arXiv subjects

Ondřej Faltus

Publications and source records attributed to Ondřej Faltus.

4 recordsLinked to original sources

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↗

arXiv2025

Non-uniform pneumatic actuation switches macroscopic properties of elastomeric honeycombs

Honeycomb microstructures with circular voids are well known to undergo pattern transformations under macroscopic strain loading. Depending on the biaxiality of the applied strain, they deform into three different patterns. Here we demonstrate that the same three patterns can be triggered also by pneumatic actuation of the voids, with resulting patterns depending on an applied pressurization scheme, i.e., the ratio of suction pressures introduced in different voids within the microstructure. Our numerically obtained findings are experimentally validated on two finite size samples made of silicone rubber cast in a 3D printed mold. In numerical studies, we first showcase the evolution of homogenized stiffness and its anisotropy during the genesis of pneumatically-induced patterns. Our loading schemes result in macroscopic stiffness varying by a factor of two with loading direction, chosen by a reversible actuation independent of the load itself. Second, we study the effect of the pneumatic actuation on acoustic properties of the microstructure, finding the proposed method viable to trigger different acoustic bandgaps.

physics.app-ph↗

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

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↗