As structures become slender their non-linear aspects become more apparent and needing of assessment. In that spirit, the authors proposed a theory for addressing the effects of these non-linearities ...in a highly flexible beam akin to an wing in aeroservoelastic analyses regarding piezoelectric control for flutter suppression. This framework was proven quite efficient for it allowed large displacements to be naturally incorporated by means of a set of generalized variables that encoded the beam mechanics (membrane and bending) and in which space some mechanical features could be linearized. Therefore, the authors investigated the consequences of solving analytically a cantilever beam problem subjected to a material load at its free tip by means of that theory and demonstrated the connection between that problem (in particular when it comes to the buckling problem) and the Weierstrass elliptic ℘-function, a relationship not yet demonstrated to the best of the authors’ knowledge. That demonstration is the subject of this article, as well as a comprehensive study of the solutions for some loading conditions in a reference slender beam and the suggestion of further applications that could be developed from the solution found, in particular in FE analysis.
•A new methodology for solving beam-like nonlinear problems is derived.•Analyses are performed with a set of dimensionless variables simplifying the problem.•A novel solution is obtained in terms of the Weierstrass elliptic ℘-function.•Formulation can be extended and combined with efficient numerical methods of solution.
This paper is concerned with the modeling of steady radially directed fluid diffusion into a fibrous two-layer thick-walled hollow cylinder undergoing large deformation The approach presented here, ...based on the mechanics of interacting continua, seems to be a viable framework to better understanding of the coupled interaction between steady fluid flow and solid large deformation in saturated porous soft materials. Taking advantage of a perfect interface hypothesis between the two-layers of the thick-walled hollow cylinder; and a particular properties of rubber–fluid mixture, new results dealing with pressure difference, stress distribution, … at each layer as well as at the interface are obtained when varying stiffness of each layer. Our results could potentially help in understanding de-stiffening therapy, which is appearing as a possible strategy to reduce the occurrence of strokes and enhance the functional prognosis; they also be adopted as an effective aid to improve methods of designing prosthetic conduits for use with living tissue.
•Steady radially fluid diffusion through a fibrous two-layer walled hollow cylinder undergoing large strain is carried out.•Mixture theory seems to be a viable framework to capture coupled interaction between fluid flow and large solid deformation.•Our results could help in understanding de-stiffening therapy, known as a possible strategy to reduce occurrence of strokes.•This study can be used as an effective aid to improve methods of designing prosthetic conduits for biomedical applications.
Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and accurate simulation of complex geometries by utilizing higher-order shape functions and an unfitted ...discretization based on rectangular elements. Since the mesh does not conform to the geometry, cut elements arise that are intersected by domain boundaries. For optimal convergence rates and the efficiency of the simulation in general, special integration schemes have to be used in such elements. In this contribution, the often used, robust octree-decomposition-based integration scheme is enhanced by a novel approach reducing the computational effort when evaluating the discontinuous integrals. This is realized by introducing an additional step, in which the local integration mesh is simplified using data compression techniques leading to fewer integration domains/points. An important advantage of the proposed method is that it can be added in a modular fashion to already existing codes. While it inherits all desired properties of the octree-decomposition-based integration scheme, it significantly reduces the number of integration points and has hardly any negative effect on the simulation accuracy. In this paper, the proposed integration scheme is introduced in detail, and investigated by means of numerical examples in the context of 3D non-linear problems.
Non linear constitutive models for lattice materials Vigliotti, Andrea; Deshpande, Vikram S.; Pasini, Damiano
Journal of the mechanics and physics of solids,
March 2014, 2014-03-00, 20140301, Letnik:
64
Journal Article
Recenzirano
Odprti dostop
We use a computational homogenisation approach to derive a non linear constitutive model for lattice materials. A representative volume element (RVE) of the lattice is modelled by means of discrete ...structural elements, and macroscopic stress–strain relationships are numerically evaluated after applying appropriate periodic boundary conditions to the RVE. The influence of the choice of the RVE on the predictions of the model is discussed. The model has been used for the analysis of the hexagonal and the triangulated lattices subjected to large strains. The fidelity of the model has been demonstrated by analysing a plate with a central hole under prescribed in plane compressive and tensile loads, and then comparing the results from the discrete and the homogenised models.
The relationship between the macroscopic non-linear mechanics and the microscopic crystal structural evolution of pre-oriented high-density polyethylene (HDPE) is investigated by in situ synchrotron ...radiation wide-angle X-ray diffraction (WAXD) measurement over a wide temperature range from −10 to 130 °C. With the concept of stress-induced disordering of crystal, the ratio (φa/b) of lattice parameters a to b is defined as a new structural variable, which can reflect the lattice distortion and then the microscopic stress state of orthorhombic crystal (O-crystal). According to the temperature-dependent non-linear variation of φa/b with strain, the contributions of O-crystal and monoclinic crystal (M-crystal) to the macroscopic mechanics including linear elasticity, yielding, stress softening and strain hardening are clarified. It is found that M-crystal bears the main extensional stress once formed, although it survives within a limited strain window relying on temperature. By further combining the extensional phase diagram constructed in strain-temperature space, the HDPE deformation is recognized to undergo successively one-dimensional (1D) chain segments rotation of crystal, two-dimensional (2D) crystal plan shearing or slipping and three-dimensional (3D) recrystallization along with increasing strain or stress, demonstrating a multiscale structural transition and energy dissipation mechanism.
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•A new structural parameter is defined to characterize the lattice distortion and the microscopic stress state of crystal.•Multiscale structural evolutions of crystal are connected to the macroscopic non-linear mechanics of HDPE under deformation.•The research method can be generalized to other semicrystalline polymers to understand the structure-mechanics relationship.
Although bending a sheet of paper is an easy operation, stretching is more limited and it leads to rupture and tears. However, well-designed cuts on the sheet can induce a large effective ...stretchability. This kirigami technique offers a large scope of engineering applications ranging from deployable structures to compliant electronics. We are here interested in the axisymmetric configuration where cuts are designed along concentric circles. Applying an increasing transverse load at the center of the sheet results into a 3D axisymmetric structure of growing amplitude which eventually saturates. We first describe the linear response of the structure and determine the evolution of the deployed shape until its asymptotic geometrical limit. Reversing the problem in the linear regime, we propose, a design procedure for the cuts leading to a desired 3D shape. The structure can also be deployed by inflating an inner balloon. Exploring further the interplay between mechanics and geometry, we finally describe the maximum volume of inflated kirigami structures as a function of the cutting pattern.
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•Describing of the deployment of kirigami structures from a linear regime to saturation limited by geometry.•Programming the cutting pattern to obtained a desired target 3D shape.
Within the context of mixture theory, an attempt is made to solve a particular problem of radially directed fluid diffusion through a two-layer thick-walled pre-stressed fibrous hollow cylinder ...submitted to combined large deformations. With respect to both limitations due to perfect interface hypothesis and particular properties of rubber-fluid mixture, our investigation exhibit new results, which show interesting effects of both arterial stiffness in each layer as well as stretching and torsion upon applied mass flux as a function of pressure difference, but also upon spatial variations of both radial and tangential stretch ratios. These results could easily be echoed as an effective aid to improve the methods of making prosthetic conduits for use with living tissue; and can potentially help in understanding de-stiffening therapy, which is appearing as a potential strategy to decrease the stroke incidence and enhance the functional prognosis.
The non-linear mechanical characteristics of tailings under high pressure are the research foundation of large-scale high tailings dams. Considering the high stress caused by high tailing ponds, ...consolidated drained triaxial shear tests were carried out. The deterioration mechanism of non-linear mechanics was revealed by particle crushing. The test results show that sample density has a great influence on volumetric strain under low pressure. However, volumetric strain is not related to sample density under high pressure. The shear strength of the tailings is significantly non-linear. The internal friction angle under low pressure can still be obtained by the traditional linear Mohr–Coulomb criterion and the internal friction angle under high pressure by the power function of the Mohr criterion. The particle crushing of tailings occurs not only at high pressure but also at low pressure. The value of the breakage index increases with sample density. The non-linear mechanics of shear strength are affected by particle breakage. The breakage index value increases linearly with increasing shear strength, indicating that the high density of the deep part of the tailings dam is prone to particle crushing, which affects the stability of the large-scale high dam.
Soft tissues account for a major fraction of the body volume and mass. They are present in all non-skeletal organs, being responsible for protecting the body, maintaining internal homeostasis, and ...allowing for mobility. Their function in different organs is highly diverse, as are their properties which are optimally suited for their specific tasks. From a mechanical perspective, specificity of structure and properties is acquired via evolutionary adaptation of the tissue composition and multi-scale structure. In modeling tissue mechanics and mechano-biology, it is thus natural to seek the structural determinants of tissues and their evolution (the “structural approach”). Earlier models were exclusively phenomenological, based either on the general principles of non-linear continuum mechanics or alternatively, on empirical mathematical expressions that fit specific response patterns. In the late 1970’s, structural models were introduced to tissue mechanics (Lanir in J. Biomechanics 12(6): 423–436,
1979
; Lanir in J. Biomechanics 16(1): 1–12,
1983
). Ever since, a gradually increasing number of structural models have been developed for different types of tissues, and today, it is the method of choice (Cowin and Humphrey in J. Elasticity 61: ix–xii,
2000
). The structural approach was recently extended to incorporate a mechanistic formulation of mechano-biological pathways by which tissue structures remodel during growth (Lanir in Biomech Model Mechanobiol, 14(2): 245–266,
2015
). Here, the characteristic features of soft tissue structures and their constitutive modeling are reviewed. The presentation starts with a brief survey of the multi-scale and multi-phasic soft tissues structure. The global mechanical characteristics of soft tissues and of their constituents are then briefly reviewed. These two aspects form the basis for structural constitutive formulation via the multi-scale structure-function link. Based on established criteria for model validity, predictions of the formulated theory are contrasted against measured response characteristics. Using this structure-function relationship, the evolutionary pathway by which tissue structure and mechanics remodel during growth to adapt to their physiological function, is laid down. The review concludes with an account of the state of the art, the big picture, and future research challenges in tissue mechanobiological modeling.
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