van Jaw Hans Dommelen

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

Abstract A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress–strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading–reloading cycles are presented.

Mechanical properties of brain tissue by indentation: Interregional variation

Although many studies on the mechanical properties of brain tissue exist, some controversy concerning the possible differences in mechanical properties of white and gray matter tissues remains. Indentation experiments are conducted on white and gray matter tissues of various regions of the cerebrum and on tissue from the thalamus and the midbrain to study interregional differences. An advantage of indentation, when compared to standard rheological tests as often used for the characterization of brain tissue, is that it is a local test, requiring only a small volume of tissue to be homogeneous. Indentation tests are performed at different speeds and the force relaxation after a step indent is measured as well. White matter tissue is found to be stiffer than gray matter and to show more variation in response between different samples which is consistent with structural differences between white matter and gray matter. In addition to differences between white matter and gray matter, also different regions of brain tissue are compared.

The influence of test conditions on characterization of the mechanical properties of brain tissue.

To understand brain injuries better, the mechanical properties of brain tissue have been studied for 50 years; however, no universally accepted data set exists. The variation in material properties reported may be caused by differences in testing methods and protocols used. An overview of studies on the mechanical properties of brain tissue is given, focusing on testing methods. Moreover, the influence of important test conditions, such as temperature, anisotropy, and precompression was experimentally determined for shear deformation. The results measured at room temperature show a stiffer response than those measured at body temperature. By applying the time-temperature superposition, a horizontal shift factor a(T)=8.5-11 was found, which is in agreement with the values found in literature. Anisotropy of samples from the corona radiata was investigated by measuring the shear resistance for different directions in the sagittal, the coronal, and the transverse plane. The results measured in the coronal and the transverse plane were 1.3 and 1.25 times stiffer than the results obtained from the sagittal plane. The variation caused by anisotropy within the same plane of individual samples was found to range from 25% to 54%. The effect of precompression on shear results was investigated and was found to stiffen the sample response. Combinations of these and other factors (postmortem time, donor age, donor type, etc.) lead to large differences among different studies, depending on the different test conditions.

Biomechanics of Traumatic Brain Injury: Influences of the Morphologic Heterogeneities of the Cerebral Cortex

Traumatic brain injury (TBI) can be caused by accidents and often leads to permanent health issues or even death. Brain injury criteria are used for assessing the probability of TBI, if a certain mechanical load is applied. The currently used injury criteria in the automotive industry are based on global head kinematics. New methods, based on finite element modeling, use brain injury criteria at lower scale levels, e.g., tissue-based injury criteria. However, most current computational head models lack the anatomical details of the cerebrum. To investigate the influence of the morphologic heterogeneities of the cerebral cortex, a numerical model of a representative part of the cerebral cortex with a detailed geometry has been developed. Several different geometries containing gyri and sulci have been developed for this model. Also, a homogeneous geometry has been made to analyze the relative importance of the heterogeneities. The loading conditions are based on a computational head model simulation. The results of this model indicate that the heterogeneities have an influence on the equivalent stress. The maximum equivalent stress in the heterogeneous models is increased by a factor of about 1.3–1.9 with respect to the homogeneous model, whereas the mean equivalent stress is increased by at most 10%. This implies that tissue-based injury criteria may not be accurately applied to most computational head models used nowadays, which do not account for sulci and gyri.

Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads

The length scales involved in the development of diffuse axonal injury typically range from the head level (i.e., mechanical loading) to the cellular level. The parts of the brain that are vulnerable to this type of injury are mainly the brainstem and the corpus callosum, which are regions with highly anisotropically oriented axons. Within these parts, discrete axonal injuries occur mainly where the axons have to deviate from their main course due to the presence of an inclusion. The aim of this study is to predict axonal strains as a result of a mechanical load at the macroscopic head level. For this, a multi-scale finite element approach is adopted, in which a macro-level head model and a micro-level critical volume element are coupled. The results show that the axonal strains cannot be trivially correlated to the tissue strain without taking into account the axonal orientations, which indicates that the heterogeneities at the cellular level play an important role in brain injury and reliable predictions thereof. In addition to the multi-scale approach, it is shown that a novel anisotropic equivalent strain measure can be used to assess these micro-scale effects from head-level simulations only.

Characterisation of the mechanical behaviour of brain tissue in compression and shear.

No validated, generally accepted data set on the mechanical properties of brain tissue exists, not even for small strains. Most of the experimental and methodological issues have previously been addressed for linear shear loading. The objective of this work was to obtain a consistent data set for the mechanical response of brain tissue to either compression or shear. Results for these two deformation modes were obtained from the same samples to reduce the effect of inter-sample variation. Since compression tests are not very common, the influence of several experimental conditions for the compression measurements was analysed in detail. Results with and without initial contact of the sample with the loading plate were compared. The influence of a fluid layer surrounding the sample and the effect of friction were examined and were found to play an important role during compression measurements.To validate the non-linear viscoelastic constitutive model of brain tissue that was developed in Hrapko et al. (Biorheology 43 (2006), 623-636) and has shown to provide a good prediction of the shear response, the model has been implemented in the explicit Finite Element code MADYMO. The model predictions were compared to compression relaxation results up to 15% strain of porcine brain tissue samples. Model simulations with boundary conditions varying within the physical ranges of friction, initial contact and compression rate are used to interpret the compression results.

Micromechanical modeling of intraspherulitic deformation of semicrystalline polymers

Semicrystalline polymers often show a spherulitic morphology, consisting of a radial assembly of twisted crystalline lamellae and amorphous layers. A multiscale numerical model is used to investigate the mechanics of intraspherulitic deformation of polyethylene. The model establishes links across the microscopic, the mesoscopic, and the macroscopic levels. Constitutive properties of the material are identified for the crystallographic and amorphous domains. The averaged fields of an aggregate of individual phases, having preferential orientations, form the constitutive behavior of intraspherulitic material. The spherulitic macrostructure is described by finite element models. The macroscopic stress ‐ strain response resembles that of a previous random polycrystalline model. However, the current model includes the geometrical effect of the anisotropic structure within a spherulite, causing strain concentrations in the centers, which spread out in the equatorial region for uniaxial loading conditions and in inclined directions for plane strain loading. The deformations are linked to microstructural processes as interlamellar deformation and intralamellar crystallographic slip. q 2003 Elsevier Ltd. All rights reserved.

Micromechanical modeling of particle-toughening of polymers by locally induced anisotropy

The impact strength of several semi-crystalline polymers can be improved by the dispersion of second-phase rubber particles. A criterion for the effect of this practice is based on the average interparticle matrix ligament thickness. The critical interparticle distance is considered to be an intrinsic material property of the matrix. A toughening mechanism has recently been suggested which considers a layer of transcrystallized material around well dispersed particles, having a reduced yield strength in certain preferentially oriented directions. In this work, the potential of local anisotropy for the toughening of semi-crystalline polymeric material is investigated. The matrix material is modeled within the framework of anisotropic Hill plasticity with a rate dependent and hardening yield stress. The applicability of different two-dimensional micromechanical models is assessed by comparison to fully three-dimensional simulations with irregularly dispersed particles. A reduced plastic shear resistance of percolating transcrystallized material is found to be very effective in inducing extensive delocalized shear deformations and alters the location of the peak tensile hydrostatic stresses.

Optical characterization of acceleration-induced strain fields in inhomogeneous brain slices

The aim of this study was to measure high-resolution strain fields in planar sections of brain tissue during translational acceleration to obtain validation data for numerical simulations. Slices were made from fresh, porcine brain tissue, and contained both grey and white matter as well as the complex folding structure of the cortex. The brain slices were immersed in artificial cerebrospinal fluid (aCSF) and were encapsulated in a rigid cavity representing the actual shape of the skull. The rigid cavity sustained an acceleration of about 900m/s(2) to a velocity of 4m/s followed by a deceleration of more than 2000m/s(2). During the experiment, images were taken using a high-speed video camera and Von Mises strains were calculated using a digital image correlation technique. The acceleration of the sampleholder was determined using the same digital image correlation technique. A rotational motion of the brain slice relative to the sampleholder was observed, which may have been caused by a thicker posterior part of the slice. Local variations in the displacement field were found, which were related to the sulci and the grey and white matter composition of the slice. Furthermore, higher Von Mises strains were seen in the areas around the sulci.

Characterization of semiconductor interfaces using a modified mixed mode bending apparatus

This research deals with the experimental assessment of the strength of bi-material interfaces as a function of mode mixity, focusing on two dimensional problems. A modified mixed mode bending apparatus is designed and tested, which can be used to measure small forces involved in the delamination of semiconductor packaging materials. Using this setup, it is possible to measure interface strength over nearly the full range of mode mixities using a single specimen design. A finite element model is used to determine interface strength and mode mixity. As an example, the combined numerical-experimental procedure is applied to the interface between copper lead frame (LF) and epoxy molding compound (MCE). A remarkable result is that a double cantilever beam (DCB) test of this interface does not yield the lowest possible interface strength, meaning that it can not be used as a worst case test.