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Of interest in this paper is a modeling framework when constitutive relations are given in incremental form. This is particularly true for aging concretes due to hydration. Furthermore, having in mind applications to 3D concrete printing, geometrical nonlinearities must be accounted for due to the soft nature of the fresh material. The kinematics must then be adapted adequately for a theoretically sound formulation. For this, the multiplicative split is chosen here for the deformation gradient into its known part at an earlier time and the relative deformation gradient. From the geometric point of view, this gives rise to an intermediate configuration on which incremental constitutive relations can be ideally defined prior to be transported back to the reference configuration for a Lagrangian formulation. Model examples are given for the purpose of demonstration and a set of simulations illustrate the effectiveness of the proposed framework.

We assess the performance of different protocols for simulating excited-state X-ray absorption spectra. We consider three different protocols based on equation-of-motion coupled-cluster singles and doubles, two of them combined with the maximum overlap method. The three protocols differ in the choice of a reference configuration used to compute target states. Maximum-overlap-method time-dependent density functional theory is also considered. The performance of the different approaches is illustrated using uracil, thymine, and acetylacetone as benchmark systems. The results provide guidance for selecting an electronic structure method for modeling time-resolved X-ray absorption spectroscopy., Revised version submitted to Structural Dynamics (January 2021)

Cartilage functionality is determined by tissue structure and composition. If altered, cartilage is predisposed to premature degeneration. This pathomimetical study of early osteoarthritis evaluated the dose-dependant effects of collagenase-induced collagen disintegration and proteoglycan depletion on cartilage functionality as assessed by serial T1, T1ρ, T2, and T2* mapping under loading. 30 human femoral osteochondral samples underwent imaging on a clinical 3.0 T MRI scanner (Achieva, Philips) in the unloaded reference configuration (δ0) and under pressure-controlled quasi-static indentation loading to 15.1 N (δ1) and to 28.6 N (δ2). Imaging was performed before and after exposure to low (LC, 0.5 mg/mL; n = 10) or high concentration (HC, 1.5 mg/mL; n = 10) of collagenase. Untreated samples served as controls (n = 10). Loading responses were determined for the entire sample and the directly loaded (i.e. sub-pistonal) and bilaterally adjacent (i.e. peri‑pistonal) regions, referenced histologically, quantified as relative changes, and analysed using adequate parametric and non-parametric statistical tests. Dose-dependant surface disintegration and tissue loss were reflected by distinctly different pre- and post-exposure response-to-loading patterns. While T1 generally decreased with loading, regardless of collagenase exposure, T1ρ increased significantly after HC exposure (p = 0.008). Loading-induced decreases in T2 were significant after LC exposure (p = 0.006), while changes in T2* were ambiguous. In conclusion, aberrant loading-induced changes in T2 and T1ρ reflect moderate and severe matrix changes, respectively, and indicate the close interrelatedness of matrix changes and functionality in cartilage.

A numerical study on a new bifurcation phenomenon in multi-void growth is carried out for a 2-D problem in nonlinear elasticity, where the reference configuration is y-axisymmetric with two pre-existing small voids. The numerical experiments show that, under large radially-symmetric displacement boundary conditions, other than the y-axisymmetric equilibrium solution one would normally expect, there are two energetically more favorable non-y-axisymmetric equilibrium solutions in which the growth of one void is overwhelmingly dominant. The relationships between the critical bifurcation boundary displacement and the compressibility of the material as well as some geometric parameters are illustrated by numerical results. The numerical experiments also show that the existence of the secondary bifurcation will effectively expedite the onset of fractures.

Recent studies suggest that cells routinely probe their mechanical environments and that this mechanosensitive behavior regulates some of their cellular activities. The finite elasticity theory of small-on-large deformation (SoL) has been shown to be effective in interpreting the mechanosensitive behavior of cells on a substrate that has been subjected to a prior large static stretch before the culturing of the cells. Small on large deformation is the superposition of a small deformation onto a prior large deformation that serves as the new reference configuration. This article aims to refine SoL theory to develop a theoretical framework for improved physical interpretation of mechanosensing. Given the initial large deformation in SoL, the stress generated by the small deformation is linearized, and the linearized elasticity tensor is taken to be a significant factor facilitating prediction of cellular behavior. The pre-stretch is shown to produce direction-based, effective elastic moduli for cellular mechanosensing. The utility of this SoL theory is illustrated by culturing of two different cell types grown on uniaxially pre-stretched surfaces that induce changes to the cell orientation and behavior.

A model of the indentation of a circular elastic membrane (neo-Hookean material) on an incompressible liquid layer and an effective numerical solution method are presented. For the interface between the indenter and the membrane, stick or slip contact conditions are considered. The solution procedure identifies the liquid pressure and, for slip contact, the radius in the reference configuration displaced to the edge of the indenter. Assuming a range of material and test performance parameters regarding deep tonometry of soft subcutaneous tissue, the predictions for the distributions of stretches, line tensions and profiles of the indented membrane are analyzed. Among the key results of this work are the dependencies of the total indentation force and the liquid pressure on the Young’s modulus of the membrane’s material that appeared to be approximately linear for a range of Young’s modulus values. The profiles of the membrane for different indentation depths are close to parabolic and can be used to relate the longitudinal line tension at the edge of the indenter to the total indentation force.

A novel finite element-based simulation method is proposed for fused deposition modeling in two dimensions. The method assumes full coupling between the mechanical and thermal response under the assumptions of infinitesimal deformation and finite temperature variation. To account for continuous temperature-induced changes in the geometry, new elements are deposited on the current configuration, while the governing equations are solved on a reference configuration generated based on the desired shape. Representative simulations are conducted to assess the predictive capacity of the method, as well as the effect of thermomechanical coupling on the final shape of the printed solid.

In this paper, the overall cooling effectiveness of double wall cooling structures with pins is experimentally investigated on the low-speed wind tunnel. The analysis of the single cooling technology contributions to improve the double wall cooling performance is provided. The effect of Biot number ( Bi = 0.03, 0.32, 2.25 ) and the film hole size ( d e = 2 mm, 3 mm, 5 mm ) on the overall cooling effectiveness are also studied. In order to further improve the overall cooling performance, the present study proposes two new shapes of film hole patterns with compound angles (compound configuration, double configuration). By numerically analyzing the cooling effectiveness of the outer film cooling and the heat transfer performance of the inner target wall, the mechanism by which film hole size and new film hole patterns affect the overall cooling performance of double wall structures is clarified. The results show that the area-averaged overall cooling effectiveness of the double cooling technology is more than 30% higher than that of the two single cooling technologies and the contribution of impingement cooling is higher than that of effusion cooling at high blowing ratios. The cooling performance of the double wall structure is greatly influenced by the Biot number of effusion plates. Low Biot number means higher thermal conductivity, resulting in higher overall cooling effectiveness under the same thermal load conditions. Increasing the film hole size could enhance the film cooling performance outside of the effusion plate, suppressing the unfavorable results of lower heat transfer performance at the inner side. The fitting correlation equation obtained using the binary linear regression method agrees well with the experimental results, with a maximum deviation of less than 4%. Both of the two compound structures can effectively improve the overall cooling performance of the double wall structure. The double configuration has the best cooling performance and the area-averaged cooling effectiveness improves by 15.1% compared to the reference configuration under the condition of M = 1.5 . The experimental results provide a vital database for the future double wall cooling design.

In this paper we show an overview of the preliminary strategy planned for remote maintenance of neutron–activated and contaminated components of DTT machine, in the 2019 reference configuration. The remote maintenance of such a complex machine has impact on different aspects of the DTT machine: layout of the tokamak hall, vacuum vessel and cryostat structures, in–vessel components. To date, the number and size of vacuum vessel ports as well as the segmentation and size of in–vessel mechanical components of DTT have been established by a compromise between operational and maintenance needs. An extensive multidisciplinary work has been done in deriving the requirements for the DTT remote maintenance strategy. Each vacuum vessel sector is divided into five ports: in the current configuration, the top and bottom divertor cassettes are expected to be removed, respectively, from four lower lateral ports and from four equatorial horizontal ports; the first wall modules at the inboard side are expected to be installed/removed from all the upper ports; the first wall modules at the outboard and upper sides are segmented such that they can be removed from four equatorial horizontal ports. The work describes the current strategies for divertor and first wall remote maintenance systems, as well as a first conceptual design of the remote maintenance equipment of DTT machine.

The simple analysis of stresses in arteries considers the artery as an incompressible elastic circular cylindrical tube. When the intact artery is unloaded and cut transmurally, it springs open to a nearly circular cylindrical sector. The resulting nonzero opening angle indicates the existence of residual stresses in the unloaded intact artery. This paper presents a new analysis of stresses in arteries based on an Eulerian formulation of elastic deformations in soft tissues that models the inelastic process of remodeling (homeostasis) towards its homeostatic state. Within the context of this new analysis it is not necessary to model details of homeostasis. Instead, it is possible to directly determine the loaded homeostatic state, which is considered as the reference configuration of the artery, and to specify the geometry and associated values of the circumferential and axial stresses by matching measurements of the geometry of the unloaded open artery. The predicted geometry of the unloaded intact artery is shown to be accurate relative to the measurements. Also, predictions of the stress distributions for remodeling due to hypertension are presented.

International audience; During urban floods, the flow is generally concentrated in streets, but lateral exchanges with building blocks can alter locally the flow pattern. These blocks include buildings, courtyards, parking lots, gardens, into which water enters through different openings, such as windows, doors, gates, fences, etc. In order to study these exchange processes and their influence on flow depth and velocity in the streets during flood events, experiments were conducted on a devoted physical model termed MURI (Urban Model for the study of Inundation Risk), at Irstea Lyon-Villeurbanne centre, France. A 2D numerical model was also used to simulate the experiments, using a constant eddy viscosity and then an eddy viscosity in relation to the flow depth. The present study focusses on two geometric configurations. The first one consists of a straight street flanked by two lateral cavities, and the second one, a straight street flanked by one-side opening. These flows are compared to a reference configuration under quasi-uniform flow conditions (without openings). The results obtained with the numerical model are consistent with the experiments, mainly in terms of flow depths. The experiments and simulations show that a detailed description of the building blocks is required if the flow pattern is estimated locally.

The purpose of this paper is to review and contrast the Lagrangian and Eulerian formulations of inelasticity as they apply to metal plasticity and growth of biological tissues. In contrast with the Lagrangian formulation of inelasticity, the Eulerian formulation is unaffected by arbitrary choices of the reference configuration, an intermediate configuration, a total deformation measure and an inelastic deformation measure. Although the Eulerian formulation for growth of biological tissues includes a rate of mass supply and can be used to understand the mechanics of growth, it does not yet model essential mechanobiological processes that control growth. Much research is needed before this theory can help design medical treatments for growth related disease. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

In this study, the peridynamic fatigue model for a homogeneous material is extended to the layered heterogeneous material. Thermal residual stress and the corresponding stress intensity factor are calculated, within the framework of the peridynamic theory, by considering the cooling process using a pairwise force function caused by the thermal loading effect. To avoid overlapping of the cracked surfaces due to compressive thermal residual stress, the notion of short range force (Macek and Silling, 2007) is newly introduced. In addition, an auxiliary reference configuration is used to define the cyclic bond strain in the constricted material. The proposed approach is validated by performing an illustrative case study.

We address a finite-plasticity model based on the symmetric tensor \(\varvec{P}^\top \! \varvec{P}\) instead of the classical plastic strain \(\varvec{P}\). Such a structure arises by assuming that the material behavior is invariant with respect to frame transformations of the intermediate configuration. The resulting variational model is lower dimensional, symmetric and based solely on the reference configuration. We discuss the existence of energetic solutions at the material-point level as well as the convergence of time discretizations. The linearization of the model for small deformations is ascertained via a rigorous evolution-\(\Gamma \)-convergence argument. The constitutive model is combined with the equilibrium system in Part II where we prove the existence of quasistatic evolutions and ascertain the linearization limit (Grandi and Stefanelli in 2016).

Computational models are increasingly being used to investigate the mechanical properties of cardiac tissue. While much insight has been gained from these studies, one important limitation associated with computational modeling arises when using in vivo images of the heart to generate the reference state of the model. An unloaded reference configuration is needed to accurately represent the deformation of the heart. However, it is rare for a beating heart to actually reach a zero-pressure state during the cardiac cycle. To overcome this, a computational technique was adapted to determine the unloaded configuration of an in vivo porcine left ventricle (LV). In the current study, in vivo measurements were acquired using magnetic resonance images (MRI) and synchronous pressure catheterization in the LV (N = 5). The overall goal was to quantify the effects of using early-diastolic filling as the reference configuration (common assumption used in modeling) versus using the unloaded reference configuration for predicting the in vivo properties of LV myocardium. This was accomplished by using optimization to minimize the difference between MRI measured and finite element predicted strains and cavity volumes. The results show that when using the unloaded reference configuration, the computational method predicts material properties for LV myocardium that are softer and less anisotropic than when using the early-diastolic filling reference configuration. This indicates that the choice of reference configuration could have a significant impact on capturing the realistic mechanical response of the heart.

In this paper, a method that enables adjustment of the free spectral range (FSR) of a swept-source is presented by introducing a right-angled prism inside a polygon-based filter. Firstly, the feasibility of this method is analyzed in theory. When adopting the prism at two different cases, the theoretical prediction value of FSR changes differently. In Case 1, when the beam incidents from the hypotenuse surface of the prism, a broader FSR is obtained. In Case 2, when the beam incidents from the right-angled surface of the prism, a narrower FSR is achieved. Then, to verify these two different changes, the filters deployed in these two cases, as well as a standard reference filter, are tested and compared on a seed swept-source. There is no prism in the reference configuration which has the FSR of 187.9 nm. Compared with that, in Case 1 and Case 2, the measured FSR increases to be 234.4 nm and decreases to be 156.6 nm, respectively. The experimental results are not only consistent with the predicted changes, but also show the ability of fine and continuous adjustment of the FSR. This method is promising to improve the performance of swept-sources, as well as the imaging systems which utilize swept-sources as the light sources.

Flow in a longitudinally grooved channel is analysed with the primary objective of quantifying intensification of transport mechanism due to the onset of secondary flows resulting from hydrodynamic instability and amplification of unstable modes into the nonlinear regime. Considered geometry consists of a channel whose walls are fitted with sinusoidal corrugations, forming a system of longitudinal grooves parallel to the streamwise direction. Such configuration is energy efficient, because it reduces drag when compared to the smooth reference configuration and at the same time results in flow destabilization, due to travelling wave mode already at very low values of the Reynolds number (

To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we carry out an experimental study that consists on recording both the shape of the fold in various loading configurations and the associated force needed to deform it. Then, an elastic model of the fold is built upon a continuous description of both the faces and the crease as a thin sheet with a non flat reference configuration. The comparison between the model and experiments yields the local fold properties and explains the significant differences we observe between tensile and compression regimes. Furthermore, an asymptotic study of the fold deformation enables us to determine the local shape of the crease and identify the origin of its mechanical behaviour., Comment: Article, 8 pages, 9 figures

This book has begun with problems at finite or large strains in Chaps. 2–4; recall the Convention 1.1.1 on p. 6. Thus it is expectable to close it with such problems. In dynamical problems at large deformation and finite/large strains, many serious difficulties are pronounced and only very few results are at disposal, in contrast to the static situations. Essentially, the absence of a clearly identifiable reference configuration and of a linear geometry that would allow for defining a time derivative in a unique way is the source of these problems.

The choice of the shape and number of cooling channels is critical when seeking for the best design of a liquid rocket engine thrust chamber. Trade-off has to be considered among the different constraints that must be satisfied in terms of thrust chamber mass and resistance to mechanical and thermal loads, while keeping acceptable the power spent to make the coolant flow in the channels. In this study attention is focused on the phenomenon of thermal stratification that occurs in liquid rocket engine cooling channels due to their asymmetric heating. Its role is studied with a suitable engineering approach that allows to emphasize when rectangular cross section channels become inefficient due to stratification. A parametric analysis is carried out on a reference configuration showing the margins required to satisfy specific wall temperature constraints.

Multibody systems are often modeled as interconnected multibody and modal components: multibody components, such as rigid bodies, beams, plates, and kinematic joints, are treated via multibody techniques whereas the modal components are handled via a modal reduction approach based on the small strain assumption. In this work, the problem is formulated within the framework of the motion formalism. The kinematic description involves simple, straightforward frame transformations and leads naturally to consistent deformation measures. Derivatives are expressed in local frames, which results in the remarkable property that the tangent matrices are independent of the position and orientation of the modal component with respect to an inertia frame. This implies a reduced level of geometric non-linearity as compared to standard description. In particular, geometrically non-linear problems can be solved with the tangent matrices of the reference configuration, without re-evaluation and re-factorization.Copyright © 2018 by ASME

We aim to maximize the pumping volume of a pulsatile ventricular assist device, where the diaphragm is covered with an endothelial cell layer. These cells are estimated to survive a cyclic strain up to fifteen percent. To increase the pumping volume under this strain constraint we use an approach based on corrugation of the diaphragm in its reference configuration. The paper explains the parametrization scheme for finding corrugation shapes, addresses modeling and evaluation schemes and reports on the results of a parameter study. The results show that corrugated diaphragm shapes are effective for increasing pumping volumes under a strain constraint.

In this article, we study the existence, uniqueness and homogenization of the heat equation in a domain with highly oscillating and evolving (time-dependent) boundary and an inhomogeneous time-dependent data on the oscillating part of boundary, motivated by fluid-structure interaction problems. We rewrite the parabolic equation in a reference configuration which transforms the boundary oscillations into rapidly oscillating coefficients. Finally, we obtain the effective coefficients and corrector results in the reference configuration.

A chemically reacting mixture of elastic solids is considered. As a constitutive assumption, the peculiar functions (such as the free energy, the entropy, and the stress) of a constituent are taken to be functions of a set of variables pertaining to that constituent. The interaction terms, namely the growth of mass, linear momentum, and energy, are allowed to depend on the set of variables pertaining to all of the constituents. While the dependence on the mass density is usually disregarded, the paper accounts also for such a dependence, which seems to be in order especially in connection with reacting mixtures where the mass densities change also in the reference configuration. The thermodynamic restrictions are derived by starting from the non-negative value of the sum of entropy growths and involving the properties of the peculiar functions. The results so obtained for stresses and chemical potentials are examined in connection with similar schemes (swelling solids). While the correct relations for the mass diffusion flux arise from balance equations, an analysis is given of whether and how Fick-type models are acceptable possibly depending on the fluid or solid character of the mixture.

The aim of this article is to propose a simple way of describing a tumour as a linear elastic material from a reference configuration that is continuously evolving in time due to growth and remodelling. The main assumption allowing this simplification is that the tumour mass is a very ductile material, so that it can only sustain moderate stresses while the deformation induced by growth, that can actually be quite big, mainly induces a plastic reorganisation of malignant cells. In mathematical terms this means that the deformation gradient can be split into a volumetric growth term, a term describing the reorganisation of cells, and a term that can be approximated by means of the linear strain tensor. A dimensional analysis of the importance of the different terms also allows to introduce a second simplification consisting of decoupling the equations describing the growth of the tumour mass from those describing the flow of the interstitial fluid.

Using multi reference configuration interaction (MRCI) method, with aug-cc-pV5Z, aug-cc-pv6z, aug-cc-pcv5z, aug-cc-pcv6z basis sets etc., the single point energy of the ground state and the first excited state and second excited state of C-2are calculated. Then LEVEL program is used to fit out the spectroscopic constants of three states. Results obtained by MRCI/aug-cc-pcv5z-dk method are close to the experimental values.

We prove the 50/50 rule of Fig. 1 by a Lagrangian technique (all fields pulled back to the reference configuration at time 0) which exposes the necessity of two circumstances for the result to hold: 1) time-invariance of currents, when expressed in “material form” and 2) equality of (magnetic) coenergy and energy, which excludes nonlinear $\boldsymbol {B}$ – $\boldsymbol {H}$ laws. A dual result, which holds in case of time-invariance of “flux linkages” (but without the linearity restriction), is found along the way.

Red cells suspended in solutions much more viscous than blood plasma assume an almost steady-state orientation when sheared above a threshold value of shear rate. This orientation is a consequence of the motion of the membrane around the red cell called tank-treading. Observed along the undisturbed vorticity of the shear flow, tank-treading red cells appear as slender bodies. Their orientation can be quantified as an angle of inclination (θ) of the major axis with respect to the undisturbed flow direction. We measured θ using solution viscosities (η0) and shear rates (γ˙) covering one and three orders of magnitude, respectively. At the lower values of η0, θ was almost independent of γ˙. At the higher values of η0, θ displayed a maximum at intermediate shear rates. The respective maximal values of θ increased by ∼10° from 10.7 to 104 mPas. After accounting for the absent membrane viscosity in models by using an increased cytoplasmic viscosity, their predictions of θ agree qualitatively with our data. Comparison of the observed variation of θ at constant γ˙ with model results suggests a change in the reference configuration of the shear stiffness of the membrane.

We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height [Formula: see text]. We study, by means of Γ-convergence, the asymptotic behavior as [Formula: see text] goes to zero of the sequence of complementary energies. The limit functional is identified as a dual problem for a two-dimensional plate. Our approach gives a direct characterization of the convergence of the equilibrating stress fields.

Glass Fiber Reinforced Polymer (GFRP) I-beam-column adhesively bonded connections are tested under combined bending and shear. The special feature of the novel connection is the wrapping of the seat angles at the connection by a carbon fiber reinforced polymer (CFRP) fabric wrap. The wrap is primarily intended to alter the connection failure mode from brittle to pseudo-ductile, thus providing adequate warning of impending failure. Four moment resisting connection configurations are tested, including the reference configuration without the wrap. It is observed that the connection failure is initiated by the fracture of the adhesive, but the provision of the wrap, together with a steel seat angle, alters the failure mode from brittle to pseudo-ductile. The post-peak load deformation is achieved without a large drop in the resistance of the connection. On other hand, the connection with the wrapping and a GFRP seat angle can also change the failure mode to pseudo-ductile, but it could not be done without a large reduction in the connection resistance after the peak load.

The hydro-morpho-sedimentary processes in confluence hydrodynamic zones (CHZ) subject to a local widening of the tributary were investigated in a series of laboratory experiments that were representative of the 20 major confluences of the Upper Rhone River in Switzerland. Three discharge ratios (low, intermediate and high ratios of tributary to main channel discharge) were investigated for each of four tributary configurations (reference configuration with constant tributary width and three geometries of the local tributary widening). In all experiments, the local tributary widening caused substantial morphodynamic changes in the CHZ and moderate sediment redistribution in the post-confluence channel. At the entrance of the local widening, the tributary main flow corridor gradually widened. Towards the confluence mouth, it narrowed and deflected in downstream direction because of a zone of flow stagnation at the confluence upstream junction corner. Dry zones and flow stagnation zones occurred in the widening zone outside the tributary main flow corridor. The results indicate that a local tributary widening considerably enhances the variability of bed substrate, velocity and depth in the CHZ, and offers an appropriate habitat for a wider range of biota than the homogeneous channelized reference configuration. None of the investigated experiments resulted in adverse impacts on water surface elevation and thereby flood safety. On the basis of the laboratory experiments, the appropriate geometry of the local tributary widening is discussed, and quantitative guidelines for practical application are proposed. Copyright (c) 2014 John Wiley & Sons, Ltd.

We present different integral-direct implementations in a local Cholesky-decomposed multi-reference configuration interaction framework. We discuss their performance, parallel efficiency and scaling properties for a range of alkyne test systems. As we are able to introduce accuracy-preserving integral truncations within a direct algorithm, we observe superior performance and, through the drastically reduced I/O operations, better parallel efficiency for the truncated integral-direct kernels compared to their conventional counterparts.

The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6] using the implicit function theorem. In contrast, the steady states considered in this article correspond to deformations of the relaxed state with no size restriction and are obtained as minimizers of the energy functional of the elastic body., Comment: 16 pages, no figures. This new version contains an additional result on the existence of steady states of self-gravitating elastic bodies with free boundary. The inclusion of the new result led to a major revision of the paper

We discuss the well-posedness of a new nonlinear model for nematic elastomers. The main novelty in our work is that the Frank energy penalizes spatial variations of the nematic director in the deformed, rather than in the reference configuration, as it is natural in the case of large deformations.

A passive control strategy, which consists in introducing contoured cavities in solid walls, is applied to a plane asymmetric diffuser at a Reynolds number that implies fully-turbulent flow upstream of the diffuser divergent part. The analysed reference configuration, for which experimental and numerical data were available, is characterized by an area ratio of 4.7 and a divergence angle of 10°. A large zone of steady flow separation is present in the diffuser without the introduction of the control. One and two subsequent contoured cavities are introduced in the divergent wall of the diffuser and a numerical optimization procedure is carried out to obtain the cavity geometry that maximizes the pressure recovery in the diffuser and minimizes the flow separation extent. The introduction of one optimized cavity leads to an increase in pressure recovery of the order of 6.9% and to a significant reduction of the separation extent, and further improvement (9.6%) is obtained by introducing two subsequent cavities in the divergent wall. The most important geometrical parameters are also identified, and the robustness of the solution to small changes in their values and in the Reynolds number is assessed. The present results show that the proposed control strategy, previously tested in the laminar regime, is effective also for turbulent flows at higher Reynolds numbers. As already found for laminar flow, the success of the control is due both to a virtual geometry modification of the diffuser and to a favourable effect of the cavities in reducing the momentum losses near the wall.

We consider a variational model which describes a complex system composed, in its reference configuration, of a periodic distribution of "small" interacting particles immersed in a continuous medium. We describe its macroscopic limit via Gamma-convergence, highlighting different regimes. In particular, we show how the interplay between the particles and the continuum leads, for a critical size of the particles, to a capacitary term. Eventually, we discuss how the presence of a continuum affects the properties of the ground states of the system of particles in terms of the validity or not of the so-called "Cauchy–Born" rule.

This study presents a constitutive material model for describing nonlinear and hysteretic responses of plant tissues subjected to mechanical loadings. The nonlinear and hysteretic response is associated with the viscoelastic nature of the constituents and microstructural changes of plant tissues during loadings. In order to incorporate the effect of microstructural changes on the macroscopic response of plant tissue, we assume that as the tissue is deformed, an additional micromechanism arises affecting the mechanical response of the tissues. The plant tissue is assumed to consist of two networks, the initial network which is associated with an original reference configuration and the new network that is formed during the deformation. The newly formed network has a new natural configuration. The responses obtained from the proposed model are compared with available experimental data of plant tissues. The model is easily extended to incorporate responses of different tissues, i.e., outer strengthening skin and inner soft core, in determining the overall nonlinear behaviors of the plant stems, which are composite materials. Thus, we can examine the contributions of different constituents in the plant tissues on their macroscopic mechanical responses.

Through mechanobiological control of the extracellular matrix, and hence local stiffness, smooth muscle cells of the media and fibroblasts of the adventitia play important roles in arterial homeostasis, including adaptations to altered hemodynamics, injury, and disease. We present a new approach to model arterial wall mechanics that seeks to define better the mechanical environments of the media and adventitia while avoiding the common prescription of a traction-free reference configuration. Specifically, we employ the concept of constituent-specific deposition stretches from the growth and remodeling literature and define a homeostatic state at physiologic pressure and axial stretch that serves as a convenient biologically and clinically relevant reference configuration. Information from histology and multiphoton imaging is then used to prescribe structurally motivated constitutive relations for a bi-layered model of the wall. The utility of this approach is demonstrated by describing in vitro measured biaxial pressure–diameter and axial force–length responses of murine carotid arteries and predicting the associated intact and radially cut traction-free configurations. The latter provides a unique validation while confirming that this constrained mixture approach naturally recovers estimates of residual stresses, which are fundamental to wall mechanics, without the usual need to prescribe an opening angle that is only defined conveniently on cylindrical geometries and cannot be measured in vivo. Among other findings, the model suggests that medial and adventitial stresses can be nearly uniform at physiologic loads, albeit at separate levels, and that the adventitia bears increasingly more load at supra-physiologic pressures while protecting the media from excessive stresses.

The growing bodies are considered as bodies with induced inhomogeneity caused by junction of inconsistently deformed parts. The body is formalized as an abstract smooth manifold, and all possible affine connections on it are classified. A method is shown for introducing a special connection—material connection—for which neighborhoods of all material points of a growing body pass into a stress-free state. A method for constructing a global stress-free reference configuration of a growing body as an embedding in a space with absolute parallelism is proposed. It is shown that in the case of layered accretion, the material connection corresponding to the stress-free embedding is determined by three independent functions and is in general non-Euclidean. The property of being non-Euclidean is determined by the fact that the torsion of the material connection is nonzero. We suggest to formalize the growing body as a fibration of a three-dimensional smooth manifold over a one-dimensional base, and this formalization characterizes the structure of the material connection.