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A simple, transparent, two-dimensional, nonlinear model of cell reorientation is constructed in this paper. The cells are attached to a substrate by "focal adhesions" that transmit the deformation of the substrate to the "stress fibers" in the cell. When the substrate is subjected to a deformation, say an in-plane bi-axial deformation with stretches λ 1 and λ 2 , the stress fibers deform with it and change their length and orientation. In addition, the focal adhesions can detach from the substrate and reattach to it at new nearby locations, and this process of detachment and reattachment can happen many times. In this scenario the (varying) fiber angle Θ in the reference configuration plays the role of an internal variable. In addition to the elastic energy of the stress fibers, the energy associated with the focal adhesions is accounted for by a wiggly energy ϵ a cos Θ / ϵ , 0 < ϵ ≪ 1 . Each local minimum of this energy corresponds to a particular configuration of the focal adhesions. The small amplitude ϵ a indicates that the energy barrier between two neighboring configurations is relatively small, and the small distance 2 π ϵ between the local minima indicates that a focal adhesion does not have to move very far before it reattaches. The evolution of this system is studied using a gradient flow kinetic law, which is homogenized for ϵ → 0 using results from weak convergence. The results determine (a) a region of the λ 1 , λ 2 -plane in which the (referential) fiber orientation remains stuck at the angle Θ and does not evolve, and (b) the evolution of the orientation when the stretches move out of this region as the fibers seek to minimize energy. [ABSTRACT FROM AUTHOR]

The fractured rock mass in the western cold region is affected by freezing and thawing disasters and is prone to local damage and fracture along the fissures' ends. The fatigue damage induced by repeated frost heave and traffic loads seriously endangers the stability of cold region roadbed. This paper selects sandstone as the research object. Firstly, 20 freeze–thaw cycles were performed on fractured sandstone samples with different inclination angles of 30°, 45°, 60°, and 90°. Subsequently, triaxial compression and triaxial fatigue loading tests were conducted to explore the mechanical properties and fracture morphology evolution mechanism during the compression process of freeze–thaw fractured sandstone. Nuclear magnetic resonance technology (NMR) was used to measure the H-containing fluid inside rock pores. The microscopic damage characteristics inside the rock were analyzed from the NMR T2 relaxation spectrum signal and pore size distribution characteristics. Based on the internal variable theory of continuum mechanics, a fatigue model of freeze–thaw fractured sandstone with different inclination angles was established. The results show that sandstone strength was negatively correlated with the fracture dip angle, and the axial deformation and shear failure angle were positively correlated with the fracture dip angle. The mechanical properties of the sandstone were deteriorated by fatigue loading. When the crack angle was 90°, the fatigue failure strength of the rock sample was the lowest. The T2 spectrum distribution of the fractured sandstone mainly had three peaks and the pore size was mainly medium and small pores. There was a small leftward shift after freeze–thaw cycles and fatigue loading. The T2 spectrum area was significantly affected by fatigue loading, with the highest rate of change at a crack angle of 30°. Through the fine correspondence between the axial residual deformation and the deformation modulus, a fatigue model with different crack inclination angles was established using the axial residual deformation as the internal variable, and the rationality of the model was verified by fatigue loading tests. [ABSTRACT FROM AUTHOR]

The fractured rock mass in the western cold region is affected by freezing and thawing disasters and is prone to local damage and fracture along the fissures’ ends. The fatigue damage induced by repeated frost heave and traffic loads seriously endangers the stability of cold region roadbed. This paper selects sandstone as the research object. Firstly, 20 freeze–thaw cycles were performed on fractured sandstone samples with different inclination angles of 30°, 45°, 60°, and 90°. Subsequently, triaxial compression and triaxial fatigue loading tests were conducted to explore the mechanical properties and fracture morphology evolution mechanism during the compression process of freeze–thaw fractured sandstone. Nuclear magnetic resonance technology (NMR) was used to measure the H-containing fluid inside rock pores. The microscopic damage characteristics inside the rock were analyzed from the NMR T2 relaxation spectrum signal and pore size distribution characteristics. Based on the internal variable theory of continuum mechanics, a fatigue model of freeze–thaw fractured sandstone with different inclination angles was established. The results show that sandstone strength was negatively correlated with the fracture dip angle, and the axial deformation and shear failure angle were positively correlated with the fracture dip angle. The mechanical properties of the sandstone were deteriorated by fatigue loading. When the crack angle was 90°, the fatigue failure strength of the rock sample was the lowest. The T2 spectrum distribution of the fractured sandstone mainly had three peaks and the pore size was mainly medium and small pores. There was a small leftward shift after freeze–thaw cycles and fatigue loading. The T2 spectrum area was significantly affected by fatigue loading, with the highest rate of change at a crack angle of 30°. Through the fine correspondence between the axial residual deformation and the deformation modulus, a fatigue model with different crack inclination angles was established using the axial residual deformation as the internal variable, and the rationality of the model was verified by fatigue loading tests.

The blanket module of nuclear fusion reactor is proposed to be made of reduced activation ferritic martensitic (RAFM) steel. Thus, in order to prevent the unprecedented failure, the creep response of RAFM steel must be studied meticulously. In that direction, physical based creep curve modeling is one of the available choices to obtain the insights about the substructural evolution during the creep deformation, hence enabling to enlighten about material weakening mechanisms. In this paper, experimental creep curves of RAFM steel at varying conditions are simulated employing an improved dislocation density reliant physical model. The microstructure based internal variables are considered for addressing the mechanisms such as hardening, recovery, coarsening of precipitates and creep cavitation. All the simulated creep curves are found to be in reasonable agreement with the experimental creep curves. Furthermore, the evolution of involved eighteen parameters, i.e., dislocation glide velocity, climb velocity, internal stress, climb stress, effective stress, mobile dislocation density, dipole dislocation density, boundary dislocation density, subgrain radius, boundary pressure, boundary dislocation spacing, subgrain mobility and dipole capture spacing is demonstrated and discussed thoroughly.

By using the weight coefficients, the Euler-Maclaurin summation formula and Abel's summation by parts formula, an extended Hardy-Hilbert's inequality with the power function as the interval variables and a new Hilbert-type inequality with the partial sums are given. As applications, the equivalent conditions of the best possible constant factor in a particular inequality related to a few parameters and some particular cases are considered. [ABSTRACT FROM AUTHOR]

The authors presented a time-independent plasticity approach, where a typical plastic-loading process is viewed as an infinitesimal state change of two neighboring equilibrium states, and the yield and consistency conditions are formulated based on the conjugate forces of the internal variables. In this paper, a stability condition is proposed, and the yield, consistency, and stability conditions are reformatted by the inelastic differential form of the Gibbs free energy. The Gibbs equation in thermodynamics with internal variables is a representation to the differential form of the Gibbs free energy by a single Gibbs free energy function. In this paper, we propose the so-called extended Gibbs equation, where the differential form may be represented by multiple potential functions. Various associated and nonassociated plasticity with a single or multiple yield functions can be derived from various representations based on the reformulated approach, where yield and plastic potential functions are in the form of inelastic differentials of the potential functions. The generalized Drucker inequality can only be derived from the one-potential representation as a stability condition. For a multiple-potential representation, the stability condition can be ensured if the multiple potentials are concave functions and possess the same stationary point. [ABSTRACT FROM AUTHOR]

In this paper, we present the hydrodynamic limit of a multiscale system describing the dynamics of two populations of agents with alignment interactions and the effect of an internal variable. It consists of a kinetic equation coupled with an Euler-type equation inspired by the thermomechanical Cucker–Smale (TCS) model. We propose a novel drag force for the fluid-particle interaction reminiscent of Stokes' law. While the macroscopic species is regarded as a self-organized background fluid that affects the kinetic species, the latter is assumed sparse and does not affect the macroscopic dynamics. We propose two hyperbolic scalings, in terms of a strong and weak relaxation regime of the internal variable towards the background population. Under each regime, we prove the rigorous hydrodynamic limit towards a coupled system composed of two Euler-type equations. Inertial effects of momentum and internal variable in the kinetic species disappear for strong relaxation, whereas a nontrivial dynamics for the internal variable appears for weak relaxation. Our analysis covers both the case of Lipschitz and weakly singular influence functions. [ABSTRACT FROM AUTHOR]

The present work proposes a phenomenological level-set model for shape memory alloys within the framework of internal variable theory and continuum thermomechanics. While the majority of constitutive models for shape memory alloys assume the martensitic volume fraction as an internal variable, in this study a level-set function is chosen to be the internal variable. Such a choice allows to account, on average, for the microstructural changes within the material by representing in an implicit manner the interfaces between different phases. Utilizing consistent thermodynamical arguments within the framework of canonical thermomechanics, the evolution equation for the level-set function is derived. Then, the model is implemented in a one dimensional case, where simple evolution equations are proposed reproducing certain characteristics of shape memory alloys, such as the pseudoelastic effect, the strain-temperature hysteresis, the one-way shape memory effect and hardening effects. Also, application of the model on functional fatigue phenomenon is thoroughly inspected. This new constitutive level-set model provides extreme flexibility and seems to be very promising for future research. [ABSTRACT FROM AUTHOR]