Rafał Drobnicki’s research while affiliated with Warsaw University of Technology and other places

The article concerns the modeling of the transverse impact of an impactor (test sample) on the surface of an infinite elastic layer. The Laplace transform with respect to time and the Hankel transform with respect to the radius for the axisymmetric case were applied. The propagation of elastic waves in the layer and local deformations in the contact zone are taken into account. Impact force, impact time and the coefficient of restitution were examined. The results are compared with the elastic half-space. The calculations carried out showed that for layer thicknesses of more than five impactor diameters, the layer can be considered as a half-space.

Polyamide 12 (PA12) is vastly utilized in many additive manufacturing methods, such as Selective Laser Sintering (SLS), and a better understanding of its mechanical behaviors promotes available knowledge on the behaviors of 3D-printed parts made from this polymer. In this paper, SLS-produced standard tensile specimens are studied under monotonic and cyclic tension tests, as well as stress relaxation experiments, and the obtained force-displacement responses are shown to be consistent with a hyper-viscoelastic material model. This finding is also observed in typical pantographic structures produced by the same manufacturing parameters. To propose a constitutive model for predicting these behaviors, the convolution integral of a strain-dependent function and a time-dependent function is developed where the material parameters are determined with the use of both short-term and long-term responses of the specimens. Numerical results of the presented model for standard test specimens are shown to be in good agreements with the experimental ones under various loading conditions. To prove the capabilities of the proposed model in studying any SLS-produced part, finite element implementation of the constitutive equations is shown to provide numerical results in agreement with the empirical findings for tensile loading of the 3D-printed pantographic structure.

Polyamide 12 (PA12) is a core material in many 3D-printing techniques, including selective laser sintering (SLS), and its mechanical characterization helps to better understand behaviors of additively manufactured parts made from this polymer. In this paper, the elastic response of SLS-produced PA12 is shown to be nonlinear. Standard test samples with different orientations with regard to the scanning direction are 3D-printed with the use of PA2200 powder, and their elastic response is investigated under uniaxial tension at different strain rates. Mooney–Rivlin hyperelastic models are proposed to address the observed nonlinear elasticity of the samples. Cyclic response of the specimens is shown to be stabilized after a few transient cycles so the material parameters are determined for trained samples after shakedown in their response. The obtained parameters are found to depend on the loading speed; thus, a rate-dependent hyperelastic constitutive model is presented for PA12 produced by selective laser sintering. This model is validated by comparing its numerical prediction with empirical responses under simple tension tests.

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 deformation loading tests (tensile, shearing, and torsion) up to rupture, while their response to loading is recorded by an optical measurement system. 3D-digital image correlation is used to quantify the deformation.

In the last decade, the exotic properties of pantographic metamaterials have been investigated and different mathematical models (both discrete or continuous) have been introduced. In a previous publication, a large part of the already existing literature about pantographic metamaterials has been presented. In this paper, we give some details about the next generation of research in this field. We present an organic scheme of the whole process of design, fabrication, experiments, models and image analyses.

Pantographic metamaterials are known for their ability to have large deformation while remaining in the elastic regime. We have performed a set of experiments on 3D printed pantographic unit cells to parametrically investigate their response when undergoing tensile, compression, and shear loading with the aim of i) studying the role of each parameter in the resultant mechanical behavior of the sample, and ii) providing a benchmark for the mathematical models developed to describe pantographic structures. Results show the existence of local extrema in the space of the geometrical parameters, suggesting the use of optimization techniques to find optimal geometrical parameters resulting in desired functionalities. We have also performed tensile relaxation tests on the samples, with the results indicating the complexity of the dynamic behavior and the existence of multiple relaxation characteristic times. Such results can be used to for calibrating mathematical models describing pantographic structures under dynamic loadings.

In this work, we will present and discuss some experimental observations of the dynamical displacement vector field on a pantographic sheet. We will sketch the experimental setup and we will qualitatively describe the observed behavior for a set of relevant frequencies.

In this paper, we propose a model for the description of bone mechanics and bone remodeling processes, including bone cell populations dynamics. The latter, described by a system of ODEs, influences the values for the elastic parameters used in the mechanical model, which in turn determines the “stimulus” function affecting the behavior of the cells. Numerical simulations concerning the behavior of the bone under external loads, as well as simple fracture healing processes are presented. The model can reproduce the qualitative behavior of bone tissue remodeling and mechanical response.