A micromechanical Sliding-Damage Model Under Dynamic Compressive Loading

For most rock materials, there exists a strong coupling between plastic flow caused by sliding along micro-crack faces and damage evolution due to nucleation and growth of wing-cracks. The aim of this article is to develop the self-consistent based micromechanical model by taking into account the coupling between frictional sliding and damage process under dynamic compressive loading. The developed model algorithm was programmed in the commercial finite difference software environment for numerical simulation of rock material to investigate the relationship between the mechanical behaviour and microstructure. Eventually while the stress intensity factor at flaw tips exceeds the material fracture toughness, the wing-cracks are sprouted and damage evolution occurs. For frictional closed cracks, an appropriate criterion for the onset of frictional sliding along micro-cracks was proposed in this paper. Also, plastic strain increments were determined by the flow rule, consistency condition and normality rule within the thermodynamic framework. The simulation results demonstrate that the developed micromechanical model can adequately reproduce many features of the rock behaviour such as hardening prior to the peak strength, softening in post-peak region, damage induced by wing-cracks and irreversible deformations caused by frictional sliding along micro-cracks. Furthermore, the softening behaviour of material in post-peak region is affected and the material undergoes higher values of strains and damage up to the residual strength. Therefore, the rock sample simulation with the coupled frictional sliding-damage model could increase plasticity and ductility of the rock in post-peak region because of regarding plastic strains caused by the frictional sliding along micro-cracks

Investigating Mechanical Interactions of Cells with Their Environment

Recent studies have shown that cells not only respond to chemical signals such as growth factors or chemoattractants, but they are also capable of detecting mechanical stimuli and responding to them. The process during which these mechanical stimuli are detected and transferred to chemical signals, that cells can process, is called mechanotransduction. The mechanical stimuli that can affect cells can be either an external stimulus applied to cells, such as shear flow or cyclic compression and tension, or they can be linked to the mechanical properties of their substrates. One of the mechanical properties of a substrate that can affect cellular behavior is known to be stiffness, mostly measured by elastic modulus. Stiffness influences a wide variety of cellular behaviour such as cell shape, adhesion to substrate, proliferation, and differentiation. Anchorage dependent cells are in direct contact with their environment, which then leads to complicated interactions. These interactions can be both biological and mechanical. In the current research, the mechanical interactions are often called the “mechanical responses” of cells. For anchorage-dependent migrating cells, mechanical responses can be the substrate deformations induced by the forces generated by cells also called cell traction forces. These mechanical responses can be studied in three levels of complexity. The first level is when cells are cultured on a 2D matrix and responses are also studied in 2D. The second level of complexity is when cells are cultured on a 2D matrix and the biological behaviour of cells, such as growth or migration, is studied in 2D, however, the mechanical responses of cells are studied in 3D, meaning that not only in plane deformation and forces are studied, but out of plane ones are also assessed. The third level of complexity is when cells are cultured inside a 3D matrix and both biological responses and mechanical responses are studied in 3D. In the current research, the second level of complexity is chosen. After testing different types of materials, polyacrylamide (PAAm) was chosen as the model biomaterial. Following mechanical characterization of PAAm samples, substrates were prepared with three different elastic moduli. Both biological responses and mechanical responses of human corneal epithelial cells (HCECs) were studied. For biological responses, cell viability, activation, adhesion molecules, apoptosis and migration behaviour were studied. For mechanical responses, confocal microscopy in junction with image processing technique, digital volume correlation (DVC), was used to measure cell induced deformations. It was found that elastic modulus, as a mechanical stimulus, affects not only biological behaviour of cells, but also their mechanical behaviour. Decreasing elastic modulus led to significantly lower migration speed of HCECs, slightly higher number of apoptotic cells as well as significantly higher number of necrotic cells. Furthermore, while no significant changes in adhesion molecules occurred, dramatic changes in cytoskeleton structure was seen on cells cultured on compliant matrices. Also, the DVC code was capable of detecting both in plane and out of plane deformations from confocal images. It was found that substrate elastic modulus can change the pattern of displacements on compliant substrate compared to stiff ones. Results of the present study suggest that the deformation pattern and magnitude does not change over the body of cells and that they are rather similar in the leading edge and trailing edge. Deformation under the nucleus was also assessed and for compliant and stiff substrates were present while no deformation was found under the cells cultured on medium stiffness substrates. It was also speculated that mechanical interaction of HCECs with their substrates can be more complicated than currently known and cells seem to be able to exert moments on their substrate as well as forces. Results presented in this thesis demonstrate that HCECs are sensitive to substrate stiffness and elastic modulus can affect their behaviour. Furthermore, considering the complexity of HCECs mechanical interaction with their substrates, it is critical to study both biology and mechanics for full comprehension of cellular interaction with the ocular environment

Gamma-irradiated human amniotic membrane decellularised with sodium dodecyl sulfate is a more efficient substrate for the ex vivo expansion of limbal stem cells

yesThe gold standard substrate for the ex vivo expansion of human limbal stem cells (LSCs) remains the human amniotic membrane (HAM) but this is not a defined substrate and is subject to biological variabil-ity and the potential to transmit disease. To better define HAM and mitigate the risk of disease transmis-sion, we sought to determine if decellularisation and/or c-irradiation have an adverse effect on culture growth and LSC phenotype. Ex vivo limbal explant cultures were set up on fresh HAM, HAM decellularised with 0.5 M NaOH, and 0.5% (w/v) sodium dodecyl sulfate (SDS) with or without c-irradiation. Explant growth rate was measured and LSC phenotype was characterised by histology, immunostaining and qRT-PCR (ABCG2, DNp63, Ki67, CK12, and CK13). Ƴ-irradiation marginally stiffened HAM, as measured by Brillouin spectromicroscopy. HAM stiffness and c-irradiation did not significantly affect the LSC phe-notype, however LSCs expanded significantly faster on Ƴ-irradiated SDS decellularised HAM (p < 0.05) which was also corroborated by the highest expression of Ki67 and putative LSC marker, ABCG2. Colony forming efficiency assays showed a greater yield and proportion of holoclones in cells cultured on Ƴ-irradiated SDS decellularised HAM. Together our data indicate that SDS decellularised HAM may be a more efficacious substrate for the expansion of LSCs and the use of a c-irradiated HAM allows the user to start the manufacturing process with a sterile substrate, potentially making it safer

Badanie krzywej odpowiedzi gruntu (GRC) w oparciu o model pękania skał

Analysis of stresses and displacements around underground openings is necessary in a wide variety of civil, petroleum and mining engineering problems. In addition, an excavation damaged zone (EDZ) is generally formed around underground openings as a result of high stress magnitudes even in the absence of blasting effects. The rock materials surrounding the underground excavations typically demonstrate nonlinear and irreversible mechanical response in particular under high in situ stress states. The dominant cause of irreversible deformations in brittle rocks is damage process. One of the most widely used methods in tunnel design is the convergence-confinement method (CCM) for its practical application. The elastic-plastic models are usually used in the convergence-confinement method as a constitutive model for rock behavior. The plastic models used to simulate the rock behavior, do not consider the important issues such as stiffness degradation and softening. Therefore, the use of damage constitutive models in the convergence-confinement method is essential in the design process of rock structures. In this paper, the basic concepts of continuum damage mechanics are outlined. Then a numerical stepwise procedure for a circular tunnel under hydrostatic stress field, with consideration of a damage model for rock mass has been implemented. The ground response curve and radius of excavation damage zone were calculated based on an isotropic damage model. The convergence-confinement method based on damage model can consider the effects of post-peak rock behavior on the ground response curve and excavation damage zone. The analysis of results show the important effect of brittleness parameter on the tunnel wall convergence, ground response curve and excavation damage radius.Analiza naprężeń i przemieszczeń powstałych wokół otworu podziemnego wymagana jest przy szerokiej gamie projektów z zakresu budownictwa lądowego, inżynierii górniczej oraz naftowej. Ponadto, wokół otworu podziemnego powstaje strefa naruszona działalnością górniczą wskutek oddziaływania wysokich naprężeń, nawet w przypadku gdy nie są prowadzone prace strzałowe. Reakcja materiału skalnego znajdującego się w otoczeniu wyrobisk podziemnych jest zazwyczaj procesem nieliniowym i nieodwracalnym, zwłaszcza w stanach wysokich naprężeń in situ. Główną przyczyną nieodwracalnych odkształceń skał kruchych jest pękanie. Jedną z najczęściej stosowanych metod w projektowaniu tuneli (wyrobisk podziemnych) jest metoda konwergencji i zamknięcia, popularna ze względu na zakres zastosowań. Metoda ta zazwyczaj wykorzystuje modele sprężysto- plastyczne, jako konstytutywne modele zachowania skał. Modele plastyczne wykorzystywane dotychczas do symulacji zachowania skał nie uwzględniają pewnych kluczowych aspektów, takich jak obniżenie sztywności czy rozmiękczanie. Dlatego też zastosowanie konstytutywnych modeli w metodzie konwergencji i zamknięcia jest sprawą kluczową przy projektach obejmujących struktury skalne. W pracy tej omówiono podstawowe założenia modelu continuum uszkodzeń i spękań. Zaimplementowano wielostopniową procedurę do badania tunelu o przekroju kolistym znajdującego się pod polem naprężeń hydrostatycznych, przy wykorzystaniu modelu pękania górotworu. Krzywą odpowiedzi gruntu oraz promień strefy naruszonej wybieraniem obliczono przy wykorzystaniu izotropowego modelu uszkodzeń. Metoda konwergencji i zamykania oparta na tym modelu uwzględnia zachowanie skał po wystąpieniu szczytowych naprężeń i powstaniu strefy naruszonej wybieraniem. Analiza wyników wykazała znaczny wpływ parametrów związanych z kruchością na konwergencję ścian wyrobiska, kształt krzywej odpowiedzi gruntu oraz promień strefy naruszonej wybieraniem

Heterogeneous Rock Simulation Using DIP-Micromechanics-Statistical Methods

Rock as a natural material is heterogeneous. Rock material consists of minerals, crystals, cement, grains, and microcracks. Each component of rock has a different mechanical behavior under applied loading condition. Therefore, rock component distribution has an important effect on rock mechanical behavior, especially in the postpeak region. In this paper, the rock sample was studied by digital image processing (DIP), micromechanics, and statistical methods. Using image processing, volume fractions of the rock minerals composing the rock sample were evaluated precisely. The mechanical properties of the rock matrix were determined based on upscaling micromechanics. In order to consider the rock heterogeneities effect on mechanical behavior, the heterogeneity index was calculated in a framework of statistical method. A Weibull distribution function was fitted to the Young modulus distribution of minerals. Finally, statistical and Mohr–Coulomb strain-softening models were used simultaneously as a constitutive model in DEM code. The acoustic emission, strain energy release, and the effect of rock heterogeneities on the postpeak behavior process were investigated. The numerical results are in good agreement with experimental data

Numerical Analysis of the Segmental Supporting System Under Earthquake Loading

Today, precast concrete lining (segmental) are used as system maintenance in the majority of tunnels excavated by TBM. On the other hand, the mechanism of the joint between two segments is not known under seismic loads. In this paper a numerical study about the effect of the earthquake on the segmental supporting system and the resultant vertical and shear forces on the contact surface between two segments is investigated. The Tehran -Karaj water conveyance tunnel (Amirkabir) was used as a case study. In this study, the UDEC software was used. At the first step, the segmental lining were simulated under no slip and full slip conditions and the normal and shear forces were studied. Finally, the effect of joint stiffness between two segments were investigated. Results showed that with increasing the interface properties, the normal and shear forces in the segmental joints increased. Also with increasing the joints stiffness, the normal and shear forces on the joints increased and the normal and shear displacement decreased. In other words, the rigidity increament of supporting system is associated with flexibility decrement of lining with respect to rock medium. So, the stresses increased and displacement decreased

Model pękania skał oparty na sprzężonym elastoplastyczno-logarytmicznym modelu uszkodzeń

The rock materials surrounding the underground excavations typically demonstrate nonlinear mechanical response and irreversible behavior in particular under high in-situ stress states. The dominant causes of irreversible behavior are plastic flow and damage process. The plastic flow is controlled by the presence of local shear stresses which cause the frictional sliding. During this process, the net number of bonds remains unchanged practically. The overall macroscopic consequence of plastic flow is that the elastic properties (e.g. the stiffness of the material) are insensitive to this type of irreversible change. The main cause of irreversible changes in quasi-brittle materials such as rock is the damage process occurring within the material. From a microscopic viewpoint, damage initiates with the nucleation and growth of microcracks. When the microcracks length reaches a critical value, the coalescence of them occurs and finally, the localized meso-cracks appear. The macroscopic and phenomenological consequence of damage process is stiffness degradation, dilatation and softening response. In this paper, a coupled elastoplastic-logarithmic damage model was used to simulate the irreversible deformations and stiffness degradation of rock materials under loading. In this model, damage evolution & plastic flow rules were formulated in the framework of irreversible thermodynamics principles. To take into account the stiffness degradation and softening on post-peak region, logarithmic damage variable was implemented. Also, a plastic model with Drucker-Prager yield function was used to model plastic strains. Then, an algorithm was proposed to calculate the numerical steps based on the proposed coupled plastic and damage constitutive model. The developed model has been programmed in VC++ environment. Then, it was used as a separate and new constitutive model in DEM code (UDEC). Finally, the experimental Oolitic limestone rock behavior was simulated based on the developed model. The irreversible strains, softening and stiffness degradation were reproduced in the numerical results. Furthermore, the confinement pressure dependency of rock behavior was simulated in according to experimental observations.Zachowanie materiału skalnego otaczającego wyrobiska podziemne w odpowiedzi na wysokie stany lokalnych naprężeń działających in situ jest zazwyczaj nieodwracalne i nieliniowe. Reakcje nieodwracalne spowodowane są w głównej mierze przez płynięcie plastyczne i procesy uszkodzeń. Płynięcie plastyczne uwarunkowane jest przez występowanie lokalnych naprężeń ścinających powodujące obsunięcia skał. W trakcie tego procesu ilość wiązań netto pozostaje praktycznie niezmieniona. Całościowy efekt płynięcia plastycznego w skali makroskopowej polega na tym, że właściwości elastyczne (np. sztywność) stają się niewrażliwe na działanie nieodwracalnych procesów tego rodzaju. Podstawową przyczyną reakcji nieodwracalnych reakcji w materiałach quasi-kruchych, do których należą skały, jest powstawanie uszkodzeń wewnątrz materiału. W skali mikroskopowej, proces uszkodzenia rozpoczyna się od zainicjowania i stopniowej propagacji mikro-pęknięć. Gdy długość mikro- pęknięć osiągnie wartość graniczną, zaczynają one łączyć się ze sobą w rezultacie powodując powstanie lokalnych mezo-pęknięć. W ujęciu makroskopowym i fenomenologicznym, następstwami procesu uszkodzenia jest obniżenie sztywności, powstawanie dylatacji szczelin oraz miękniecie materiału. W pary wykorzystano sprzężony model elastoplastyczno- logarytmiczny do symulacji nieodwracalnych odkształceń i utraty sztywności materiału skalnego pod wpływem naprężeń. W modelu tym ewolucje uszkodzeń i opis płynięcia plastycznego sformułowano w oparciu o reguły nieodwracalnych przemian termodynamicznych. Aby uwzględnić utratę sztywności oraz miękniecie materiału w obszarach gdzie występowały największe naprężenia wykorzystano zmienną logarytmiczną opisującą uszkodzenie. Odkształcenia plastyczne zamodelowano z wykorzystaniem modelu plastycznego opartego na warunku plastyczności Drukera-Pragera. Zaproponowano także algorytm do obliczania kolejnych kroków procedury numerycznej, oparty na zaproponowanym modelu plastycznym oraz konstytutywnym modelu uszkodzeń. Opracowany model pracuje w środowisku VC++. Został on następnie wykorzystany jako osobny, nowy model konstytutywny zapisany w kodzie DEM (UDEC). W części końcowej przeprowadzono symulację zachowania wapienia oolitowego w oparciu o zaproponowany model. Nieodwracalne odkształcenia, utrata sztywności zostały odtworzone w postaci wyników procedury numerycznej. Ponadto, przeprowadzono symulacje zachowania skał w zależności od działającego na nie ciśnienia w oparciu o obserwacje eksperymentalne

A new constitutive model for the time-dependent behavior of rocks with consideration of damage parameter

Deformation and time-dependent behavior of rocks are closely related to the stability and safety of underground structures and mines. In this paper, a numerical-analytical model is presented to investigate time-dependent damage and deformation of rocks under creep. The proposed model is obtained by combining the elastic-visco-plastic model based on the theory of over-stress and stress hardening law with the sub-critical crack growth model. The advantage of this model is that it is in incremental form and therefore can be implemented numerically. First, the governing equations of the model and its numerical computational algorithm are described. The proposed constitutive model is then implemented in the FLAC code using the FISH function. Determination of model parameters and calibration is done by various laboratory tests performed on a type of gypsum. The creep test was performed on gypsum under a stress of 13 MPa, which is equal to 70% of its compressive strength. After determining the parameters, by fitting the creep curve of the presented analyticalnumerical model, a good agreement is observed with the creep curve obtained from the laboratory data. It is also observed that during creep, the damage parameter and wing crack length increase