large deformations
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2022 ◽  
Vol 41 (2) ◽  
pp. 1-16
Author(s):  
Yuichi Nagata ◽  
Shinji Imahori

Escher tiling is well known as a tiling that consists of one or a few recognizable figures, such as animals. The Escherization problem involves finding the most similar shape to a given goal figure that can tile the plane. However, it is easy to imagine that there is no similar tile shape for complex goal shapes. This article devises a method for finding a satisfactory tile shape in such a situation. To obtain a satisfactory tile shape, the tile shape is generated by deforming the goal shape to a considerable extent while retaining the characteristics of the original shape. To achieve this, both goal and tile shapes are represented as triangular meshes to consider not only the contours but also the internal similarity of the shapes. To measure the naturalness of the deformation, energy functions based on traditional as-rigid-as-possible shape modeling are incorporated into a recently developed framework of the exhaustive search of the templates for the Escherization problem. The developed algorithms find satisfactory tile shapes with natural deformations for fairly complex goal shapes.


Author(s):  
Sowmya N. Sundaresh ◽  
John D. Finan ◽  
Benjamin S. Elkin ◽  
Andrew V. Basilio ◽  
Guy M. McKhann ◽  
...  

Vibration ◽  
2022 ◽  
Vol 5 (1) ◽  
pp. 20-58
Author(s):  
Xiaoquan Wang ◽  
Ricardo A. Perez ◽  
Bret Wainwright ◽  
Yuting Wang ◽  
Marc P. Mignolet

The focus of this investigation is on reduced order models (ROMs) of the nonlinear geometric response of structures that are built nonintrusively, i.e., from standard outputs of commercial finite element codes. Several structures with atypical loading, boundary conditions, or geometry are considered to not only support the broad applicability of these ROMs but also to exemplify the different steps involved in determining an appropriate basis for the response. This basis is formed here as a combination of linear vibration modes and dual modes, and some of the steps involved follow prior work; others are novel aspects, all of which are covered in significant detail to minimize the expertise needed to develop these ROMs. The comparisons of the static and dynamic responses of these structures predicted by the ROMs and by the underlying finite element models demonstrate the high accuracy that can be achieved with the ROMs, even in the presence of significant nonlinearity.


2022 ◽  
Vol 8 ◽  
Author(s):  
Mirit Sharabi

Through years of evolution, biological soft fibrous tissues have developed remarkable functional properties, unique hierarchical architectures, and -most notably, an unparalleled and extremely efficient deformation ability. Whereas the structure-function relationship is well-studied in natural hard materials, soft materials are not getting similar attention, despite their high prevalence in nature. These soft materials are usually constructed as fiber-reinforced composites consisting of diverse structural motifs that result in an overall unique mechanical behavior with large deformations. Biomimetics of their mechanical behavior is currently a significant bioengineering challenge. The unique properties of soft fibrous tissues stem from their structural complexity, which, unfortunately, also hinders our ability to generate adequate synthetic analogs, such that autografts remain the “gold standard” materials for soft-tissue repair and replacement. This review seeks to understand the structural and deformation mechanisms of soft collagenous tissues, with a particular emphasis on tendon and ligaments, the annulus fibrosus (AF) in the intervertebral disc (IVD), skin, and blood vessels. We examined and compared different mechanical and structural motifs in these different tissue types, which are subjected to complex and varied mechanical loads, to isolate the mechanisms of their deformation behavior. Herein, we focused on their composite structure from a perspective of the different building blocks, architecture, crimping patterns, fiber orientation, organization and their structure-function relationship. In the second part of the review, we presented engineered soft composite applications that used these structural motifs to mimic the structural and mechanical behavior of soft fibrous tissues. Moreover, we demonstrated new methodologies and materials that use biomimetic principles as a guide. These novel architectural materials have tailor-designed J-shaped large deformations behavior. Structural motifs in soft composites hold valuable insights that could be exploited to generate the next generation of materials. They actually have a two-fold effect: 1) to get a better understanding of the complex structure-function relationship in a simple material system using reverse biomimetics and 2) to develop new and efficient materials. These materials could revolutionize the future tailor-designed soft composite materials together with various soft-tissue repair and replacement applications that will be mechanically biocompatible with the full range of native tissue behaviors.


2022 ◽  
pp. 108128652110635
Author(s):  
Leonid Zubov ◽  
Mikhail Karyakin

The paper presents an exact solution for the problem of large deformations of torsion, axial tension–compression, and radial expansion or shrinkage of an elastic hollow circular cylinder equipped with pre-stressed elastic coatings. Surface coatings are modeled using the six-parameter nonlinear shell theory. The constitutive material of the cylinder is described by a three-dimensional nonlinear model of the isotropic incompressible body of the general form. Special boundary conditions describe the interaction of this material with thin coatings on the inner and outer surface of the pipe. Based on the solution obtained, numerical calculations were performed on the effect of preliminary stresses in coatings on the stress–strain state of a cylindrical pipe.


Author(s):  
Oksana Andriivna Tatarinova ◽  
Dmytro Vasylovych Breslavsky

The paper presents the formulation of a two-dimensional problem of the creep theory for the case of finite strains. A description of the foundations of the calculation method presents. The method is based on the use of the generalized Lagrange-Euler (ALE) approach, in which the boundary value problem in the current solid configuration is solved by using FEM. A triangular element is involved in the numerical modeling. At each stage of creep calculations in the current configuration, the initial problem is solved numerically using the finite difference method. The preprocessing data preparation is carried out in the homemade RD program, in which two-dimensional model is surrounded by a mesh of special elements. This feature implements the ALE algorithm for the motion of material elements along the model. The examples of preprocessing as well as of the mesh rebuilding in the case of finite elements transition are given. Creep calculations are performed in the developed program, which is based on the use of the FEM Creep software package in the case of finite strains. The regular mesh is used for calculations, which allow us to use the efficient algorithm for transition between current configurations. The numerical results of the creep of specimens made from aluminum alloys are compared with the experimental and calculated ones obtained by integrating the constitutive equations. It was concluded that for material with ductile type of fracture the presented method and software allow to obtain results very close to experimental only by use of creep rate equation. Creep simulations of material with mixed brittle-ductile fracture type demand use the additional equation for damage variable.


2021 ◽  
Vol 67 (12) ◽  
pp. 666-681
Author(s):  
Gábor Ladányi ◽  
Viktor Gonda

The modelling and simulation of material degradations, particularly fractures in solids of different lengths and time scales, remains challenging despite the numerous approaches that have been developed. In this review, the focus is set on research work concerned with a very promising non-local method: peridynamic modelling. With this approach, continuous phenomena may be described, and the complete evolution (i.e., initiation, propagation, branching, or coalescence) of cracks and other discontinuities can be followed in solids in an integrated framework. Evaluating the large number of publications on this topic, the authors chose to present concisely the key concepts, applications, and results in identifying possible future paths: the incorporation of mechanics of large deformations and material nonlinearities, and the development of high-efficiency peridynamic solvers. This review does not intersect with recent relevant reviews, which reflects its significance to readers.


Author(s):  
Ludwig Herrnböck ◽  
Paul Steinmann

AbstractThis work investigates the possibility of applying two-scale computational homogenization to rod lattice structures emerging, for instance, from additive manufacturing. The influence of the number of unit cells within the representative volume element (RVE), thus, the RVE’s size on the homogenized mechanical response is studied for occurring microscopic structural instabilities. Therein, the macro-scale, described in terms of three-dimensional continuum mechanics, is coupled to the micro-scale described by geometrically exact rods, enabling arbitrary large deformations and rotations. A special feature of the presented framework is that the rods building the lattice structures are not restricted to deform purely elastically but may deform inelastically. The mechanical response of lattice structures is investigated by applying the developed homogenization method to an exemplary lattice. Under special loads the structure reaches an instable state and may buckle. The appearance of instabilities depends on the geometric properties of the lattice’s underlying rods and the RVE’s size.


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