Jouni Freund

A direct simulation method for the effective in-plane stiffness of cellular materials

A simulation model is presented in order to provide the near-exact geometrical description of the actual cellular materials and to determine the effective in-plane stiffness of them. The model consists of a geometric input generator and a micromechanical model. The input generator is used to describe the cellular material geometry including the cell wall thicknesses, cell connectivity, vertex and center coordinates through the in situ specimen images while the micromechanical model is used to incorporate the geometrical description and the mechanical behavior of the cell walls. For model validation, a case study is performed on Nomex honeycomb specimens, the results of which are expressed in terms of the effective in-plane stiffness properties and compared to the measured values provided in the literature.

STATISTICAL STRENGTH ANALYSIS FOR HONEYCOMB MATERIALS

In the present study, a statistical strength model is proposed, which aims at describing how the strength of geometrically irregular honeycomb material is affected by the scale. Hence, the samples are designed based on the selected geometrical irregularity and the number of the cells/scale. Simulation experiments are conducted on these samples under different loading combinations. The experiment results are linked to possible failure mechanisms in order to obtain the critical loads which are expressed in terms of cumulative distribution functions. The discrete distribution data of the critical loads are then fitted to analyze the effect of scale on different strength percentiles by virtue of the least squares function and closed quadric surface fitting. Eventually, the outcome is expressed in terms of ellipsoid surface representing the honeycomb material strength in three-dimensional stress space.

Stochastic fracture of additively manufactured porous composites

Extrusion-based fused deposition modeling (FDM) introduces inter-bead pores into dense materials, which results in part-to-part mechanical property variations, i.e., low mechanical reliability. In addition, the internal structure of FDMed materials can be made porous intentionally to tailor mechanical properties, introduce functionality, reduce material consumption, or decrease production time. Despite these potential benefits, the effects of porosity on the mechanical reliability of FDMed composites are still unclear. Accordingly, we investigated the stochastic fracture of 241 FDMed short-carbon-fiber-reinforced-ABS with porosity ranging from 13 to 53 vol.% under tensile load. Weibull analysis was performed to quantify the variations in mechanical properties. We observed an increase in Weibull modulus of fracture/tensile strength for porosity higher than ~40 vol.% and a decrease in Weibull modulus of fracture strain for an increase in porosity from 25 to 53 vol.%. Micromechanics-based 2D simulations indicated that the mechanical reliability of FDMed composites depends on variations in bead strength and elastic modulus of beads. The change in raster orientation from 45°/−45° to 0° more than doubled the Weibull modulus. We identified five different types of pores via high-resolution X-ray computed tomography. A 22% and 48% decrease in carbon fiber length due to extrusion was revealed for two different regions of the filament.

Two-scale Reissner-Mindlin plate model

A two-scale plate model, in which the displacement assumption consists of the Reissner-Mindlin and warping parts, is presented. To reduce the modelling error of the classical Reissner-Mindlin model, the warping part is chosen so that the overall displacement satisfies the full 3D elasticity equations as well as possible. Pressure loaded isotropic homogeneous plate is used as an application example.

Effect of size and measurement domain on the in-plane elasticity of wood-like cellular materials

The current study presents a simulation model comprising an input generation method, micromechanical model, and a method minimizing the boundary artifacts through micropolar elasticity, also known as Cosserat elasticity. The present input generation method provides the geometric description of the actual cellular materials in two-dimensional space including the cell wall thicknesses, cell connectivity, vertex, and center coordinates. The gathered data are then used to mimic the mechanical behavior of actual cellular material in the virtual environment. As a case study, microscope images of Norway spruce (Picea abies) were used to form the near-exact geometry to be used as the solution domain for the micromechanical model. Thereafter, simulation experiments were conducted to understand the size effect and measurement domain selection on the in-plane elasticity of wood-like cellular materials.

A new approach for determining the hidden material parameters of a honeycomb

An optimization method to obtain the cell wall properties of Nomex honeycomb material is presented. There, the outcomes of physical experiments and micromechanical simulations are compared in an effort to identify the geometric or/and material parameters for the best match. Only the cell wall thickness and Young’s modulus, called here as the hidden parameters, are used in the matching as the Young’s modulus is difficult measure reliably. The mean values and standard deviations of the geometric parameters of the cell structure model are obtained through image analysis. In the micromechanical model used, the cell walls are considered as linearly elastic Bernoulli beams. The optimum hidden parameter values for the Nomex case turn out not to be unique but they appear in a combination known as the bending stiffness.