Chemo-mechanical Model Research Articles

The Non-Equilibrium Thermodynamics and Kinetics of Focal Adhesion Dynamics

BackgroundWe consider a focal adhesion to be made up of molecular complexes, each consisting of a ligand, an integrin molecule, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes and thereby controls the focal adhesion's dynamic modes of growth, treadmilling and resorption.Principal FindingsWe have identified a competition among four thermodynamic driving forces for focal adhesion dynamics: (i) the work done during the addition of a single molecular complex of a certain size, (ii) the chemical free energy change associated with the addition of a molecular complex, (iii) the elastic free energy change associated with deformation of focal adhesions and the cell membrane, and (iv) the work done on a molecular conformational change. We have developed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. We also express the rates as being driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow focal adhesions to exhibit a rich variety of behavior without the need to introduce special constitutive assumptions for their response. For the reaction-limited case growth, treadmilling and resorption are all predicted by a very simple chemo-mechanical model. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (i) above. In contrast, depending on its numerical value (ii) causes symmetric growth, resorption or is neutral, (iii) causes symmetric resorption, and (iv) causes symmetric growth. These findings hold for a range of conditions: temporally-constant force or stress, and for spatially-uniform and non-uniform stress distribution over the FA. The symmetric growth mode dominates for temporally-constant stress, with a reduced treadmilling regime.SignificanceIn addition to explaining focal adhesion dynamics, this treatment can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility.

Muscle contraction: A mechanical perspective

In this paper we present a purely mechanical analog of the conventional chemo-mechanical modeling of muscle contraction. We abandon the description of kinetics of the power stroke in terms of jump processes and instead resolve the continuous stochastic evolution on an appropriate energy landscape. In general physical terms, we replace hard spin chemical variables by soft spin variables representing mechanical snap-springs. This allows us to treat the case of small and even disappearing barriers and, more importantly, to incorporate the mechanical representation of the power stroke into the theory of Brownian ratchets. The model provides the simplest non-chemical description for the main stages of the biochemical Lymn-Taylor cycle and may be used as a basis for the artificial micro-mechanical reproduction of the muscle contraction mechanism.

Chemomechanics with molecular force probes

Chemomechanics is an emerging area at the interface of chemistry, materials science, physics, and biology that aims at quantitative understanding of reaction dynamics in multiscale phenomena. These are characterized by correlated directional motion at multiple length scales—from molecular to macroscopic. Examples include reactions in stressed materials, in shear flows, and at propagating interfaces, the operation of motor proteins, ion pumps, and actuating polymers, and mechanosensing. To explain the up to 1015-fold variations in reaction rates in multiscale phenomena—which are incompatible within the standard models of chemical kinetics—chemomechanics relies on the concept of molecular restoring force. Molecular force probes are inert molecules that allow incremental variations in restoring forces of diverse reactive moieties over hundreds of piconewtons (pN). Extending beyond the classical studies of reactions of strained molecules, molecular force probes enable experimental explorations of how reaction rates and restoring forces are related. In this review, we will describe the utility of one such probe—stiff stilbene. Various reactive moieties were incorporated in inert linkers that constrained stiff stilbene to highly strained macrocycles. Such series provided the first direct experimental validation of the most popular chemomechanical model, demonstrated its predictive capabilities, and illustrated the diversity of relationships between reaction rates and forces.

A multiscale model for modulus of elasticity of concrete at high temperatures

In this paper, the thermal degradation of modulus of elasticity of concrete is modeled by composite mechanics at three scales of observation: (a) at the level of concrete, (b) at the level of mortar, and (c) the cement paste level. At the latter, the change of volume fractions of the constituents are evaluated based on phase transformations which take place in different temperature ranges. Stoichiometric models are used to determine the volume changes of the constituents. At the mortar and concrete levels, the temperature dependence of fine and coarse aggregates is considered based on available test data. The multiscale chemo-mechanical model can be used to predict the temperature dependence and thermal degradation of the elastic concrete modulus. The model predictions are compared with test data in the literature as well as in-house test data.

A Transient Simulation for Analysis of Volume Transition of pH-Sensitive Hydrogel in Micro-Channel

Based on Donnan’s equilibrium, a simple chemo-mechanical model is developed to study the transient swelling behavior of the pH-sensitive hydrogel for design and optimization of smart hydrogel-based BioMEMS device. The model is mathematically composed of several governing equations, including Fick’s law which describes the diffusion process in the buffer solution, the fixed charge density formula associated with pH value of the buffer solution, and mechanical equation which gives the swelling ratio responding to pH. The model also considers several chemical conditions, including Donnan’s equilibrium condition which gives Donnan partitioning ratio relating to the concentrations of ionic species in the interior hydrogel and the external solution, the electroneutrality condition in the interior hydrogel and bathing solution as well. The model is capable of predicting the kinetics process of the smart hydrogel immersed in buffer solution with change in pH. The simulation of the diffusion-swelling behavior of the pH-sensitive hydrogel is presented, and the responsive deformation of the smart hydrogel to the solution pH is discussed in detail.

Feedback mechanisms in chemo-mechanical multi-scale modeling of soil and sediment compaction

Geomaterials respond to some environmental circumstances through generation of a series of feedback mechanisms of damage, deformation, erosion, and chemical processes or reactions: e.g. osmosis, dissolution and precipitation, mineral transformations. These mechanisms are coupled at different scales. Several natural geomechanical processes, as sediment compaction, rock weathering or landsliding appear to include such sequences of mechanisms. A multi-physics model of sediment compaction is examined from the point of view of feedbacks and feedforwards for the phenomena involved at micro- and meso-scale. Two types of feedback are identified: constitutive feedbacks and boundary condition feedbacks. A numerical sensitivity study points out which feedbacks and feedforwards are strong and which are weak.

Interfacial properties of compressible polymer solutions

AbstractA chemomechanical model for the interfacial concentration and density in compressible polymer solutions is formulated using variational principles. The nonlinear model with boundary conditions obtained from phase equilibrium calculations gives the coupled concentration and density profiles. The couplings between chemical and mechanical balances are identified and efficient ways to calculate the interfacial structure is identified. A specific model appropriate to high‐pressure processing of the polyolefins is developed using the modified Sanchez Lacombe equation of state. Bakker's formula for the interfacial tension is adapted to compressible polymer solutions. The structure and tension of a flat interface is characterized using the developed model and material properties of three molecular weight hydrogenated polybutadiene; the main variables of interest were the pressure, polymer molecular weight, and temperature. The relation between the pressure profile across the interface and the interfacial tension is characterized. Scaling power laws for interfacial tension and interfacial thickness as a function of pressure are obtained and contrasted with the corresponding laws observed and predicted for incompressible polymer solutions. It is found that the modified Sanchez Lacombe‐based power law prediction predictions for compressible solutions in terms of pressure quenches are similar to those from those obtained by the Flory‐Huggins incompressible model for temperature quenches. The present results provide the basis for the future study of the kinetics of pressure‐induced phase separation in compressible polymer solutions. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 640–654, 2009

Experimental study of mechanical behaviour of cement paste under compressive stress and chemical degradation

This paper presents experimental investigations of mechanical behaviour of a pure cement paste subjected to compressive stresses and chemical degradation. Two series of laboratory tests have been performed: decoupled and coupled chemical-mechanical tests. Hydrostatic and triaxial compression tests have first been realized respectively on sound and chemically degraded samples. The obtained results allow the characterization of basic mechanical responses of the tested cement paste and the identification of chemical degradation effects on the mechanical behaviour. In the coupled tests, the samples are simultaneously subjected to deviatoric stresses and chemical leaching by aggressive solution flow. Variations of deformation of cement paste samples are measured during chemical degradation process. The results obtained in these tests can be used for the validation of chemo-mechanical constitutive modelling.

Articular cartilage with intra and extrafibrillar waters – Simulations of mechanical and chemical loadings by the finite element method

In line with previous constitutive developments, a three-phase multi-species electro-chemo-mechanical model of articular cartilage that accounts for the effect of two water compartments is pursued. Here, a finite element formulation is presented in order to solve initial and boundary value problems and to simulate the time and space heterogenous fields generated by mechanical and chemical loadings in laboratory samples. The formulation capitalizes upon (1) the chemo-mechanical model in Loret and Simões [B. Loret, F.M.F. Simões, Articular cartilage with intra- and extra-fibrillar waters. A chemo-mechanical model, Mech. Mater. 36 (5–6) (2004) 515–541; B. Loret, F.M.F. Simões, Mechanical effects of ionic replacements in articular cartilage. I. The constitutive model, Biomech. Model. Mechanobiol. 4 (2–3) (2005) 63–80; Mechanical effects of ionic replacements in articular cartilage. II. Simulations of successive substitutions of NaCl and CaCl 2 , Biomech. Model. Mechanobiol. 4 (2–3) (2005) 81–99] which was restricted to successive equilibria, and from which both time and space were excluded; and (2) the model in Loret and Simões [B. Loret, F.M.F. Simões, Articular cartilage with intra- and extra-fibrillar waters. Mass transfer and generalized diffusion, Eur. J. Mech.-A/Solids 26 (1995) 759–788], where the equations of mass transfer between the two fluid phases and the generalized diffusion equations in the extrafibrillar phase have been established. A thin cartilage layer, laterally confined, is loaded through time varying mechanical and chemical conditions applied on the lower and upper boundaries. Two types of chemical loadings are simulated. First the concentration of NaCl in the bath in contact with the cartilage is changed according to several time schemes, including in particular free swelling and cyclic changes. A more complex process consists in replacing NaCl by CaCl 2 . Chemical loading gives rise to heterogeneous fields during a transient period, whose extend depends on geometry and on a number of characteristic material properties, e.g. Darcy’s seepage time, Fick’s diffusion time, and typical times for intercompartmental mass transfer. Mechanical confined compression and swelling tests are simulated as well. Spatial profiles of the various chemical species and mechanical, chemical and electrical entities highlight the influences of the existence of two water compartments. At steady state, the strains, stresses, pressures and the distribution of water and ions in the two compartments obtained in Loret and Simões [B. Loret, F.M.F. Simões, Articular cartilage with intra- and extra-fibrillar waters. A chemo-mechanical model, Mech. Mater. 36 (5–6) (2004) 515–541; B. Loret, F.M.F. Simões, Mechanical effects of ionic replacements in articular cartilage. I. The constitutive model, Biomech. Model. Mechanobiol. 4 (2–3) (2005) 63–80; Mechanical effects of ionic replacements in articular cartilage. II. Simulations of successive substitutions of NaCl and CaCl 2 , Biomech. Model. Mechanobiol. 4 (2–3) (2005) 81–99] are recovered.

Chemo-Mechanical Removal of Caries in an Adolescent Patient Using a Papain Gel: Case Report

The chemo-mechanical model of caries removal has been introduced as an alternative method of caries removal and is indicated to overcome the inconvenience of using burs and local anesthesia, causing less discomfort to the patient, and preserving healthy dental structure. Papacarie is a papain gel composed basically of papain, chloramines, and toluidine blue. Papain interacts with exposed collagen by the dissolution of dentin minerals through bacteria, making the infected dentin softer, and allowing its removal with non-cutting instruments without local anesthesia and burs. This paper proposes the use of a papain-based gel for the removal of active caries with infected tissue followed by a glass ionomer restoration in an adolescent patient. Removal of caries tissue with Papacarie proved to be efficient, easy and comfortable for the patient.

Chemo-mechanical coupling behaviour of leached concrete: Part II: Modelling

The paper is concerned with a coupled chemo-mechanical model describing the interaction between the calcium leaching and the mechanical damage in concrete materials. On the one hand, the phenomenological chemistry is described by the nowadays well-known simplified calcium leaching approach. It is based on the dissolution–diffusion process together with the chemical equilibrium relating the calcium concentration of the solid's skeleton and the calcium in the pore solution. For concrete, a homogenization approach using asymptotic expansions is used to take into account the influence of the presence of the aggregates leading to an equivalent homogeneous medium. On the other hand, the continuum damage mechanics is used to describe the mechanical degradation of concrete. The modelling accounts for the fact that concrete becomes more and more ductile as the leaching process grows. The model also predicts the inelastic irreversible deformation as damage evolves. The growth of inelastic strains observed during the mechanical tests is described by means of an elastoplastic-like model. The coupled nonlinear problem at hand is addressed within the context of the finite element method. And finally, numerical simulations are compared with the experimental results of first part of this work.

Articular cartilage with intra- and extrafibrillar waters – mass transfer and generalized diffusion

The present analysis complements the chemo-mechanical model of articular cartilage developed in Loret and Simões [Loret, B., Simões, F.M.F., 2004. Articular cartilage with intra- and extrafibrillar waters. A chemo-mechanical model. Mech. Mater. 36 (5–6), 511–541; Loret, B., Simões, F.M.F., 2005a. Mechanical effects of ionic replacements in articular cartilage. Part I – The constitutive model. Biomech. Model. Mechanobiol. 4 (2–3), 63–80. Part II – Simulations of successive substitutions of NaCl and CaCl 2 , 81–99], where only equilibria were considered, and therefore time was absent. The focus here is, first, to present how transport phenomena are aggregated to the porous media framework, and, second, to detail the constitutive equations of these transports. Indeed, these equations are developed in the context of a three-phase multi-species electro-chemo-mechanical model that accounts for the effects of two water compartments, namely intrafibrillar water stored between collagen fibrils and extrafibrillar water covering the negatively charged proteoglycans. The electrolyte circulating the two fluid phases contains ions sodium Na + , calcium Ca 2+ and chloride Cl − . Species diffuse within their phase. They transfer from one fluid phase to the other. The various sources of dissipation are built in a thermodynamic framework, segregated and decoupled via the Clausius–Duhem inequality. Linear and non-linear equations of mass transfer are proposed along an onsagerist approach. The generalized diffusion in the extrafibrillar compartment accounts for Darcy's law of seepage through the porous solid skeleton, Fick's law of ionic diffusion, and Ohm's law of electric flow. An original derivation of the constitutive equations of generalized diffusion is proposed. Indeed, the dissipation inequality is written in two forms, which are required to be equivalent. This approach has the advantage of delivering the general structure of the diffusion matrix. It also displays in explicit form the degrees of freedom for possible refinements. Simple assumptions, phrased in terms of entities that are standard in transport of porous media, allow to recover arrowhead diffusion matrices. Comparison with an earlier proposal is detailed. An osmotic coefficient is found to be hidden in the equations, and anomalous negative osmosis is observed to take place for both sodium chloride and calcium chloride electrolytes. Finally, an experimental setup to measure transport properties is analyzed. The model describes correctly the increase and leveling of the experimental diffusion coefficient, and no additional ad hoc constitutive assumptions are needed in contrast to some suggestions in the literature. The results are presented for sodium chloride NaCl and calcium chloride CaCl 2 .

Chemo-mechanical Model for Actuation Based on Biological Membranes*

Plants have the ability to develop large mechanical force from chemical energy available with bio-fuels. The energy released by adenosine tri-phosphate (ATP) hydrolysis assists the transport of ions and fluids to achieve volumetric expansion and homeostasis. Materials that develop pressure and hence strain similar to bio-materials are classified as nastic materials. Recent calculations for controlled actuation of an active material inspired by biological transport mechanism demonstrated the feasibility of developing such a material with actuation energy densities on the order of 100 kJ/m3. The initial investigation was based on capsules that generate pressure, thus causing strain in the surrounding matrix material. This paper focuses on our efforts to fabricate a representative actuation structure and describes the chemo-mechanical constitutive equation for such a material. The actuator considered in this work is a laminated plate dispersed with biological transporters. The initial design and a mathematical model to predict the fluid flux and strain developed in such an actuator are presented here.

An instructive chemo-mechanical model for bonded geomaterials

An instructive chemo-mechanical model for bonded geomaterials

Interaction of mechanical and electrochemical factors in erosion–corrosion of carbon steel

The interaction of mechanical and electrochemical factors in the erosion–corrosion process of carbon steel A1045 was investigated in Na 2SO 4 solution/silica sand slurry with a rotating cylinder electrode system. In line with the mechanism associated with material wastage, the synergism due to the interaction of erosion and corrosion was divided into corrosion-enhanced erosion and erosion-enhanced corrosion. The electrochemical experimental results indicated that the carbon steel showed active dissolution behavior, and the corrosion process was not controlled by the mass transfer when the rotating velocity is high enough. Scratching electrode tests and tensile tests were conducted to simulate the effect of sand impingement on corrosion process. Results showed that the impingement of the solid did not affect the corrosion behavior significantly in the present system. For the effect of corrosion on erosion, a half-logarithm relationship was found between weight loss due to corrosion-enhanced erosion and the applied anodic current density. According to a chemo-mechanical model, this effect can be attributed to the hardness degradation in metal surface with corrosion current.

An instructive chemo-mechanical model for bonded geomaterials

ABSTRACT An elementary constitutive model to describe the behaviour of bonded soils or soft rocks subject to mechanical and/or chemical degradation is presented. To limit formalism as much as possible, the original Cam Clay model is taken as a starting point and axisymmetric conditions are considered. The effect of grain bonding is taken into account by one parameter that decreases with increasing strains and amount of chemical attack. Comparisons with experimental data in laboratory tests are shown together with two applications.

A computational setting of calcium leaching in concrete and its coupling with continuum damage mechanics

We present in this work a coupled phenomenological chemo-mechanical model that represents the degradation of concrete-like materials. The chemical behaviour is described by the nowadays well known simplified calcium leaching approach. And the mechanical damage behaviour is described by a continuum damage model which involves the gradient of the damage quantity. The coupled nonlinear problem at hand is addressed within the context of the finite element method. For the equation governing the calcium dissolution-diffusion part of the problem, special care is taken to treat the highly nonlinear calcium conductivity and solid calcium functions. The algorithmic design is based on a Newton-type iterative scheme where use is made of a recently proposed relaxed linearization procedure. And for the equation governing the damage part of the problem, an augmented Lagrangian formulation is used to take into account the damage irreversibility constraint. Finally, numerical simulations are compared with experimental results on cement paste.

Coupled chemo-mechanical deterioration of cementitious materials Part II: Numerical methods and simulations

The paper is concerned with numerical solution procedures for coupled chemo-mechanical simulations of concrete structures subjected to calcium leaching and mechanical damage. The analyses are based upon the chemo-mechanical damage model for cementitious materials presented in the first part of the paper [Int. J. Solids Struct., in press]. These analyses are characterized by a non-linear transient two-field problem described by the displacement field, the pore fluid calcium concentration field and its rate as state variables. The related non-linear first order initial boundary value problem is solved numerically by a semi-discretization strategy. For the temporal discretization the second order accurate implicit generalized mid-point rule is used. The spatial discretization is based upon hierarchical finite elements. The non-linear algebraic system of equations is solved by consistent linearization and Newton–Raphson iteration. Representative simulations of calcium leaching and the coupled chemo-mechanical degradation of concrete structures are presented. In particular, the process of calcium leaching is studied in detail by means of a one-dimensional model problem. Chemo-mechanical interactions on the structural level are investigated in the numerical simulation of a concrete beam subjected simultaneously to mechanical loads and deionized water. It is demonstrated that chemical damage not only reduces the limit load and the stiffness of concrete structures but also their structural behavior.

Coupled chemo-mechanical deterioration of cementitious materials. Part I: Modeling

The paper is concerned with a coupled chemo-mechanical model describing the interaction of calcium leaching and mechanical damage in cementitious materials on a macroscopic level. Starting from the definition of the total porosity described in terms of the chemical dissolution and mechanical damage and the assumptions of chemical and mechanical potentials, the model is consistently developed within the theories of mixtures and thermodynamics. The displacement vector and the calcium concentration of the pore fluid are taken as the primary variables of the coupled field problem. The model is able to capture degradation of the stiffness and strength following from chemical and mechanical damage as well as the increasing conductivity due to matrix dissolution and the opening of micro-cracks. The irreversible character of chemical and mechanical degradation processes is taken into account by internal variables and related chemical reaction and mechanical damage criteria together with conditions for progressing chemical dissolution in the form of Kuhn–Tucker conditions. The properties and the capabilities of the present model are illustrated by a detailed analysis.

Apport de la modélisation à l'expertise des infrastructures atteintes par la réaction alcali–silice

The alkali–silica reaction is an internal chemical process in concrete between the reactive silica in aggregate and the pore solution. The chemical product is more or less structured and could create an internal material expansion and the accumulated pressure surpassing the material tension strength. The reaction's impact on the durability of infrastructure in concrete is well-known and becomes a structure management and maintenance concern. To this end numerous research efforts are dedicated to quantify the behavior of affected concrete. After a brief retrospective of the acquired chemical knowledge and the available chemo-mechanical models, the structural degradation quantification is treated in two typical cases: one with the reconstituted expansion characteristics of original concrete and the other without this information. Then the use of available models in each case and the result's credibility are discussed. Finally, some general conclusions are drawn on how to make a rational use of the laboratory models.