51,927 research outputs found
Free-form solid modeling using deformations
One of the most important problems of available solid modeling systems is that the range of shapes generated is limited. It is not easy to model objects with free-form surfaces in a conventional solid modeling system. Such objects can be defined arbitrarily, but then operations on them are not transparent and complications occur. A method for achieving free-form effect is to define regular objects or surfaces, then deform them. This keeps various properties of the model intact while achieving the required visual appearance. This paper discusses a number of geometric modeling techniques with deformations applied to them in attempts to combine various approaches developed so far. © 1990
Free-form solid modeling using deformations
Ankara : The Department of Computer Engineering and Information Sciences and the Institute of Engineering and Science of Bilkent Univ. , 1989.Thesis (Master's) -- Bilkent University, 1989.Includes bibliographical references leaves 46-48.One of the most important problems of available solid modeling systems
is that the range of shapes generated is limited. It is not easy to model objects
with free-form surfaces in a conventional solid modeling system. Such
objects can be defined arl^itrarily but then operations on them are not transparent
and complications occur. A method for achieving free-form effect is
to define regular objects or surfaces, then deform them. This keeps various
properties of the model intact while achieving the required visuaJ appearance.
This thesis explains a number of geometric modeling techniques with
deformations applied to them in attempts to combine various approaches developed
so far. Regular deformations, which include twisting, bending, and
tapering, and free-form deformation technique are combined as a new deformation
method. This eliminates some of the disadvantages peculiar to each
method and utilizes the advantages of both.GĂĽdĂĽkbay, UÄźurM.S
Modeling of grain boundary dynamics using amplitude equations
We discuss the modelling of grain boundary dynamics within an amplitude
equations description, which is derived from classical density functional
theory or the phase field crystal model. The relation between the conditions
for periodicity of the system and coincidence site lattices at grain boundaries
is investigated. Within the amplitude equations framework we recover
predictions of the geometrical model by Cahn and Taylor for coupled grain
boundary motion, and find both and
coupling. No spontaneous transition between these modes occurs due to
restrictions related to the rotational invariance of the amplitude equations.
Grain rotation due to coupled motion is also in agreement with theoretical
predictions. Whereas linear elasticity is correctly captured by the amplitude
equations model, open questions remain for the case of nonlinear deformations.Comment: 21 pages. We extended the discussion on the geometrical
nonlinearities in Section
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
The aim of this paper is to compare a hyperelastic with a hypoelastic model
describing the Eulerian dynamics of solids in the context of non-linear
elastoplastic deformations. Specifically, we consider the well-known
hypoelastic Wilkins model, which is compared against a hyperelastic model based
on the work of Godunov and Romenski. First, we discuss some general conceptual
differences between the two approaches. Second, a detailed study of both models
is proposed, where differences are made evident at the aid of deriving a
hypoelastic-type model corresponding to the hyperelastic model and a particular
equation of state used in this paper. Third, using the same high order ADER
Finite Volume and Discontinuous Galerkin methods on fixed and moving
unstructured meshes for both models, a wide range of numerical benchmark test
problems has been solved. The numerical solutions obtained for the two
different models are directly compared with each other. For small elastic
deformations, the two models produce very similar solutions that are close to
each other. However, if large elastic or elastoplastic deformations occur, the
solutions present larger differences.Comment: 14 figure
A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: material model and strain localization analysis
Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell’s kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr–Coulomb, von Mises (J2) and Drucker–Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.Peer ReviewedPostprint (author's final draft
Animating Human Muscle Structure
Graphical simulations of human muscle motion and deformation are of great interest to
medical education. In this article, the authors present a technique for simulating muscle
deformations by combining physically and geometrically based computations to reduce
computation cost and produce fast, accurate simulations
Closing the gap between atomic-scale lattice deformations and continuum elasticity
Crystal lattice deformations can be described microscopically by explicitly
accounting for the position of atoms or macroscopically by continuum
elasticity. In this work, we report on the description of continuous elastic
fields derived from an atomistic representation of crystalline structures that
also include features typical of the microscopic scale. Analytic expressions
for strain components are obtained from the complex amplitudes of the Fourier
modes representing periodic lattice positions, which can be generally provided
by atomistic modeling or experiments. The magnitude and phase of these
amplitudes, together with the continuous description of strains, are able to
characterize crystal rotations, lattice deformations, and dislocations.
Moreover, combined with the so-called amplitude expansion of the phase-field
crystal model, they provide a suitable tool for bridging microscopic to
macroscopic scales. This study enables the in-depth analysis of elasticity
effects for macro- and mesoscale systems taking microscopic details into
account.Comment: 9 pages, 7 figures, Supporting Information availabl
Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
We investigate non-linear elastic deformations in the phase field crystal
model and derived amplitude equations formulations. Two sources of
non-linearity are found, one of them based on geometric non-linearity expressed
through a finite strain tensor. It reflects the Eulerian structure of the
continuum models and correctly describes the strain dependence of the
stiffness. In general, the relevant strain tensor is related to the left
Cauchy-Green deformation tensor. In isotropic one- and two-dimensional
situations the elastic energy can be expressed equivalently through the right
deformation tensor. The predicted isotropic low temperature non-linear elastic
effects are directly related to the Birch-Murnaghan equation of state with bulk
modulus derivative for bcc. A two-dimensional generalization suggests
. These predictions are in agreement with ab initio results for
large strain bulk deformations of various bcc elements and graphene. Physical
non-linearity arises if the strain dependence of the density wave amplitudes is
taken into account and leads to elastic weakening. For anisotropic deformations
the magnitudes of the amplitudes depend on their relative orientation to the
applied strain.Comment: 16 page
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