Continuum Mechanics-based Model Research Articles

Physical determinants of fibrinolysis in single fibrin fibers.

Fibrin fibers form the structural backbone of blood clots; fibrinolysis is the process in which plasmin digests fibrin fibers, effectively regulating the size and duration of a clot. To understand blood clot dissolution, the influence of clot structure and fiber properties must be separated from the effects of enzyme kinetics and perfusion rates into clots. Using an inverted optical microscope and fluorescently-labeled fibers suspended between micropatterned ridges, we have directly measured the lysis of individual fibrin fibers. We found that during lysis 64 ± 6% of fibers were transected at one point, but 29 ± 3% of fibers increase in length rather than dissolving or being transected. Thrombin and plasmin dose-response experiments showed that the elongation behavior was independent of plasmin concentration, but was instead dependent on the concentration of thrombin used during fiber polymerization, which correlated inversely with fiber diameter. Thinner fibers were more likely to lyse, while fibers greater than 200 ± 30 nm in diameter were more likely to elongate. Because lysis rates were greatly reduced in elongated fibers, we hypothesize that plasmin activity depends on fiber strain. Using polymer physics- and continuum mechanics-based mathematical models, we show that fibers polymerize in a strained state and that thicker fibers lose their prestrain more rapidly than thinner fibers during lysis, which may explain why thick fibers elongate and thin fibers lyse. These results highlight how subtle differences in the diameter and prestrain of fibers could lead to dramatically different lytic susceptibilities.

A numerical model for the deterministic analysis of adhesive rough contacts down to the nano-scale

A numerical model based on the Multi-Level Multi-Integration technique has been developed to study the adhesion between two surfaces. The model provides a self-consistent solution of surface separation and contact pressure throughout an arbitrary surface contact (including random surface roughness) with the adhesive interactions governed by the Lennard-Jones potential. Using this approach, the behaviour of rough surfaces can be assessed with a deterministic description of the surface, and contact stresses include valid adhesive interactions between all non-contacting surface nodes. The model is first compared to similar analyses from smooth surface models, where good agreement with published results is obtained. The model is then applied to randomly rough surfaces and shows both the significant impact of roughness on adhesive behaviour and how individual surface asperities influence the loading–unloading response of adhesive contacts. Lastly, the ability of the model to investigate nano-scale contacts is assessed through comparisons with atomistic simulations previously published elsewhere. It is clearly shown that our continuum mechanics-based model, in which an atomistic configuration is represented by a discretised continuum representation of the surface using a hard-sphere atomic model, is capable of reproducing many of the features identified through detailed atomistic simulations. The suitability of the presented model for studying adhesive contacts from the nano-scale to much larger, soft contacts, where adhesive forces can alter the contact mechanics, is demonstrated. The developed modelling tool and the algorithms implemented by the authors open the possibility to perform fast and accurate calculations using a deterministic description of the roughness for a wide variety of contact conditions.

GPU‐based acceleration of computations in nonlinear finite element deformation analysis

The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation.

The role of 3-D collagen organization in stromal elasticity: a model based on X-ray diffraction data and second harmonic-generated images

Examining the cross-section of the human cornea with second harmonic-generated (SHG) imaging shows that many lamellae do not lie parallel to the cornea's anterior surface but have inclined trajectories that take them through the corneal thickness with a depth-dependent distribution. A continuum mechanics-based model of stromal elasticity is developed based on orientation information extracted and synthesized from both X-ray scattering studies and SHG imaging. The model describes the effects of inclined lamella orientation by introducing a probability function that varies with depth through the stroma, which characterizes the range and distribution of lamellae at inclined angles. When combined with the preferred lamellar orientations found from X-ray scattering experiments, a fully 3-D representation of lamella orientation is achieved. Stromal elasticity is calculated by a weighted average of individual lamella properties based on the spatially varying 3-D orientation distribution. The model is calibrated with in vitro torsional shear experiments and in vivo indentation data and then validated with an in vitro inflation study. A quantitative explanation of the experimentally measured depth dependence of mechanical properties emerges from the model. The significance of the 3-D lamella orientation in the mechanics of the human cornea is demonstrated by investigating and contrasting the effects of previous modeling assumptions made on lamella orientation.

Numerical study on the entrainment of bed material into rapid landslides

The entrainment of channel-path material plays an important role during runout of many rapid landslides. Such a mechanism is able to change the mobility of a flow significantly, through rapid changes of the flow volume and rheology. The purpose of this paper is to use mathematical, rheological and constitutive models to analyse the entrainment effect on runout analysis results. After a brief review and classification of some well-established erosion laws, a simple, yet effective, empirical formula for the entrainment rate has been selected, and is implemented in a continuum mechanics-based numerical model. First, some hypothetical examples are used to test the effectiveness of the implemented entrainment process, and to evidence the respective role of entrainment and topography on a flow propagation. Then a back-analysis is presented of the 2000 Tsing Shan event (Hong Kong), where a small volume of 150 m3 of material grew to 1620 m3 because of the strong erosion along the slope. From the results obtained, it emerges that the new model with erosion implemented can provide a useful contribution in describing the consequences of mass movements in which the entrainment process can play a key role.

생체조직의 원격촉진시스템을 위한 연속체역학 기반의 환경 모델링

The capability to bilaterally telemanipulate soft-tissues for medical applications could increase the quality of telemanipulation systems. Since most soft-tissue manipulation tasks include constrained motion interacting with an unknown and dynamic bioenvironment through contact, bilateral telemanipulation raises problems due to stability and transparency issues. It is well understood that knowledge of environments plays an important role in pursuing transparent telemanipulation and achieving telepresence, and in particular, online estimation of environmental parameters with an explicit environment model can improve these systems' performance. In this study, a continuum mechanics-based environment model with an online environmental property estimation algorithm and an adaptive telemanipulation control scheme is proposed. The proposed method can improve the telemanipulation performance in terms of stability and transparency and can offer valuable information (e.g., elastic modulus of soft tissues) pertaining to diagnostic examinations.

A mechanobiological investigation of platelets

Understanding mechanotransduction pathways leading to thrombosis will require progressive steps, including determination of the mechanical behavior of the platelet membrane in response to applied loads. The platelet membrane deformation capacity, as quantified by membrane progression into a borosilicate glass micropipette of defined internal diameter, was probed in murine platelets using a controlled range of negative pressure (0-7cmH(2)O). Based on our observations that the platelet portion outside the micropipette was mostly spherical and that the platelet volume did not change upon aspiration, a novel continuum mechanics-based model of the platelet micropipette aspiration experiment was created, and a new hyperelastic isotropic material model including membrane residual tension was proposed for the platelet membrane. Murine platelet membranes maintained an average linear deformation behavior: L (p)/R (p) =146,100p (i)× R (p) + 19.923, where L (p) is the platelet length aspirated in the micropipette (m), R (p) is micropipette radius (m) and p (i) is the aspiration pressure (Pa). The theoretical model was used to generate material constants for the murine platelet membrane that allowed for an accurate simulation of the micropipette aspiration experiments. From published results, another set of material constants was established for the human platelet membrane. Limited cases of platelet lysis upon aspiration were analyzed using the theoretical model to determine preliminary membrane tension strength values.

Size effects in polyurethane bonds: experiments, modelling and parameter identification

In this study we examine polyurethane bonds of varying thickness between anodised aluminium substrates. The performed shear tests showed an intriguing size effect of the kind “thinner equals softer”. This size effect occurs not only in the basic elasticity (relaxed state), but also in the viscoelastic behaviour of the tested material. The cause of such size effects is supposed to be found in the existence of so-called interphases or boundary layers, which may differ considerably from the bulk in terms of mechanical behaviour, thus having an enormous impact on thin bonds. In thick bonds, however, these interphases or boundary layers have a minor effect on the overall mechanical behaviour. To account for these experimental results in bond modelling, an extended phenomenological continuum mechanics-based model, which explicitly includes such size effects in its calculation, is developed and presented. For this purpose, an abstract structure parameter with its corresponding balance equation is established describing the formation of the interphases by means of a phase transition. This makes it possible to define the bond stiffness at a macroscopic level, without entering into the microstructure. The extended model brings up a set of model parameters, which are determined efficiently by an ES (evolution strategy). The study concludes with a summary and an outlook on our further research work.

Advances in continuum mechanics-based models of the arterial wall

Advances in continuum mechanics-based models of the arterial wall

Application of Finite Deformation Theory to the Development of an Orthogonal Cutting Model—Part I: Model Development

An orthogonal cutting model is developed using the finite deformation theory of continuum mechanics. A family of flowlines is proposed to describe the chip flow during orthogonal cutting, and the shape of the flowlines is described in terms of three parameters, one of which is the shear angle. The velocity, Eulerian strain, and Eulerian strain rate distribution along the assumed flowlines are obtained analytically for the orthogonal cutting operation based on this model. The temperature distribution along the flowline is predicted via a finite difference method. Values for the three flowline parameters are selected that minimize the total power associated with primary shear zone deformation and chip-tool interaction using the Davidon-Fletcher-Powell optimization scheme. The model utilizes a general constitutive equation for material behavior, which is a function of strain, strain rate, and temperature. In Part I of this two-part paper, the continuum mechanics-based model for the orthogonal cutting process is established. Experimental assessment and adequacy checking of the model, including determination of the material constitutive equation using a split Hopkinson pressure bar technique, is presented in Part II of the paper.

A Continuum Mechanics-based Model for Cortical Growth

One method for the synthesis of object shapes is by using physical laws. A continuum mechanics-based model of growth is proposed here. An energy functional of the shape of an elastic object, is defined. At every instant of the growth process, the shape of the object corresponds to a minimum of this energy functional; growth is taken to be aquasistaticprocess. The model is used to simulate the growth of a one-dimensional “brain cortex”. Starting from almost smooth initial configurations, growth leads to the formation of complex folds or convolutions. It is demonstrated that apart from the constraint of fitting in the skull, two other constraints are both necessary and sufficient to robustly generate patterns actually seen in cortical contours. These are: a minimum thickness for cortical folds due to white matter, and a shear constraint on the white matter tracts. Finally, an interesting difference between periodic and non-periodic initial conditions is pointed out.

Prediction of steady state creep behavior of two phase composites

A simple continuum mechanics-based model has been developed to predict the steady state creep rates of composites containing coarse and rigid reinforcements from the matrix creep behavior. The model has been derived on the basis of a unit cell, representative of the composite microstructure, which is idealized to a pattern of periodic, cubic inclusions distributed uniformly in a continuous creeping matrix. Comparisons of the predicted creep rates are made with the experimental data of a number of two phase systems as well as transversely loaded continuous fiber reinforced composites. A good agreement between the predicted and measured creep rates is seen for most of the systems. However, for some composites, the calculations overestimate the creep rates significantly at intermediate volume fractions, typically, 0.3–0.4. It is suggested that factors such as the differences between the microstructure of the matrix in the composite and that of the monolithic matrix could be responsible for the differences in the predicted and experimentally measured creep behavior. Finally, an assessment of the predictions of the model proposed in this study with rigorous, self-consistent calculations as well as finite element simulations has been made.