D. Terzopoulos, Kurt F., "Modeling inelastic deformation: viscoelasticity, plasticity, fracture", Computer Graphics, Vol 22, 4, pp. 269-278, Aug., 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... surfaces between catenary curves [36] Barr, Terzopoulos, Platt and Fleisher have used discrete molecular components to model the elastic behavior of objects [22] Terzopoulos and Fleischer have extended the model mixing flexible and rigid components [33] and to simulate also inelastic behavior [32]. Many other techniques have been proposed to improve physically based deformations, as the methods based on constraints presented by Platt and Barr [23] and Metaxas and Terzopoulos [17] Approaches based on discretising the object into a number of particles, whose connectivity is maintained ....

Terzopoulos, D. and Fleischer, K. "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture", Computer Graphics, v. 22, n. 4, p. 269-278, 1988.

.... of medical training simulators has been ongoing since the early 1990 s [67] The simulation is based on KISMET (Kinematic Simulation, Monitoring and O# Line Programming Environment for Telerobotics) The Karlsruhe Endoscopic Surgery Trainer employs two types of deformable models: particle systems [125] and linear elastostatic finite element models with and without condensation [18] The sti#ness of living tissue is estimated based on ultrasound measurements and compared to stress strain curves of animal samples obtained in tension test machines and with a compression test [78] The ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: viscoelasticity, plasticity, fracture. In Computer Graphics, Annual Conference Series, pages 269--278, Atlanta, USA, Aug 1988. ACM SIGGRAPH.

....popularity of subdivision geometry, we have witnessed increasing number of applications in computer graphics using subdivision objects. The next few sections will cover several research that utilize subdivision geometry as a underlying tool. 5. 1 Interactive Modeling Since Terzopoulos et al.[90, 89] s research, a deformable model has played an important role in computer graphics, especially in animation. The deformable model is the geometric object that is governed by the Lagrangian equation of motion: ## # (r)# = f (r,t) 63) where r(p,t) is the displacement of p at time t, ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In Computer Graphics (SIGGRAPH '88 Proceedings), pages 269--278, 1988.

....with regard to memory. The system handles individual patient data sets. While the model of the patient s bone structure and the patient s face is provided by a CT scan and a surface laser scan, respectively, the patient s soft tissue is represented by a mass spring system. Mass spring systems [22, 23] are not only used to model deformable soft tissue in surgical simulation environments, but they are also widely used to model other deformable objects. They have been applied to a variety of problems, such as cloth modeling [6, 10] and facial animation [18] Mass spring models assume a ....

D. Terzopoulos, K. Fleischer. "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture", SIGGRAPH '88, ACM Computer Graphics, 22(4):269--278, 1988.

....deformable models in graphics was pioneered by Terzopoulos et al. 32] The original work applied the Lagrangian equations of motion using a finite difference scheme to simulate elastic objects with regular parameterizations. This framework was extended to include inelastic behaviors [31], and to handle stiff rotating bodies using linearized equations [33] Following their introduction, physically based deformations were extended in many ways. Platt and Barr [24] introduced better constraint handling via Lagrange multipliers. Pentland and Williams [23] obtained realtime ....

....to achieve fast deformations. Baraff and Witkin [1] added non penetration constraints to this framework. Metaxas and Terzopoulos [21] combined global deformations with local finite element deformations. Implicit solvers are enjoying a renaissance in dynamic deformations. Terzopoulos et al. 32][31] used semi implicit solvers in their initial work. Baraff and Witkin [2] used a fully implicit scheme to greatly improve the speed and stability of cloth simulation. Desbrun et al. 9] used a semi implicit scheme to stabilize stiff systems. Hierarchical methods have also been used to speed up ....

[Article contains additional citation context not shown here]

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. Computer Graphics (Proceedings of SIGGRAPH 88), 22(4):269--278, August 1988. Held in Atlanta, Georgia.

....Fig. 15 shows a metallic flag animated using this method. For a rigid surface, explicit motions can be generated by a force field acting on the height vectors, thus deforming the texels. The force field can be for instance a Laplace field [WH91] a stochastic flow [SF92] or a mass spring [TF88] network connecting the tip of the height vectors. Fig. 16 left shows a lawn under the wind animated by this way (the force field we use is a mix of a moving periodic function and a stochastic function) Successive steps of a simple motion, such as oscillations of leaves in foliage, can be ....

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In John Dill, editor, Computer Graphics (SIGGRAPH '88 Proceedings), volume 22, pages 269--278, August 1988.

.... painting on surface [16] procedural tools which let the user control the parameters of an automatic detail generator, which can be generic [20, 11, 13] or specialized [12, 23, 22, 1, 32] simulation tools which reproduce physical laws to be solved, used in particular for cloth material [25, 5, 2] and for some biological patterns [14, 31, 27] The second aspect, i.e. the way to represent the details, may involve: polygonal meshes and other 3D surface encodings, displacement maps, i.e. texture encoded relief that can be translated into geometry at rendering time [29, 15] ....

....the surfaces. Transition between these representations are defined in [3, 6] The idea of simulating growth has been introduced in the scope of biological objects [28, 23, 22] The shape of elastic surfaces such as cloth material at equilibrium is generally obtained through physical simulations [25, 5, 2] although some geometric tools are also used to fake the physics [9] As D Arcy Thompson [26] suggests for natural objects, there are several possible approaches to explain a given shape. Interactive tools like Maya Artisan tm are convenient for the user, but they require the explicit design of ....

D. Terzopoulos and K. Fleisher. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In SIGGRAPH'88 Conference Proceedings, pages 269--278, 1988.

....deformable models in graphics was pioneered by Terzopoulos et al. 42] The original work applied the Lagrangian equations of motion using a finite difference scheme to simulate elastic objects with regular parameterizations. Their framework was extended to include inelastic behaviors [41], and to handle stiff rotating bodies using linearized equations [44] Physically based deformations have since been extended in many ways. Platt and Barr [33] introduced better constraint handling via Lagrange multipliers. Pentland and Williams [31] obtained realtime simulations by using only a ....

....deemed necessary so static and quasi static methods have been employed [6, 18, 21, 22, 37] Since our interest is in realistic motion, we build on dynamic methods. Implicit solvers have been enjoying a renaissance in dynamic deformations for computer graphics in recent years. Terzopoulos et al. [41, 42] used semi implicit solvers in their initial work. Baraff and Witkin [4] used an implicit scheme to greatly improve the speed and stability of cloth simulation. Desbrun et al. 14] used a semiimplicit scheme to stabilize stiff systems. Hauth and Etzmuss [20] recently showed that the implicit ....

[Article contains additional citation context not shown here]

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. Computer Graphics (Proceedings of SIGGRAPH 88), 22(4):269--278, August 1988.

....which is less accurate but simpler and appropriate for some applications. Indeed a linear finite di #erence method over a uniform mesh is just a special case of FEM. Its accuracy and mathematical rigorousness make FEM a better choice for applications such as surgical simulations. Terzopoulos et al.[21, 20, 22] applies both finite difference and finite element methods in modeling elastically deformable objects. Celniker et al.[15] applies FEM to generate primitives that build continuous deformable shapes designed to support a new free form modeling paradigm. Pieper et al.[16] applies FEM to computer aided ....

....are more optimally positioned in the matrix. 6 Collision Handling For collisions involving deformable objects, the collision time can be assumed finite (unlike the instantaneous collision of rigid bodies) This allows a larger time step for numerical integration. The popular penalty methods [21, 20, 22] model the collision by adding an artificial spring of large sti#ness at the point of collision. This sti# spring requires tiny integration time steps to stably simulate a collision. Various experiments show that the ratio between a collision free integration time step and that of a penalty ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. Computer Graphics, 22, August 1988.

....which is less accurate but simple and appropriate for some applications. Indeed a linear finite difference method over a uniform mesh is just a special case of FEM. Its accuracy and mathematical rigorousness make FEM a better choice for applications such as surgical simulations. Terzopoulos et al.[29, 28, 30] applies both finite difference and finite element methods in modeling elastically deformable objects. Celniker et al.[15] applies FEM to generate primitives that build continuous deformable shapes designed to support a new free form modeling paradigm. Pieper et al.[17] applies FEM to computer aided ....

....states. 5.1 Collision with the Proxy A virtual proxy is a rigid object with a piecewise differentiable surface. Usually a proxy has a very regular shape, such as a sphere or a cylinder. However In this section, we will discuss collisions using a general proxy. The popular penalty methods [29, 28, 30] model the collision by adding an artificial spring of large stiffness at the point of collision. This stiff spring requires tiny integration time steps to stably simulate a collision. Various experiments show that the ratio between a collision free integration time step and that of a penalty ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. Computer Graphics, 22, August 1988.

....which is less accurate but simple and appropriate to some applications. Indeed a linear finite difference method over a uniform mesh is just a special case of FEM. Its accuracy and mathematical rigorousness makes FEM a better choice for applications such as surgical simulations. Terzopoulos et al.[12, 11, 13] applies both finite difference and finite element methods in modeling elastically deformable objects. Celniker et al.[6] applies FEM to generate primitives that build continuous deformable shapes designed to support a new free form modeling paradigm. Pieper et al.[8] applies FEM to computer aided ....

....for cloth simulation [2] 4 Collision Integration Scheme For deformable object collisions, the collision time can be assumed finite (unlike the instantaneous collision of rigid bodies) This allows a larger time step for integration. The popular penalty methods for collision handling [12, 11, 13] did not take advantage of this. A penalty method models the collision by adding an artificial spring of large stiffness at the point of collision. This stiff spring requires tiny time steps to stably simulate a collision. Various experiments show that the ratio between a collision free time step ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. Computer Graphics, 22, August 1988.

.... potential energy due to the motion of the point (it is a force term) The definition of the energy function is a crucial task; pioneering attempts to give a mathematical model of plasticity, viscoelasticity and fracture have been produced by Terzopoulos et al. 21] and Terzopoulos and Fleischer [23]. In these works the points on the object are defined as the sum of a reference component so that the rigid body motion and the deformation are separated. The FEM model The most widely used, accurate and expensive way to model the deformation of tissues is the Finite Element Method (FEM) This ....

Demetri Terzopoulos and Kurt Fleischer, Modeling inelastic deformation: Viscoelasticity, plasticity, fracture, Computer Graphics (SIGGRAPH '88 Proceedings) (John Dill, ed.), vol. 22, August 1988, pp. 269--278.

....de deformation. Travaux anterieurs La plupart des modeles physiques deformables sont bases sur une approche nodale, c est a dire modelisant les deformations d un objet par des deplacements de noeuds elementaires a l interieur de ce dernier. C est le cas des modeles de Demetri Terzopoulos [TPBF87, TF88] qui discretisent une equation di#erentielle issue de la theorie mecanique des milieux continus. En echantillonnant l espace et le temps, on peut en e#et approximer par di#erences finies les derivees des parametres du mouvement sur les noeuds d un maillage, et donc resoudre le mouvement de facon ....

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformations: Viscoelasticity, plasticity, fracture. Computer Graphics, 22(4):269--278, August 1988. Proceedings of SIGGRAPH'88 (Atlanta, Georgia).

....live objects) are non rigid, or even more problematic: deformable. The representation typically used for representation of non rigid objects is an articulated object with links between rigid sub parts. An acceptable representation of deformable objects has been the subject of much recent research[Terzopoulos88] Platt88] One new deformable object representation, which is promising due to its low computing requirements, describes the deformations using a modal analysis [Pentland89] The rendering stage that gives these representations much of their manipulability is computationally expensive, and well ....

D. Terzopoulos, K. Fleischer, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture", ACM Computer Graphics, Vol. 22, No. 4, Aug. 1988, p.269.

....the total volume remains approximately constant. This paper presents an integrated set of methods for simulating these behaviors. 1.1 Previous inelastic models Contrary to elastic objects, the shape of inelastic bodies depends on the entire history of applied forces. Terzopoulos et al. [10] use two layers to simulate this behavior: an inelastic reference component, that computes motion and absorbs large scale deformations, and an elastic layer that represents the difference between the current and reference shapes. The model handles visco elasticity, plasticity and fractures. ....

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformations: Viscoelasticity, plasticity, fracture. Computer Graphics, 22(4):269--278, August 1988. Proceedings of SIGGRAPH'88 (Atlanta, Georgia).

....nodes inside a flexible body. Some of them derive from the elasticity theory. Di#erential equations of motion are discretized in space, and then integrated over time by resolving a matrix equation at each time step. This scheme has been used for modeling both elastic [37] 39] 19] and inelastic [36] deformations. However, since the topology of the network of nodes does not vary over time, this approach is restricted to the animation of structured objects. A solution for modeling soft inelastic bodies that absorb deformations and may separate into pieces or melt during an animation is a ....

....such as separation or fusion. This allows simulation of behaviors that would be extremely difficult to treat with other methods. Section II presents the layered approach we use. Section III details the collision processing method associated 2 As for instance Terzopoulos et al. models [37] 39] [36], and Pentland s Thing World system [32] 35] with the implicit layer. Section IV introduces volume preservation to the model. Section V presents two di#erent applications of this formalism: the design of simplified characters made of articulated skeletons coated with elastic flesh, and the ....

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformations: Viscoelasticity, plasticity, fracture. Computer Graphics, 22(4):269--278, August 1988. Proceedings of SIGGRAPH '88 (Atlanta, Georgia).

....a third crack[3] In this manner, a crack tree is formed. 3.2 Previous Computer Graphics Fracture Models Previous attempts at modelling fracture for computer graphics have been based on spring mass models. Much of the work on these models was done by Terzopoulos with various collaborators [21, 22] and was applied specifically to the problem of fracture by Norton et al. 15] The models represent materials as a grid of distributed masses connected together by springs. Often, the modelling efforts have focused on relatively thin surfaces, although they are extensible to full three ....

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In Computer Graphics (SIGGRAPH '88 Proceedings), volume 22, pages 269--278, August 1988.

....of simple short cuts, such as slicing the surface of an object into faces or the use of RenderMan shaders. Consequently, the simulation of breaking and shattering has received some attention within the graphics community. An early attempt at modeling fracture is given in Terzopoulus and Fleischer[12], where they presented a technique for modeling viscoelastic and plastic deformations. While not specifically intended to model the breaking of brittle objects, their work allowed the simulation of tearing cloth and paper with techniques that could conceivably have be applied to this task. In ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. SIGGRAPH 88 Conference Proceedings, 22:287-- 296, 1988.

....graphics. We refer the reader to a recent, thorough survey [10] which describes much of this work. We mention some relevant physically based models here, which include cloth models (e.g. 4] linked volumetric objects [11] modal models [23] and the pioneering work of Terzopoulos and colleagues [26, 24, 25, 22]. In the following we focus mainly on models specifically designed to simulate physical deformation of objects, rather than purely geometric deformable models. Among physically based models, the most popular are mass spring models (e.g. 4, 19, 28] They divide the domain # into set of mass ....

Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In John Dill, editor, Computer Graphics (SIGGRAPH 88 Proceedings),vol- ume 22, pages 269--278, August 1988.

....theorem from differential geometry states that two solids in space will have the same instantaneous shape if their metric tensors are equal. Non linear Dynamic Behavior Much research on deformable models was derived from the above work on linear elastic behavior. Terzopoulos and Fleischer [TF88b, TF88a] extended previous results to simulating inelastic deformations, including viscoelasticity (a generalization of viscosity and elasticity) plasticity, and fracture. Unlike elastic bodies, inelastic objects do not return to their initial shape, yet their deformation is still computed in ....

....The authors use an implicit solver and adaptive time steps in order to avoid numerical instability. Traditional collision detection algorithms are employed to avoid self penetration and solid cloth penetration. Application: Fracture Animation Terzopoulos and Fleischer s deformable models [TF88b] discussed earlier, can also be used to simulate tearing cloth. The cloth is defined by a mesh of criss crossing fibers that break when stretched beyond their fracture limit. The limit is defined uniformly over the entire mesh and causes linear tears that one would expect to obtain with cloth. ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: viscoelasticity, plasticity, fracture. In Computer Graphics (SIGGRAPH 88 Proceedings), pages 269--278, August 1988.

....mesh points, as well as on the spatial partial derivatives. Plastic behavior considers the time history of the deformations, and MERL TR 97 19 November 1997 20 fracture is modeled by breaking connections between mesh points by removing interdependencies in the equations of motion. Details are in [TF88b, TF88a] Terzopoulos and Metaxas proposed deformable superquadric ellipsoids as useful models for image analysis [TM91, Met97] They first parameterize the shape of a (rigid) superquadric ellipsoid by six parameters: a scale parameter a, aspect ratio parameters a 1 ; a 2 , and a 3 , and ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: viscoelasticity, plasticity, fracture. In Computer Graphics Proceedings, Annual Conference Series, Proceedings of SIGGRAPH 88, pages 269--278. ACM SIGGRAPH, 1988.

....sophisticated data structures. 3.2 Physics based Modeling Our dynamic subdivision solid model is based on well established techniques and algorithms from physics based modeling. Dynamic solid models were introduced to the modeling and computer graphics communities by Terzopoulos and colleagues [24, 23, 22, 14]. In a nutshell, the geometry of their models is discretized from continuous surfaces and solids and is attached to mass spring meshes. Others have used modal dynamics [17] and the finite element method [5] in order to improve the stability and accuracy of dynamic models. Baraff, Witkin, Kass and ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: viscoelasticity, plasticity, fracture. In Computer Graphics (SIGGRAPH 88 Proceedings), pages 269--278, August 1988.

....this technique and used linear elasticity theory to govern the dynamics of the deformable component. While the rigid reference body handled rigid body transformations, the deformable component reflected the deformation of the object from its rest state. Immediately Terzopoulos and Fleischer [terz88b] extended the technique by evolving the reference component in response to the forces the surface is subjected to. This makes it possible to simulate viscoelasticity, plasticity, and fracture. Additionally, it allows stiffer objects and broadens the range of possible behaviors of the objects, but ....

....expensive as the number of state variables easily reaches magnitudes in the tens of thousands. The application of multigrid methods to these systems has been attempted, but is difficult to correctly code due to the irregularities that evolve within a system undergoing irreversible deformations [terz88b]. 2.1.4 Finite element models Finite element models of deformable objects have been used to model surfaces, human skin, and even the motion dynamics of snakes and worms. As a discrete representation of continuous media, the three dimensional lattices of springs and masses used in an FEM are ....

[Article contains additional citation context not shown here]

Demetri Terzopoulos and Kurt Fleischer. "Modeling inelastic deformation: Viscoelasticity, plasticity, fracture". Computer Graphics (SIGGRAPH '88 Proceedings), Vol. 22, No. 4, pp. 269--278, August 1988.

....in dealing with complex energy functions that allow for (a) b) Figure 1: a) Non penetration is enforced by preventing only the four contacting vertices from moving below the plane. b) The entire lower rim of the cylinder must be prevented from moving below the plane. plasticity or fracture[8]. For second order polynomial deformations, a small number of sample points (on the order of fifty) yields adequate results. 3. Non penetration Constraints The derivation for the contact forces between flexible bodies that prevent inter penetration closely parallels the derivation of contact ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In Computer Graphics (Proc. SIGGRAPH), volume 22, pages 269--278. ACM, August 1988.

....) l(t) Physically, u(t) is the elongation caused by a unit step function. As described above under deformation modeling, the viscoelastic model (also called spring damping model in a discrete system) is applied as the deformable material property model. Other viscoelastic models (Kelvin, Maxwell [33]) are possible as well. Among the rectangular grid and polygonal meshes, triangle mesh is fast, memory efficient and robust for the deformable analysis approach. As is well known, guaranteed quality 2 D meshes are generated using a Delaunay triangulation refinement algorithm [31] Figure 1: ....

D. Terzopoulos, K. Fleischer, 1988, "Modeling Inelastic Deformation:Viscoelasticity, Plasticity, Fractures", Computer Graphics,. 22,(4), Aug. 1988, pp. 269-278

....been studied in computer graphics. All methods are based on non rigid elastic physical models using different mathematical physics approaches [5] to solve a series of differential equations. The set of methods can be classified into those that use traditional differential equation solution such as [1,2,3,6,7], those that use a mass spring model [5,8,10,11] and those that use FEMs (finite element method) 4,9,12,15,16] Terzopolous et al. [1] and Platt, and Barr [2] have shown the advantages of physically based models over kinematic models for computer animation. The particular shape an elastic body is ....

....[5] to solve a series of differential equations. The set of methods can be classified into those that use traditional differential equation solution such as [1,2,3,6,7] those that use a mass spring model [5,8,10,11] and those that use FEMs (finite element method) 4,9,12,15,16] Terzopolous et al. [1], and Platt, and Barr [2] have shown the advantages of physically based models over kinematic models for computer animation. The particular shape an elastic body is a function of both the internal stress and strain within the object and external forces applied to it. Generally, some modification ....

D. Terzopoulos, K. Fleischer, 1988, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture," ACM Computer Graphics,.22(4) August 1988, 269-278.

.... hybrid model incorporating physical and geometrical techniques to model garment wrinkles [18] Aono simulated wrinkle propagation on a handkerchief using an elastic model [2] Terzopoulos and Fleischer developed a general elastic model and applied it to a wide range of objects including cloth [28] [29]. Interaction of clothes with synthetic actors in motion [19] 10] 39] marked the beginning of a new era in cloth animation in more complex situations. However, there were still a number of restrictions on the simulation conditions on the geometrical structure and the mechanical situations, ....

: D. Terzopoulos, K. Fleischer, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture", Computer Graphics (proc. SIGGRAPH'88), 22, pp 269-278, 1988.

....have been used for fast surgery simulation [9, 10, 11, 12] For most materials, the linear elastic model is only valid for small displacements. For large displacements, more complex non linear models have been been introduced such as the Mooney Rivlin model [13, 14] or the St. Venant Kirchooe [15, 9, 16] where the stress strain or stress displacement relationships are no longer linear. Additional physical constraints may be considered, such as incompressibility. Furthermore, for many tissues, plastic deformations, where the strain does not reverse to zero after unloading (see gure 4 (a) occur ....

....invariant to rigid transformation, thin plate bending energy is used to model large deformations. In [41] a dynamic model similar to [32] is proposed but the damping factor is replaced by the time derivative of the strain tensor. The most advanced surface deformation model has been proposed in [15]. In this paper, a Maxwell and Voigt viscoelastic model has been implemented using a semi implicit scheme with nite dioeerences on a regular grid. The addition of plastic units enabled non reversible behavior to be modeled. However, those results required substantial computational power for ....

[Article contains additional citation context not shown here]

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. Computer Graphics (SIGGRAPH'88), 22(4):269278, 1988.

....work are: 1] 21] 14] and [9] The next step is the dynamics of non rigid bodies. The foundations for the animation of deformable objects, considering primarily the problem of elasticity, are in [18] A more complete formulation, including also inelastic deformation, can be found in [15]. 2 The control problem in a physically based system demands the introduction of constraints allowing the specification of relationships and interaction among objects. A discussion of constraint mechanisms for rigid and non rigid models can be found respectively in [3] and in [13] The discrete ....

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: viscoelasticity, plasticity and fracture. Computer Graphics, 22(4), 1988.

....Fortunately, constraining a curve to remain fixed is an exact interpolation. Gortler and Cohen [16] developed geometric modeling using wavelets, defining point constraints and point tangent constraints similar to those in Fowler [12] and Welch and Witkin [33] 6 Terzopoulos and Fleischer [28] present finite elements to demonstrate how real materials undergo inelastic deformation. A yield condition is imposed on a model to describe its elastic behavior. When the condition is exceeded through forces, then the model may behave inelastically and possibly fracture. Free form shape design ....

....tension, which uniformly scales both partial derivatives, and directional tension, which is in a user defined direction in the tangent plane. Geometric properties can be applied and modified at any selected point on the surface. The elastically deformable finite element models presented in [22, 28, 29] are also governed by surface energy. Surface properties can be defined, such as those of rubber, cloth, paper, and springy metal. The values for bending and stretching parameters are adjusted accordingly, and can be set independently for each surface point. This ability allows for local control ....

[Article contains additional citation context not shown here]

Terzopoulos, D., and Fleischer, K. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In Computer Graphics (SIGGRAPH '88 proceedings) (August 1988), vol. 22, pp. 269--278.

....coordinates by using finite differences or finite elements. The use of elastic models in the context of graphics was first presented by Terzopoulos et al. 4] These physicsbased deformable models have been generalized to include visco elastic properties and inelastic behavior, such as fracture [5]. A deformable model is formulated by Metaxas and Terzopoulos [6] which includes global superquadric deformations and local spline deformations. The most straightforward deformable model consists of a network of springs and point masses. Haumann et al. 7] animate deformable objects using ....

D. Terzopoulos and K. Fleischer, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture," Proc. ACM SIGGRAPH: Computer Graphics, vol. 22, no. 4, pp. 269--278, Aug. 1988.

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D. Terzopoulos, Kurt F., "Modeling inelastic deformation: viscoelasticity, plasticity, fracture", Computer Graphics, Vol 22, 4, pp. 269-278, Aug., 1988.

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D. Terzopoulos and K. Fleischer "Modeling inelastic deformation: viscoelasticity, plasticity, fracture", Computer Graphics, Vol 22, 4, pp. 269-278, Aug., 1988.

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Terzopoulos D, Fleischer K. Modeling inelastic deformation: viscoelasticity. Plast, Fract, Comput Graph (SIGGRAPH'88 proceedings) 1988;22:269--78.

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Terzopoulos D, Fleischer K. Modeling inelastic deformation: viscoelasticity, plasticity, fracture. Computer Graphics 1988;22(4):269}78.

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D. Terzopoulos, and K. Fleischer, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture", Computer Graphics, Vol. 22, No.4, 1988, pp.269-278.

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D. Terzopoulos and K. Fleischer, "Modeling inelastic deformation: viscoelasticity, plasticity, fracture", Computer Graphics 22, Siggraph'88, 1988, pp. 269-- 278.

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D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. 22(4):269--278, 1988. 7

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D. Terzopoulos and K. Fleischer. Modeling inelastic deformations: Viscoelasticity, plasticity, fracture. Computer Graphics, 22(4):269--278, Aug. 1988. Proceedings of SIGGRAPH '88 (Atlanta).

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D. Terzopoulos and K. Fleischer "Modeling inelastic deformation: viscoelasticity, plasticity, fracture", Computer Graphics, Vol 22, 4, pp. 269-278, Aug., 1988.

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Terzopoulos D., Fleischer K.: Modeling inelastic deformation: viscoelasticity, plasticity, fracture. In ACM SIGGRAPH Conference Proceedings, 269-278 (1988).

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Terzopoulos, D., and Fleischer, K. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. Proceedings of SIGGRAPH'88 (Atlanta, August 1--5, 1988.

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D. Terzopoulos, K. Fleischer, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture," Proc. of SIGGRAPH '88, Atlanta, Georgia, pp. 269-278, 1988.

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D. Terzopoulos, Kurt F., "Modeling inelastic deformation: viscoelasticity, plasticity, fracture", Computer Graphics, Vol 22, 4, pp. 269-278, Aug., 1988.

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D. Terzopoulos, K. Fleischer, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture," Proc. of SIGGRAPH '88, Atlanta, Georgia, pp. 269-278, 1988.

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D. Terzopoulos and K. Fleisher. Modeling Inelastic Deformation : Viscoelasticity, plasticity, fracture. In Computer Graphics (SIGGRAPH '87), volume 22, no. 4, pages 269-278, 1988.

No context found.

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: viscoelasticity, plasticity, fracture. Comput. Graph. (SIGGRAPH Proc.), pages 269--278, 1988.

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Terzopoulos D, Fleischer K (1988), "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture," Computer Graphics, Proc. SIGGRAPH'88, Vol. 22, No. 4. pp. 269-278.

No context found.

D. Terzopoulos and K. Fleischer. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. SIGGRAPH 88 Conference Proceedings, 22:287--296, 1988.

No context found.

Terzopoulos D, Fleisher K (1988), "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture," Computer Graphics, Proc. SIGGRAPH'88, Vol. 22, No. 4. pp. 269-278.

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