Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

Mean-Field critical behavior and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

Earthquake statistics in a Block Slider Model and a fully dynamic Fault Model

We examine the event statistics obtained from two differing simplified models for earthquake faults. The first model is a reproduction of the Block-Slider model of Carlson et al. (1991), a model often employed in seismicity studies. The second model is an elastodynamic fault model based upon the Lattice Solid Model (LSM) of Mora and Place (1994). We performed simulations in which the fault length was varied in each model and generated synthetic catalogs of event sizes and times. From these catalogs, we constructed interval event size distributions and inter-event time distributions. The larger, localised events in the Block-Slider model displayed the same scaling behaviour as events in the LSM however the distribution of inter-event times was markedly different. The analysis of both event size and inter-event time statistics is an effective method for comparative studies of differing simplified models for earthquake faults.

Automatic refinement of constructive solid geometry models

Geometric information relating to most engineering products is available in the form of orthographic drawings or 2D data files. For many recent computer based applications, such as Computer Integrated Manufacturing (CIM), these data are required in the form of a sophisticated model based on Constructive Solid Geometry (CSG) concepts. A recent novel technique in this area transfers 2D engineering drawings directly into a 3D solid model called `the first approximation'. In many cases, however, this does not represent the real object. In this thesis, a new method is proposed and developed to enhance this model. This method uses the notion of expanding an object in terms of other solid objects, which are either primitive or first approximation models. To achieve this goal, in addition to the prepared subroutine to calculate the first approximation model of input data, two other wireframe models are found for extraction of sub-objects. One is the wireframe representation on input, and the other is the wireframe of the first approximation model. A new fast method is developed for the latter special case wireframe, which is named the `first approximation wireframe model'. This method avoids the use of a solid modeller. Detailed descriptions of algorithms and implementation procedures are given. In these techniques utilisation of dashed line information is also considered in improving the model. Different practical examples are given to illustrate the functioning of the program. Finally, a recursive method is employed to automatically modify the output model towards the real object. Some suggestions for further work are made to increase the domain of objects covered, and provide a commercially usable package. It is concluded that the current method promises the production of accurate models for a large class of objects.

Simulation of the micro-physics of rocks using LSMearth

The particle-based Lattice Solid Model (LSM) was developed to provide a basis to study the physics of rocks and the nonlinear dynamics of earthquakes (MORA and PLACE, 1994; PLACE and MORA, 1999). A new modular and flexible LSM approach has been developed that allows different microphysics to be easily included in or removed from the model. The approach provides a virtual laboratory where numerical experiments can easily be set up and all measurable quantities visualised. The proposed approach provides a means to simulate complex phenomena such as fracturing or localisation processes, and enables the effect of different micro-physics on macroscopic behaviour to be studied. The initial 2-D model is extended to allow three-dimensional simulations to be performed and particles of different sizes to be specified. Numerical bi-axial compression experiments under different confining pressure are used to calibrate the model. By tuning the different microscopic parameters (such as coefficient of friction, microscopic strength and distribution of grain sizes), the macroscopic strength of the material and can be adjusted to be in agreement with laboratory experiments, and the orientation of fractures is consistent with the theoretical value predicted based on Mohr-Coulomb diagram. Simulations indicate that 3-D numerical models have different macroscopic properties than in 2-D and, hence, the model must be recalibrated for 3-D simulations. These numerical experiments illustrate that the new approach is capable of simulating typical rock fracture behaviour. The new model provides a basis to investigate nucleation, rupture and slip pulse propagation in complex fault zones without the previous model limitations of a regular low-level surface geometry and being restricted to two-dimensions.

Single side damage simulations and detection in beam-like structures

Beam-like structures are the most common components in real engineering, while single side damage is often encountered. In this study, a numerical analysis of single side damage in a free-free beam is analysed with three different finite element models; namely solid, shell and beam models for demonstrating their performance in simulating real structures. Similar to experiment, damage is introduced into one side of the beam, and natural frequencies are extracted from the simulations and compared with experimental and analytical results. Mode shapes are also analysed with modal assurance criterion. The results from simulations reveal a good performance of the three models in extracting natural frequencies, and solid model performs better than shell while shell model performs better than beam model under intact state. For damaged states, the natural frequencies captured from solid model show more sensitivity to damage severity than shell model and shell model performs similar to the beam model in distinguishing damage. The main contribution of this paper is to perform a comparison between three finite element models and experimental data as well as analytical solutions. The finite element results show a relatively well performance.

Ruuvipurkaimen DFMA

Tämän työn tarkoituksena oli soveltaa valmistusystävällisen ja kokoonpanon huomioivan suunnittelun(DFMA) periaatteita ajavalle ruuvipurkaimelle valmistuskustannusten alentamiseksi. Työn teoriaosassa esitellään valmistusystävällisen suunnittelun periaatteita. Yhtä tarkemmin noudatettua DFMA-menetelmää esitellään hieman enemmän. Teoriassa käsitellään myös valmistuskustannusten laskentaa, lähinnä hitsauksen ja koneistuksen osalta. Ruuvipurkaimen rakenteeseen perehdyttiin tekemällä siitä 3D-malli. Purkaimen valmistuskustannukset selvitettiin ja kustannusten painopisteet määritettiin. Niiden pohjalta valittiin kohteet joihin paneuduttiin ja joihin sovellettiin DFMA:n periaatteita. Ruuvipurkaimen valmistettavuuden parantamisessa saavutettiin tavoite, 10 % kustannussäästö valmistuskustannuksissa. Valmistettavuutta saatiin paremmaksi DFMA-menetelmiä soveltaen ja sitä kautta tuli kustannussäästöjä. Ostokomponenttien toimittajakartoituksella saatiin myös kustannuksia karsittua. Käytetty DFMA-menetelmä hieman sovellettuna oli tälle tuotteelle toimiva vaihtoehto. Jatkamalla valmistusystävällistä suunnittelua kalleimmille osille, saataisiin enemmän kustannussäästöjä mihin tässä työssä päästiin.