity curricula. To help computing educators adopt this innovative method, we survey academic publications that deal with tabletop exercises. From 140 papers we identified and examined, we selected 14 papers for a detailed review. The results show that the existing research deals predominantly with exercises that follow a linear format and exercises that do not systematically collect data about trainees' learning. Computing education researchers can investigate novel approaches to instruction and assessment in the context of tabletop exercises to maximize the impact of this teaching method. Due to the relatively low number of published papers, the potential for future research is immense. Our review provides researchers, tool developers, and educators with an orientation in the area, a synthesis of trends, and implications for further work.

cs.CY↗

arXiv2023

Want to Raise Cybersecurity Awareness? Start with Future IT Professionals

As cyber threats endanger everyone, from regular users to computing professionals, spreading cybersecurity awareness becomes increasingly critical. Therefore, our university designed an innovative cybersecurity awareness course that is freely available online for students, employees, and the general public. The course offers simple, actionable steps that anyone can use to implement defensive countermeasures. Compared to other resources, the course not only suggests learners what to do, but explains why and how to do it. To measure the course impact, we administered it to 138 computer science undergraduates within a compulsory information security and cryptography course. They completed the course as a part of their homework and filled out a questionnaire after each lesson. Analysis of the questionnaire responses revealed that the students valued the course highly. They reported new learning, perspective changes, and transfer to practice. Moreover, they suggested suitable improvements to the course. Based on the results, we have distilled specific insights to help security educators design similar courses. Lessons learned from this study are relevant for cybersecurity instructors, course designers, and educational managers.

cs.CY↗

arXiv2022

Integral Micromorphic Model for Band Gap in 1D Continuum

The design of band-gap metamaterials, i.e., metamaterials with the capability to inhibit wave propagation of a specific frequency range, has numerous potential engineering applications, such as acoustic filters and vibration isolation control. In order to describe the behavior of such materials, a novel integral micromorphic elastic continuum is introduced, and its ability to describe band gaps is studied in the one-dimensional setting. The nonlocal formulation is based on a modification of two terms in the expression for potential energy density. The corresponding dispersion equation is derived and converted to a dimensionless format, so that the effect of individual parameters can be described in the most efficient way. The results indicate that both suggested nonlocal modifications play an important role. The original local micromorphic model reproduces a band gap only in the special, somewhat artificial case, when the stiffness coefficient associated with the gradient of the micromorphic variable vanishes. On the other hand, the nonlocal formulation can provide band gaps even for nonzero values of this coefficient, provided that the penalty coefficient that enforces coupling between the micromorphic variable and nonlocal strain is sufficiently high and the micromorphic stiffness is sufficiently low.

physics.app-ph↗

arXiv2022

Efficient formulation of a two-noded geometrically exact curved beam element

The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic relations and sectional equations that link the internal forces to sectional deformation variables. The resulting first-order differential equations are approximated by the finite difference scheme and the boundary value problem is converted to an initial value problem using the shooting method. The paper develops the theoretical framework based on the Navier-Bernoulli hypothesis, with a possible extension to shear-flexible beams. Numerical procedures for the evaluation of equivalent nodal forces and of the element tangent stiffness are presented in detail. Unlike standard finite element formulations, the present approach can increase accuracy by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant. The efficiency and accuracy of the developed scheme are documented by seven examples that cover circular and parabolic arches, a spiral-shaped beam, and a spring-like beam with a zig-zag centerline. The proposed formulation does not exhibit any locking. No excessive stiffness is observed for coarse computational grids and the distribution of internal forces is not polluted by any oscillations. It is also shown that a cross effect in the relations between internal forces and deformation variables arises, i.e., the bending moment affects axial stretching and the normal force affects the curvature. This coupling is theoretically explained in the appendix.

cs.CE↗

arXiv2021

Efficient formulation of a geometrically nonlinear beam element

The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first-order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. Accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant, which leads to high computational efficiency. The element has been implemented into an open-source finite element code. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

math.NA↗

arXiv2019

Gradient polyconvex material models and their numerical treatment

Gradient polyconvex materials are nonsimple materials where we do not assume smoothness of the elastic strain but instead regularity of minors of the strain is required. This allows for a larger class of admissible deformations than in the case of second-grade materials. We describe a possible implementation of gradient polyconvex elastic energies. Besides, a new geometric interpretation of gradient-polyconvexity is given and it is compared with standard second-grade materials. Finally, we demonstrate application of the proposed approach using two different models, namely, a St.-Venant Kirchhoff material and a double well stored energy density.

math.AP↗

arXiv2014

Evaluation of nonlocal approaches for modelling fracture near nonconvex boundaries

Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the stress-strain equations. However, there is no consensus yet how the influence of boundaries should be taken into account by the averaging procedures. In the present study, nonlocal damage models with different averaging procedures are applied to the modelling of fracture in specimens with various boundary types. Firstly, the nonlocal models are calibrated by fitting load-displacement curves and dissipated energy profiles for direct tension to the results of mesoscale analyses performed using a discrete model. These analyses are set up so that the results are independent of boundaries. Then, the models are applied to two-dimensional simulations of three-point bending tests with a sharp notch, a V-type notch, and a smooth boundary without a notch. The performance of the nonlocal approaches in modelling of fracture near nonconvex boundaries is evaluated by comparison of load-displacement curves and dissipated energy profiles along the beam ligament with the results of meso-scale simulations. As an alternative approach, elastoplasticity combined with nonlocal or over-nonlocal damage is also included in the comparative study.

cond-mat.mtrl-sci↗