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Highlights • The theory of screws is undergoing a revival in machines and robotics. • The theory is significantly generalized and extended in various directions. • Use is made of exterior algebra of multi-vectors. • A formulation in terms of tensor densities is also provided. Abstract The theory of screws is generalized to yield a formulation of Statics in higher-dimensional spaces in the absence of any distinguished metric structure. This level of generality necessitates the use of the tools of the exterior algebra of multi-vectors. The minimal structure retained serves to bring into relief the essential difference between screws and counter-screws as well as a weak version of the notion of rigid-body velocity field. An essential feature of the theory is the introduction of higher-order forces and displacements, whose relevance in the context of structured media can be determined in specific potential applications. [ABSTRACT FROM AUTHOR]

Highlights • Laminates and bundles are important cases of functionally graded materials. • Classical inhomogeneity theory is not able to treat defects in these materials. • A novel definition of inhomogeneity in laminates and bundles is introduced. Abstract Laminates and bundles are common particular cases of functionally graded materials (FGMs). Within this class of non-uniform media, laminates and bundles are distinguished by a property of partial uniformity along surfaces or lines. The question addressed in this paper is whether this property can be exploited to define rigorously a notion of homogeneity eventually leading to a quantitative measure of a density of continuous defects. [ABSTRACT FROM AUTHOR]

The notion of embedded homogeneity of thin-walled structures is introduced as the property characterizing the provenance of such a structure from a homogeneous material. This property needs to be distinguished from other definitions of homogeneity formulated exclusively in terms of a purely structural constitutive equation. Necessary conditions for embedded homogeneity are derived for planar beams and their geometric interpretation is expressed as the condition for the elastic hodograph to lie on a hypersphere containing the origin of a six-dimensional space of tensors. [ABSTRACT FROM AUTHOR]

A unified theory of material defects, incorporating both the smooth and the singular descriptions, is presented based upon the theory of currents of Georges de Rham. The fundamental geometric entity of discourse is assumed to be represented by a single differential form or current, whose boundary is identified with the defect itself. The possibility of defining a less restrictive dislocation structure is explored in terms of a plausible weak formulation of the theorem of Frobenius. Several examples are presented and discussed. [ABSTRACT FROM AUTHOR]

Abstract: Boundary growth is defined as a particular case of surface growth. Within this restricted context, it is shown that the kinetics of boundary growth is not essentially distinguishable from that of volumetric growth and that, consequently, the a-priori notion of material particle may be devoid of an intrinsic meaning. [ABSTRACT FROM AUTHOR]

Abstract: We present a unified purely hyperbolic model for compressible and incompressible viscoelastic liquids. The proposed model is then solved numerically using the least-squares finite element method (LSFEM). [Copyright &y& Elsevier]

Abstract: After drawing a distinction between anelastic evolution and aging, it is shown that for certain solid classes a canonical decomposition of any symmetry-preserving evolutive process into an anelastic-like component and an aging component can be achieved. The theory thus obtained can be regarded as the time-like counterpart of the theory of inhomogeneities in functionally graded bodies. [Copyright &y& Elsevier]

Abstract: A method to derive the stiffness of self-similar elastic fractals is presented based on structural mechanics principles and a physically motivated similarity criterion, which is assumed as a postulate. Using this method, the stiffnesses of both the Von Koch curve and the Sierpiński gasket in the small-deformation regime are derived. For these fractal structures, it is shown that the stiffness matrix is completely determined by a single elastic constant. The procedure to tile a planar domain with Sierpiński gaskets is explored and shown to require the consideration of hexagonal-shaped combinations of gaskets joined continuously along their edges. This continuity leads to a phenomenon of geometrically induced inextensibility along the common edges. After deriving the stiffness matrix for the basic hexagon, the analog of the Boussinesq–Flamant problem for a tiled half-plane is solved numerically to demonstrate the potential of the method in modeling of solid mechanics applications. [Copyright &y& Elsevier]

Abstract: A systematic procedure to extract a projected first-grade constitutive equation from a given second-grade one is proposed and proven to be independent of the reference configuration used. The symmetry group of the projected material is shown to contain the first-grade projection of the symmetry group of the original material. The proposed method is illustrated by means of an example. [Copyright &y& Elsevier]

Abstract: Fibres, aponeuroses, and tendons are often considered mechanically “in series” in skeletal muscles. This notion has led to oversimplified calculations of fibre forces from tendon forces, to incorrect derivations of constitutive laws for aponeuroses, and to misinterpretations of the recovery of elastic energy in stretch-shortening cycles of muscles. Here, we demonstrate theoretically, using examples of increasing complexity, that tendon and aponeurosis are not in series in a muscle fibre–aponeurosis–tendon complex. We then demonstrate that assuming the tendon and aponeurosis to be in series can lead to the appearance of mechanical work creation in these passive viscoelastic structures, a result that is mechanically impossible. Finally, we explain the mechanical role of the incompressible muscle matrix in force transmission from fibres to aponeuroses and tendon, and emphasize that incompressibility necessitates the introduction of extra forces necessary to maintain this constraint. Unfortunately, this requirement eliminates, for all but the simplest cases, a theoretical approach of muscle modeling based on intuitive free-body diagrams. [Copyright &y& Elsevier]

The purpose of this note is to reaffirm the fact that there exists a natural connection between Noll’s theory of inhomogeneities and the Eshelby tensor. One way to expose this connection consists in allowing the inhomogeneity pattern to evolve in time and then exploring the thermodynamic implications. [Copyright &y& Elsevier]

• We apply a difference of potential to the inner/outer boundaries of the tube. • For a larger difference of potential, the hoop deformation solitary wave decreases. • The period of the hoop solitary wave increases for a larger difference of potential. [Display omitted] The influence of an electric field on the propagation of axially symmetric solitary waves in a fluid-filled thin-walled tube made of a dielectric elastomer is analysed. The electric field is applied by means of soft flexible electrodes lining the internal and external surfaces of the tube and connected to a power source with a given constant difference of potential. For a specific hyperelastic constitutive law, numerical results are obtained and discussed. [ABSTRACT FROM AUTHOR]

• A new model for coupled diffusive processes with a TLP bonding application. • Model framed within the theory of partial differential equations of a mixed order. • Comparison between single interlayer, separate and nanocomposite interlayers. • Spatial distribution variance of concentration as a measure of the diffusive process. A model for coupled diffusive processes is framed within the theory of partial differential equations of mixed order. Its numerical implementation is achieved by a technique that does not require additional tools beyond the standard procedures for the solution of the diffusion equation. The interface between the diffusant and the substrate retains its sharpness during the bulk of the diffusive process. The results demonstrate that, as expected in pharmaceutical and diffusion bonding applications, the amount of material made available for diffusion is controlled by the area of the interface and, therefore, the use of nanoparticle layers may greatly accelerate the rate of the overall process. [ABSTRACT FROM AUTHOR]

• Background on differential geometric concepts is provided in the short space available. • The theory of G-structures is shown to be relevant to both approaches mentioned in title. • A non-trivial example is presented to illustrate the theory. • Some epistemological questions are addressed, if very briefly. An attempt is made to bring into harmony two of the paradigms commonly used in the theory of continuous distributions of defects. It is shown that the common differential geometric apparatus is provided neatly by the theory of G-structures. In the case of a structural model, based on putative experimental observations at the microscopic level, a G-structure can be shown to emerge from the group of linear transformations that preserve a tensorial quantity. For the phenomenological (macroscopic) constitutive model, the G-structure arises from the notion of material isomorphism and the underlying local symmetry group of the constitutive law. A comparative example is presented in the framework of certain smectic liquid crystals. [ABSTRACT FROM AUTHOR]

• Description of fibre recruitment by means of a material implant (theory of uniformity). • Description of the evolution of the recruitment parameters and the fibre orientation by use of the theory of uniformity. • Benchmark problem describing an idealised blood vessel, representing, e.g., a case of hypertension. This study focusses on the remodelling of biological tissues in the framework of the theory of material uniformity. A constitutive evolution model is introduced, including fibre recruitment and reorientation, and subjected to the entropy inequality, which enforces the Second Principle of Thermodynamics. The model is applied to a numerical example describing a pressurised fibre-reinforced cylinder, roughly representing an artery, and is able to capture the major characteristics of remodelling in arteries, as reported in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Linear viscoelastic structures are characterized by dissipative forces that depend on the history of the velocity response via hereditary damping functions. The free motion equation leads to a nonlinear eigenvalue problem characterized by a frequency-dependent damping matrix. In the present paper, a novel and efficient numerical method for the computation of the eigenvalues of linear and proportional or lightly non-proportional viscoelastic structures is developed. The central idea is the construction of two complex-valued functions of a complex variable, whose fixed points are precisely the eigenvalues. This important property allows the use of these functions in a fixed-point iterative scheme. With help of some results in fixed point theory, necessary conditions for global and local convergence are provided. It is demonstrated that the speed of convergence is linear and directly depends on the level of induced damping. In addition, under certain conditions the recursive method can also be used for the calculation of non-viscous real eigenvalues. In order to validate the mathematical results, two numerical examples are analyzed, one for single degree-of-freedom systems and another for multiple ones. [Copyright &y& Elsevier]

Abnormal, excessive stresses acting on articular joint surfaces are speculated to be one of the causes for joint degeneration. However, articular surface stresses have not been studied systematically, since it is technically difficult to measure in vivo contact areas and pressures in dynamic situations. Therefore, we implemented a numerical model of articular surface contact using accurate surface geometries. The model was developed for the cat patellofemoral joint. We demonstrated that small misalignments of the patella relative to the femur change the joint contact mechanics substantially for a given external load. These results suggest that misalignment might be studied as one of the factors causing articular cartilage disorder and joint degeneration. [Copyright &y& Elsevier]