Jens Christian M. Rauhe

IUTAM Symposium on Modelling Nanomaterials and Nanosystems

Separation of two particles is characterized by a magnitude of the bond energy that limits the accumulated energy of the particle interaction. In the case of a solid comprised of many particles there exist a magnitude of the average bond energy that limits the energy that can be accumulated in a small material volume. The average bond energy can be calculated if the statistical distribution of the bond density is known for a particular material. Alternatively, the average bond energy can be determined in macroscopic experiments if the energy limiter is introduced in a material constitutive model. Traditional continuum models of materials do not have energy limiters and, consequently, allow for the unlimited accumulation of the strain energy. The latter is unphysical, of course, because no material can sustain large enough strains without failure. The average bond energy limits the strain energy and controls material softening, which indicates failure. Thus, by limiting the strain energy we include a description of material failure in the constitutive model. Generally, elasticity including energy limiters can be called softening hyperelasticity because it can describe material failure via softening. We illustrate the capability of softening hyperelasticity in examples of brittle fracture and arterial failure. First, we analyze the overall strength of arteries under the blood pressure. For this purpose we enhance various arterial models with the energy limiters. The models vary from the phenomenological Fung-type theory to the microstructural theories regarding the arterial wall as a bi-layer fiber-reinforced composite. Based on the simulation results we find, firstly, that residual stresses accumulated during artery growth can significantly delay the onset of arterial rupture like the pre-existing compression in the pre-stressed concrete delays the crack opening. Secondly, we find that the media layer is the main load-bearing layer of the artery. And, thirdly, we find that the strength of the collagen fibers dominates the media strength. Second, we numerically simulate tension of a thin plate with a preexisting central crack within a softening hyperelasticity framework and we find that the critical load essentially depends on the crack sharpness: the sharper is the crack the lower is the K.Y. Volokh Technion – Israel Institute of Technology, Haifa 32000, Israel; e-mail: cvolokh@technion.ac.il R. Pyrz and J.C. Rauhe (eds.), IUTAM Symposium on Modelling Nanomaterials and Nanosystems, 1–12.

Foaming of Microcellular PP-MWCNT Nanocomposite in a Sub-Critical CO2 Process

The present work covers the processing route and investigation of PP-MWCNT nanocomposite foams. CO2 is used as a blowing agent in a batch foaming process with a saturation pressure range of 3-7 MPa. Carbon nanotubes act as nucleating agents during the foaming process, which is supported by SEM image analysis and DSC study. Relative density measurements have demonstrated that even though MWCNT promote nucleation of a large amount of cells, the densities of PP-MWCNT nanocomposite foams do not differ significantly from pure PP samples.

Synthesis and characterization of montmorillonite-carbon nanotubes hybrid fillers for nanocomposites

Montmorillonite-carbon nanotubes hybrids were prepared by growth of carbon nanotubes (CNT) on five different types of iron-montmorillonite clays using the chemical vapour deposition (CVD) method. Microscopy studies revealed the presence of carbon nanotubes protruding from clay surfaces and linking the clay layers in a network structure. X-ray diffraction results showed changes in the clay interlayer spacing induced by growth of carbon nanotubes within the layers of iron-montmorillonites. The quality of the resulting carbon nanotubes was evaluated by Raman spectroscopy and thermogravimetric analyzes were used to evaluate the amount of carbon nanotubes and its thermal stability. The method used for the preparation of the iron-montmorillonites appeared to be critical for the quality and quantity of carbon nanotubes obtained in each hybrid. In a preliminary study the hybrids were used to reinforce polyurethane nanocomposite foams.

Fabrication of microcellular PP-MMT nanocomposite foams in a subcritical CO2 process

The present paper is dedicated to fabrication of microcellular PP-MMT nanocomposite foams blown by CO2 at 3-7 MPa pressure range. XRD and TEM studies showed that MMT particles were well exfoliated upon PP-MMT nanocomposite processing, however presence of the nanoclay particles did not facilitate the foaming process, resulting in non-uniform cell structure and low expansion ratios. SEM images demonstrate that clay nanoparticles have not improved the foam morphology; and no nucleation effect of the clay was observed in the produced foams. These data were supported by DSC studies.

Proceeding of the IUTAM Symposium on Modelling Nanomaterials and Nanosystems

Separation of two particles is characterized by a magnitude of the bond energy that limits the accumulated energy of the particle interaction. In the case of a solid comprised of many particles there exist a magnitude of the average bond energy that limits the energy that can be accumulated in a small material volume. The average bond energy can be calculated if the statistical distribution of the bond density is known for a particular material. Alternatively, the average bond energy can be determined in macroscopic experiments if the energy limiter is introduced in a material constitutive model. Traditional continuum models of materials do not have energy limiters and, consequently, allow for the unlimited accumulation of the strain energy. The latter is unphysical, of course, because no material can sustain large enough strains without failure. The average bond energy limits the strain energy and controls material softening, which indicates failure. Thus, by limiting the strain energy we include a description of material failure in the constitutive model. Generally, elasticity including energy limiters can be called softening hyperelasticity because it can describe material failure via softening. We illustrate the capability of softening hyperelasticity in examples of brittle fracture and arterial failure. First, we analyze the overall strength of arteries under the blood pressure. For this purpose we enhance various arterial models with the energy limiters. The models vary from the phenomenological Fung-type theory to the microstructural theories regarding the arterial wall as a bi-layer fiber-reinforced composite. Based on the simulation results we find, firstly, that residual stresses accumulated during artery growth can significantly delay the onset of arterial rupture like the pre-existing compression in the pre-stressed concrete delays the crack opening. Secondly, we find that the media layer is the main load-bearing layer of the artery. And, thirdly, we find that the strength of the collagen fibers dominates the media strength. Second, we numerically simulate tension of a thin plate with a preexisting central crack within a softening hyperelasticity framework and we find that the critical load essentially depends on the crack sharpness: the sharper is the crack the lower is the K.Y. Volokh Technion – Israel Institute of Technology, Haifa 32000, Israel; e-mail: cvolokh@technion.ac.il R. Pyrz and J.C. Rauhe (eds.), IUTAM Symposium on Modelling Nanomaterials and Nanosystems, 1–12.

IUTAM Symposium on Modelling Nanomaterials and Nanosystems: Proceedings of the IUTAM Symposium held in Aalborg, Denmark, 19-22 May, 2008

Separation of two particles is characterized by a magnitude of the bond energy that limits the accumulated energy of the particle interaction. In the case of a solid comprised of many particles there exist a magnitude of the average bond energy that limits the energy that can be accumulated in a small material volume. The average bond energy can be calculated if the statistical distribution of the bond density is known for a particular material. Alternatively, the average bond energy can be determined in macroscopic experiments if the energy limiter is introduced in a material constitutive model. Traditional continuum models of materials do not have energy limiters and, consequently, allow for the unlimited accumulation of the strain energy. The latter is unphysical, of course, because no material can sustain large enough strains without failure. The average bond energy limits the strain energy and controls material softening, which indicates failure. Thus, by limiting the strain energy we include a description of material failure in the constitutive model. Generally, elasticity including energy limiters can be called softening hyperelasticity because it can describe material failure via softening. We illustrate the capability of softening hyperelasticity in examples of brittle fracture and arterial failure. First, we analyze the overall strength of arteries under the blood pressure. For this purpose we enhance various arterial models with the energy limiters. The models vary from the phenomenological Fung-type theory to the microstructural theories regarding the arterial wall as a bi-layer fiber-reinforced composite. Based on the simulation results we find, firstly, that residual stresses accumulated during artery growth can significantly delay the onset of arterial rupture like the pre-existing compression in the pre-stressed concrete delays the crack opening. Secondly, we find that the media layer is the main load-bearing layer of the artery. And, thirdly, we find that the strength of the collagen fibers dominates the media strength. Second, we numerically simulate tension of a thin plate with a preexisting central crack within a softening hyperelasticity framework and we find that the critical load essentially depends on the crack sharpness: the sharper is the crack the lower is the K.Y. Volokh Technion – Israel Institute of Technology, Haifa 32000, Israel; e-mail: cvolokh@technion.ac.il R. Pyrz and J.C. Rauhe (eds.), IUTAM Symposium on Modelling Nanomaterials and Nanosystems, 1–12.

Large Scale Finite Element Modelling of the Effective Elastic Properties of Particle Reinforced Composites

Over the years several methods have been proposed for the determination of the effective elastic properties of particle reinforced composites. The material microstructures used in the present analysis is a real microstructure and a numerically generated microstructure. X‐ray microtomography is used to determine the material microstructure and with this method the interior microstructure is determined in a non‐destructive way. Using the commercially available equipment, SkyScan 1072, the maximum resolution is approximately 5 microns. The data obtained from the tomographic examination is used to generate three‐dimensional finite element models of the microstructure. The models contain a large number of elements, up to 1 million, and are solved iteratively using an element‐by‐element formalism. Models containing 100 particles have been statistically generated and the material properties of each particle is assigned using a Gaussian distribution of the properties. Various distributions have been used to deter...