Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil

In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.

Determination of material properties of a linearly elastic peridynamic material

We investigate the properties of an isotropic linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which considers both length and relative angle changes, and is based on a free energy function proposed in previous work that contains four material constants. To this end, we consider a class of equilibrium problems in mechanics to show that, in interior points of the body where deformations are smooth, the corresponding solutions in classical linear elasticity are also equilibrium solutions in peridynamics. More generally, we show that the equations of equilibrium are satisfied even when two of the four peridynamic constants are arbitrary. Pure torsion of a cylindrical shaft and pure bending of a cylindrical beam are particular cases of this class of problems and are used together with a correspondence argument proposed elsewhere to determine these two constants in terms of the elasticity constants of an isotropic material from the classical linear elasticity. One of the constants has a singularity in the Poisson ratio, which needs further investigation. Two additional experiments concerning bending of cylindrical beam by terminal load and anti-plane shear of a hollow cylinder, which do not belong to the previous class of problems, are used to validate these results.

High-temperature effect on the material constants and elastic moduli for solid rocks

Thermally coupled constitutive relations are generally used to determine material constants and elastic moduli (Young's modulus and shear modulus) of solid media. Conventional studies on this issue are mainly based on the linear temperature dependence of elastic moduli, whereas analytical difficulties are often encountered in theoretical studies on nonlinear temperature dependence, particularly at high temperatures. This study investigates the thermally coupled constitutive relations for elastic moduli and material constants using the assumption of axisymmetric fields, with applications to geologic materials (marble, limestone and granite). The Taylor power series of the Helmholtz free energy function within dimensionless temperatures could be used to develop the thermally coupled constitutive relations. The thermoelastic equivalent constitutive equations were formulated under the generalized Hooke's law. The material constants of solid rocks were determined by fitting experimental data using axisymmetric stress and strain fields at different temperatures, based on their thermomechanical properties. For these geologic materials, the resultant equivalent elastic moduli and deformations were in good agreement with those from the experimental measurements. Thermal stresses, internal moisture evaporation and internal rock compositions significantly affected the experimental results. This study provides a profound understanding of the thermally coupled constitutive relations that are associated with the thermomechanical properties of solid rocks exposed to high temperatures.

Run-and-Tumble Motion: The Role of Reversibility

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

A hybrid $$ H ^1\times H (\mathrm {curl})$$ finite element formulation for a relaxed micromorphic continuum model of antiplane shear

One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric microdistortion in the free energy function. This suggests the existence of solutions not belonging to $$ H ^1$$ H 1 , such that standard nodal $$ H ^1$$ H 1 -finite elements yield unsatisfactory convergence rates and might be incapable of finding the exact solution. Our approach is to use base functions stemming from both Hilbert spaces $$ H ^1$$ H 1 and $$ H (\mathrm {curl})$$ H ( curl ) , demonstrating the central role of such combinations for this class of problems. For simplicity, a reduced two-dimensional relaxed micromorphic continuum describing antiplane shear is introduced, preserving the main computational traits of the three-dimensional version. This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations and their respective convergence rates.

Time-Independent Plasticity Formulated by Inelastic Differential of Free Energy Function

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.

Structure-Based Virtual Screening and De Novo Design of PIM1 Inhibitors with Anticancer Activity from Natural Products

Background: the proviral insertion site of Moloney murine leukemia (PIM) 1 kinase has served as a therapeutic target for various human cancers due to the enhancement of cell proliferation and the inhibition of apoptosis. Methods: to identify effective PIM1 kinase inhibitors, structure-based virtual screening of natural products of plant origin and de novo design were carried out using the protein–ligand binding free energy function improved by introducing an adequate dehydration energy term. Results: as a consequence of subsequent enzyme inhibition assays, four classes of PIM1 kinase inhibitors were discovered, with the biochemical potency ranging from low-micromolar to sub-micromolar levels. The results of extensive docking simulations showed that the inhibitory activity stemmed from the formation of multiple hydrogen bonds in combination with hydrophobic interactions in the ATP-binding site. Optimization of the biochemical potency by chemical modifications of the 2-benzylidenebenzofuran-3(2H)-one scaffold led to the discovery of several nanomolar inhibitors with antiproliferative activities against human breast cancer cell lines. Conclusions: these new PIM1 kinase inhibitors are anticipated to serve as a new starting point for the development of anticancer medicine.

A multifractal analysis for cuspidal windings on hyperbolic surfaces

In this paper, we investigate the multifractal decomposition of the limit set of a finitely generated, free Fuchsian group with respect to the mean cusp-winding number. We completely determine its multifractal spectrum by means of a certain free energy function and show that the Hausdorff dimension of sets consisting of limit points with the same scaling exponent coincides with the Legendre transform of this free energy function. As a by-product we generalize previously obtained results on the multifractal formalism for infinite iterated function systems to the setting of infinite graph directed Markov systems.

Phase Field Study of the Microstructural Dynamic Evolution and Mechanical Response of NiTi Shape Memory Alloy under Mechanical Loading

For the purpose of investigating the microstructural evolution and the mechanical response under applied loads, a new phase field model based on the Ginzburg-Landau theory is developed by designing a free energy function with six potential wells that represent six martensite variants. Two-dimensional phase field simulations show that, in the process of a shape memory effect induced by temperature-stress, the reduction-disappearance of cubic austenite phase and nucleation-growth of monoclinic martensite multi-variants result in a poly-twined martensitic microstructure. The microstructure of martensitic de-twinning consists of different martensite multi-variants in the tension and compression, which reveals the microstructural asymmetry of nickel-titanium (NiTi) alloy in the tension and compression. Furthermore, in the process of super-elasticity induced by tensile or compressive stress, all martensite variants nucleate and expand as the applied stress gradually increases from zero. Whereas, when the applied stress reaches critical stress, only the martensite variants of applied stress-accommodating continue to expand and others fade gradually. Moreover, the twinned martensite microstructures formed in the tension and compression contain different martensite multi-variants. The study of the microstructural dynamic evolution in the phase transformation can provide a significant reference in improving properties of shape memory alloys that researchers have been exploring in recent years.