Continuum Mechanics - Science topic

This article gives an assessment of the stress-strain state of the rock massif in the ar-ea of the downcast shaft located in rocks. The development of geomechanical processes in the rock massif in the downcast shaft area is considered. The problem of continuum mechanics is applied in a flat setting, taking into account the influence of camera phase...

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminisce...

The results of numerical simulation of perforation of monolithic and multi-layered targets are presented. The objects of study were monolithic, two-layer, three-layer and air gap targets made of steel 3. The influence of the placement of an additional layer on impact resistance in high-velocity impact (initial velocity was more than the ballistic l...

In this paper recent results regarding generalized continuum mechanics on oriented Riemannian manifolds are reviewed and summarized. The mass, the momentum and the energy conservation laws are given. Thermodynamics arising in such media is also considered as a La-grangian manifold endowed with a Riemannian structure. Thermodynamic model of moving m...

Muscle wrapping influences its moment arm and alters the dynamic response of the musculoskeletal system. Conventional musculoskeletal multibody models often simplify muscle wrapping as the shortest path problem, while these models cannot consider the three-dimensional muscular geometry. In comparison, the finite element description of skeletal musc...

By developing the previously proposed method of combining continuum mechanics with Einstein Field Equations, it has been shown that the classic relativistic description, curvilinear description, and quantum description of the physical system may be reconciled using the proposed Alena Tensor. For a system with an electromagnetic field, the Lagrangia...

This study discusses the effect of various geometrical and physical parameters on the hydrogen charging time in a cylindrical metal hydride (MH) bed. A two-dimensional transient mathematical model is used to simulate a transient heat and mass transfer in MH based LaNi5 hydrogen storage reactor as a function of different factors viz. aspect ratio, h...

To reveal the size effect and lateral pressure effect of columnar jointed basalts (CJBs), the meso-damage mechanics, statistical strength theory, continuum mechanics and digital image correlation are combined, and a series of heterogeneous numerical models of CJBs orthogonal and parallel to column axis are established. The elastic modulus, Poisson'...

The development of reliable miniaturized devices capable of performing sensing, actuation, and computing functions in a robust manner strongly depends on the mechanical performance of arrays of micromachines subjected to alternating stresses during operation. Consequently, to enhance the functionality and longevity of these micromachines, it is ess...

In this paper, we provide a brief overview of certain fundamental concepts which can be used to derive constitutive relations for the stress tensor of granular materials. These include concepts such as dilatancy, cohesion, yield criterion, shear banding, etc. The focus will be on the constitutive relations which are used in the so-called ‘frictiona...

The Material Point Method (MPM) is an Eulerian-Lagrangian numerical technique used to solve partial differential equations in continuum mechanics. It was initially introduced by Sulsky and co-authors in 1994 (Sulsky et al., 1994) as an extension of the Particle-In-Cell method, and has since then mainly been used and further developed in the geomech...

Recently, Man and Du, in the context of classical texture analysis where the orientation distribution function (ODF) is defined on the rotation group SO(3), presented a systematic procedure by which the classical expansion of an ODF truncated at the order l=L can be directly rewritten as a tensorial Fourier expansion truncated at the same order. In...

We consider a general causal relativistic theory of divergence type in the framework of rational extended thermodynamics (RET) for a compressible, possibly dense, gas. We require that the system converges in the Maxwellian iteration’s first step to the parabolic Eckart equations. This requirement implies a constraint between the two coefficients pr...

In this work, we deal with a one-dimensional stress-rate type model for the response of viscoelastic materials, in relation to the strain-limiting theory. The model is based on a constitutive relation of stress-rate type. Unlike classical models in elasticity, the unknown of the model under consideration is uniquely the stress, avoiding the use of...

We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large curvature of the interface, we include a geometric term featuring a curvature varifold. Equilibrium solutions...

In this paper, we formulate a geometric nonlinear theory of the mechanics of accreting–ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio & Yavari (Sozio & Yavari 2019 J. Nonlinear Sci. 29, 1813–1863 (doi:10.1007/s00332-019-09531-w)). More specifically, we are interested in large deformation analysis of bodies t...

We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points, changes. The setting we propose may be relevant to phenomena such as plasticity, fracture, discontinuities and non-injectivity...

This is a Theme Issue of the Philosophical Transactions of the Royal Society concerning foundational issues, results of analysis and geometry in Continuum Mechanics.

We develop a continuum framework applicable to solid-state hydrogen storage, cell biology and other scenarios where the diffusion of a single constituent within a bulk region is coupled via adsorption/desorption to reactions and diffusion on the boundary of the region. We formulate content balances for all relevant constituents and develop thermody...

In a seminal paper in the Philosophical Transactions of the Royal Society (A244, 87–112). Eshelby (Eshelby 1951 Phil. Trans. R. Soc. Lond. A 244, 87–112. (doi:10.1098/rsta.1951.0016)) introduced the concept of ‘the force on an elastic singularity’ and suggested that the extensions to dynamics include the application of the momentum flux. In this di...

We look at a mechanical dissipation inequality differing from the standard one by what we call a relative power, a notion that is appropriate in the presence of material mutations. We prove that a requirement of structural invariance for such an inequality under the action of diffeomorphism-based changes of observers (covariance) implies (i) the re...

A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our p-energy is defined through a relaxation process, where a suitable p-rotation of inscribed polygons is adopted. The discrete p-rotation we choose has a geometric flavour: a polygon is viewed as an approximation to a smooth curve,...

Formation of porous 'pancake' ice floes in the Antarctic Marginal Ice Zone (MIZ) is a complex phenomenon associated with interactions between the saline seawater and temperature. Ocean warming and future environmental conditions in the Southern Ocean will most likely have an impact on the porous microstructure and thus, also on the connected biogeo...

The classical theory of continuum mechanics is formulated using partial differential equations (PDEs) that fail to describe structural discontinuities, such as cracks. This limitation motivated the development of peridynamics, reformulating the classical PDEs into integral-differential equations. In this theory, each material point interacts with i...

The precise construction of the master-slave control strategy is a fundamental requirement for robot-assisted surgery. In this study, we propose a master-slave control strategy for gastrointestinal surgical robots based on the natural orifice transluminal endoscopic surgery surgical robot developed by Tianjin University. The forward and inverse kin...

The linear and nonlinear torsion-kinematic equations are developed in this study using the position-gradient vectors. It is shown that pure torsion of circular shafts leads to stretch and change of orientation of longitudinal fibers away from the shaft centerline. In addition to the stretch, there are two nonzero Green–Lagrange shear strains, demon...

Transport phenomena draw from the fields of continuum mechanics and thermodynamics with diverse industrial applications [...]

Continuum mechanics describes compressive failure as a standard bifurcation in the response of a material to an increasing load: Damage, which initially grows uniformly in the material, localizes within a thin band at failure. Yet, experiments recording the acoustic activity preceding localization evidence power-law-distributed failure precursors o...

Carbon nanotubes are one of the most influential constituents of advanced engineering systems. The classical continuum mechanics, however, ceases to hold in accurate description of the structural response of nanobars. The mixture unified gradient theory of elasticity is invoked for the nanoscopic study of the structural characteristics of nanobars....

This paper analyzes the linear stability of an horizontal layer of fluid consisting of a mixture of water and salt. The layer is hotter at the bottom and cooler at the top thus having a tendency to destabilize. To counteract this a salt concentration gradient (denser at the bottom and lighter at the top) is sometimes present, either naturally as in...

Disordered solids, straddling the solid-fluid boundary, lack a comprehensive continuum mechanical description. They exhibit a complex microstructure wherein multiple meta-stable states exist. Deforming disordered solids induces particles rearrangements enabling the system to transition between these meta-stable states. A dramatic consequence of the...

Creep deformation is of vital importance on the thin-walled tube structure under external loadings, such as in-service cladding tubes. To improve the efficiency and accuracy of the creep deformation computation of the cladding tube, a novel continuum-based degenerated 5 degree of freedom (DOF) shell element is developed based on the continuum mecha...

Solid and fluid mechanics problems often involve the computation of eigenvalues and eigenvectors. One has short algebraic expressions for the Euler equations and the perfect gas equation of state. However, algebraic expressions for solid mechanics models can become substantial. Computing the eigenvalues and eigenvectors algebraically for different...

Analytical cutting models have recently become quite widespread due to the simplicity and rapidity of calculations as well as the stability of the solutions. This paper considers a procedure for determining the mechanical properties of machined material based on parameters for the analytical model of oblique cutting for a certain range of changes i...

By developing the previously proposed method of combining continuum mechanics with Einstein Field Equations, it has been shown that the classic relativistic description, curvilinear description, and quantum description of the physical system may be reconciled using the proposed Alena Tensor. For a system with an electromagnetic field, the Lagrangia...

Hameroff-Penrose engage Mesgarani linguistics by humanizing a sub-neuronal helical solution for what is “little understood” as “phonetic feature encoding.” Orch OR microtubulin (MT) computation potentiates Watson–Crick 1953 helx information storage as 1957 Bell Lab twistor memory, a system in which many messages pass simultaneously” substantiating...

The K–BKZ (Kaye–Bernstein, Kearsley, Zapas) rheological constitutive model is now 60 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experimental evidence in polymer melt flow, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction, an histori...

Global and large failures are now the reality of some mines. The risk management process and monitoring system are approaches used to mitigate the problem. However, they can't avoid the problem when the slope felt or is in a continuum deformation process. Considering slopes in a deformation process, it's important to well know the limits of the aff...

In this paper, a novel multi-node plate element with absolute node coordinate formulation (ANCF) is proposed. The nodes of the element are collocated to coincide with the in-plane integral quadrature points, which are used to calculate the elastic and inertia functions. The unevenly distributed nodes of the element are the zero points of the second...

Wave propagation in solids is discussed, based upon inherently non-local Λ-fractional analysis. Following the governing equations of Λ-fractional continuum mechanics, the Λ-fractional wave equations are derived. Since the variational procedures are only global, in the present Λ-fractional analysis, various jumpings, either in the strain or the stre...

This paper proposes an arbitrary-order immersed interface method for simulating the two-dimensional propagation of acoustic and elastic waves through fluid/solid interfaces. The present technique involves two main ingredients: (1) the linearized equations of continuum mechanics are simulated through an ADER (Arbitrary high-order schemes using DERiv...

Storing CO2 in deep underground reservoirs is key to reducing emissions to the atmosphere and standing against climate change. However, the risk of CO2 leakage from geological reservoirs to other rock formations requires a careful long-term analysis of the system. Mostly, oil well cement used for the operation must withstand the carbonation process...

In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation characterized by the nontrivial interactions between nonlocality and the regimes of low and high frequencies are studied a...

The research code MARPLE was originally created to model high-speed dynamic processes caused by the action of high-intensity energy fluxes on matter. At present, it is a universal tool able to solve various continuum mechanics problems. The implemented physical models are the following: single-fluid two-temperature MHD model of plasma dynamics, inc...

A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal state vect...

As complex and heterogeneous materials, the mechanical properties of rocks are still in need of further investigation regarding the mechanisms of the effects of water. In engineering projects such as goaf foundation treatment and ecological restoration, it is particularly important to describe the fracturing process of non-uniform water-containing...

In this study we derive Fick's law on the basis of the principles of chemical species mass and momentum conservation. The goal is to provide a simple derivation of this equation using a continuum mechanics approach. In addition, the associated assumptions and constraints that may limit its application are clearly identified. Our result is an analys...

In recent years, the development of lattice Boltzmann methods (LBMs) for solids has gained attention. Fracture mechanics as a viable application for these methods has been presented before, albeit for mode III cracks in the context of an LBM for antiplane shear deformation. The performance of the LBM itself is promising, while the usage of a regula...

Regarding microstructured materials, a quantitative prediction of phase transformation processes is highly desirable for a wide range of applications. With respect to polycrstalline materials, the plastic material behavior is commonly investigated using a crystal plasticity (CP) theory, since it accounts for the underlying microstructure, that is,...

In order to ensure the reliability of a numerical simulation software, verification and validation are unavoidable tasks. In this paper, we present a new rigorous code verification strategy based on manufactured solutions for the static analysis of geometrically non-linear Kirchhoff-Love shells and apply it to Isogeometric Analysis (IGA). While IGA...

Spheroids are microtissues containing cells organized in a spherical shape whose diameter is usually less than a millimetre. Depending on the properties of the environment they are placed in, some nearby spheroids spontaneously fuse and generate a tissue. Given their potential to mimic features typical of body parts and their ability to assemble by...

The peridynamic (PD) theory is a nonlocal reformulation of mechanics with various advantages over common approaches, mainly local continuum mechanics and molecular dynamics (MD). PD theory can capture phenomena at different dimensions, including nanoscale. However, limited studies have been performed by this theory in nanoscale, which have generall...

In the differential geometric formulation of nonlinear elasticity, the strain tensor can intrinsically be regarded as a measure of change of the metric of the Riemannian manifold that embodies the continuum undergoing a deformation. Here, this classical concept is revisited and complemented with two newly defined higher order deformation measures,...

The contribution at hand focuses on the introduction of a novel approach to model biological growth. The proposed formulations are chosen to represent plant like structures. Therefore, thermomechanically open systems are considered. The balance laws are presented for such systems. Furthermore, the proposed formulations are coupled with an adaptive...

Peridynamics (PD) is a new continuum mechanics formulation introduced to overcome limitations of classical continuum mechanics (CCM). This is mainly achieved by using integro-differential equations rather than partial differential equations. Another important difference of PD is its nonlocal nature with respect to local characteristic of CCM. Moreo...

Inspired by biology and engineered soft active material systems, we propose a new constitutive formulation for a soft material consisting of soft contractile fibers embedded in a soft matrix. The mathematical implementation of the model is based on a multi-field invariant formulation within a nonlinear continuum mechanics framework. The coupled con...

In this article, microscopic understanding of the surface tension are provided, which needs basic knowledge of thermodynamics, statistical mechanics as well as continuum mechanics. By introducing the intermolecular interaction potential and temperature definition, and by showing conceptual pictures including some results obtained by molecular dynam...

In this study, four absolute nodal coordinate formulation (ANCF)-based approaches are utilized in order to predict the buckling load of Lee’s frame under concentrated load. The first approach employs the standard two-dimensional shear deformable ANCF beam element based on the general continuum mechanics (GCM). The second approach adopts the standar...

This contribution proposes a second-order computational homogenisation formulation for natural and architected materials in the presence of voids. The macro-scale is described by a second gradient continuum theory in the finite strain regime, and the micro-scale is modelled by the concept of representative volume element (RVE) within the classical...

Rocks can be viewed as composites of solid minerals and pores or cracks filled with softer material such as pore fluids, kerogen, bitumen, and other organic matters. Rigidities and particularly viscosities of these soft phases are highly sensitive to the ambient temperature, which can significantly influence both static and dynamic properties of th...

A new, and extremely efficient, computational modeling paradigm is introduced here for specific finite elasticity problems that arise in the context of soft robotics. Whereas continuum mechanics is a very classical area of study that is broadly applicable throughout engineering, and significant effort has been devoted to the development of intricat...

The present master thesis discovers the state of the art of acceleration techniques for visco-plasticity of structures, which is the key element in durability analyses of mechanical components and assemblies with a low-frequency cyclic loading (thermal or mechanical). Instead of ad hoc durability models based on one cycle of loading and a lot of em...

Recent findings in action mechanics showing torques result from rates of variation in impulsive action motivated this more fundamental approach to estimate maximum power from wind turbines. Newton’s third law of equality of action and reaction provides a strictly causal mechanism of wind power from the deflection of wind momentum by twice its angle...

Magnetically manipulated interventional robotic systems offer outstanding advantages for improving vascular interventions, including minimizing radiation exposure to physicians and increasing the controllability of magnetic interventional devices in hard‐to‐reach vessels. However, automatic control of magnetic guidewires (MGs) is still challenging...

In this study, a numerical approach based upon the moving Kriging meshfree (MKM) formulations within the framework of the Gurtin–Murdoch continuum mechanics in conjunction with the three-dimensional shell theory is established. Thereafter, with the aid of proposed surface elastic-based MKM formulations incorporating proper polynomial basis function...

It is well known that “Physics and Symmetry/Asymmetry” is a topical Section of Symmetry [...]

In this work, we present a computational formulation based on continuum mechanics to study the interaction of fluid membranes embedded with semiflexible filaments. This is motivated by systems in membrane biology, such as cytoskeletal networks and protein filaments aiding the cell fission process. We model the membrane as a fluid shell via the Helf...

The paper explains the explosion of the Chelyabinsk asteroid - chondrite LL5 weighing about 10-15 thousand tons, which exploded in the sky over Chelyabinsk as 500 thousand tons in TNT equivalent. This explosion can't be explained by continuum mechanics or Newton's molecular kinetic theory. It is shown that the explosion of the Chelyabinsk asteroid...

Describing morphogenesis generally consists in aggregating the multiple high resolution spatiotemporal processes involved into repeatable low dimensional morphological processes consistent across individuals of the same species or group. In order to achieve this goal, biologists often have to submit movies issued from live imaging of developing emb...