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V A Lubarda - One of the best experts on this subject based on the ideXlab platform.
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constitutive theories based on the multiplicative decomposition of Deformation Gradient thermoelasticity elastoplasticity and biomechanics
Applied Mechanics Reviews, 2004Co-Authors: V A LubardaAbstract:Some fundamental issues in the formulation of constitutive theories of material response based on the multiplicative decomposition of the Deformation Gradient are reviewed, with focus on finite Deformation thermoelasticity, elastoplasticity, and biomechanics. The constitutive theory of isotropic thermoelasticity is first considered. The stress response and the entropy expression are derived in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. Basic kinematic and kinetic aspects of the phenomenological and single crystal elastoplasticity within the framework of the multiplicative decomposition are presented. Attention is given to additive decompositions of the stress and strain rates into their elastic and plastic parts. The constitutive analysis of the stress-modulated growth of pseudo-elastic soft tissues is then presented. The elastic and growth parts of the Deformation Gradient and the rate of Deformation tensor are defined and used to construct the corresponding rate-type biomechanic theory. The structure of the evolution equation for growth-induced stretch ratio is discussed. There are 112 references cited in this review article. DOI: 10.1115/1.1591000 The objective of this survey is to give an overview of the application of the multiplicative decomposition of the Deformation Gradient in constitutive theories of finite Deformation thermoelasticity, elastoplasticity, and biomechanics. The multiplicative decomposition of the Deformation Gradient is based on an intermediate material configuration, which is obtained by a conceptual destressing of the currently deformed material configuration to zero stress. The significance of such configuration for material modeling was pointed out ˙
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Constitutive analysis of large elasto-plastic Deformation based on the multiplicative decomposition of Deformation Gradient
International Journal of Solids and Structures, 2003Co-Authors: V A LubardaAbstract:Abstract By using Lee's (1969, J. Appl. Mech. 36 , 1–6) multiplicative decomposition of the Deformation Gradient into its elastic and plastic part of Hill and Rice's (1973, SIAM J. Appl. Math. 25 , 448–461) constitutive framework, explicit and consistent constitutive analysis of large elastoplastic Deformation is given. Both isotropic and anisotropic material behaviour is considered, so that some earlier results come as particular cases of this more general formulation. The relationship with other related work is also given.
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On the mechanics of solids with a growing mass
International Journal of Solids and Structures, 2002Co-Authors: V A Lubarda, Anne HogerAbstract:A general constitutive theory of the stress-modulated growth of biomaterials is presented with a particular accent given to pseudo-elastic soft living tissues. The governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite Deformation continuum thermodynamics. The multiplicative decomposition of the Deformation Gradient into its elastic and growth parts is employed to study the growth of isotropic, transversely isotropic, and orthotropic biomaterials. An explicit representation of the growth part of the Deformation Gradient is given in each case, which leads to an effective incremental formulation in the analysis of the stress-modulated growth process. The rectangular components of the instantaneous elastic moduli tensor are derived corresponding to selected forms of the elastic strain energy function. Physically appealing structures of the stress-dependent evolution equations for the growth induced stretch ratios are proposed. © 2002 Elsevier Science Ltd. All rights reserved.
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finite strain thermoelasticity based on multiplicative decomposition of Deformation Gradient
Theoretical and Applied Mechanics, 2002Co-Authors: L Vujosevic, V A LubardaAbstract:The constitutive formulation of the finite-strain thermoelasticity is revisited within the thermodynamic framework and the multiplicative decomposition of the Deformation Gradient into its elastic and thermal parts. An appealing structure of the Helmholtz free energy is proposed. The corresponding stress response and the entropy expressions are derived. The results are specified in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. The specific and latent heats are discussed, and the comparison with the results of the classical thermoelasticity are given. .
Stephane Mallat - One of the best experts on this subject based on the ideXlab platform.
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The texture Gradient equation for recovering shape from texture
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002Co-Authors: Maureen Clerc, Stephane MallatAbstract:Studies the recovery of shape from texture under perspective\nprojection. We regard shape from texture as a statistical estimation\nproblem, the texture being the realization of a stochastic process. We\nintroduce warplets, which generalize wavelets over the 2D affine group.\nAt fine scales, the warpogram of the image obeys a transport equation,\ncalled texture Gradient equation. In order to recover the 3D shape of\nthe surface, one must estimate the Deformation Gradient, which measures\nmetric changes in the image. This is made possible by imposing a notion\nof homogeneity for the original texture, according to which the\nDeformation Gradient is equal to the velocity of the texture Gradient\nequation. By measuring the warplet transform of the image at different\nscales, we obtain a Deformation Gradient estimator
Mahmood Jabareen - One of the best experts on this subject based on the ideXlab platform.
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elastic viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative Deformation Gradient
International Journal for Numerical Methods in Biomedical Engineering, 2014Co-Authors: Johannes Weickenmeier, Mahmood JabareenAbstract:SUMMARY The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic–viscoplastic constitutive equations. The specific elastic–viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic–viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative Deformation Gradient—the Deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery. Copyright © 2014 John Wiley & Sons, Ltd.
Y. Q. Li - One of the best experts on this subject based on the ideXlab platform.
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Constitutive Equations for Hyperelastic Materials Based on the Upper Triangular Decomposition of the Deformation Gradient
Mathematics and Mechanics of Solids, 2018Co-Authors: Y. Q. LiAbstract:The upper triangular decomposition has recently been proposed to multiplicatively decompose the Deformation Gradient tensor into a product of a rotation tensor and an upper triangular tensor called...
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The upper triangular decomposition of the Deformation Gradient: possible decompositions of the distortion tensor
Acta Mechanica, 2018Co-Authors: Y. Q. LiAbstract:In the upper triangular decomposition, the Deformation Gradient is multiplicatively decomposed into a product of a rotation tensor and an upper triangular tensor called the distortion tensor. In this paper, it is shown that the upper triangular decomposition can be viewed as an extended polar decomposition. The six components of the distortion tensor can be directly related to pure stretch and simple shear Deformations. Also, it is demonstrated that the distortion tensor can be non-uniquely decomposed into a product of matrices for one triaxial stretch and two simple shear Deformations or for one triaxial stretch and three simple shear Deformations. There are six possible decompositions for the former and 24 possible decompositions for the latter. Only one of these 30 possible decompositions was examined earlier. In addition, the distortion tensor is shown to be frame-invariant and can therefore be used as an independent kinematic variable to construct strain energy density functions.
Victor H. Barocas - One of the best experts on this subject based on the ideXlab platform.
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Automatic Segmentation of Mechanically Inhomogeneous Tissues Based on Deformation Gradient Jump
IEEE Transactions on Medical Imaging, 2016Co-Authors: Colleen M. Witzenburg, Rohit Y. Dhume, Spencer P. Lake, Victor H. BarocasAbstract:Variations in properties, active behavior, injury, scarring, and/or disease can all cause a tissue's mechanical behavior to be heterogeneous. Advances in imaging technology allow for accurate full-field displacement tracking of both in vitro and in vivo Deformation from an applied load. While detailed strain fields provide some insight into tissue behavior, material properties are usually determined by fitting stress-strain behavior with a constitutive equation. However, the determination of the mechanical behavior of heterogeneous soft tissue requires a spatially varying constitutive equation (i.e., one in which the material parameters vary with position). We present an approach that computationally dissects the sample domain into many homogeneous subdomains, wherein subdomain boundaries are formed by applying a betweenness based graphical analysis to the Deformation Gradient field to identify locations with large discontinuities. This novel partitioning technique successfully determined the shape, size and location of regions with locally similar material properties for: (1) a series of simulated soft tissue samples prescribed with both abrupt and gradual changes in anisotropy strength, prescribed fiber alignment, stiffness, and nonlinearity, (2) tissue analogs (PDMS and collagen gels) which were tested biaxially and speckle tracked (3) and soft tissues which exhibited a natural variation in properties (cadaveric supraspinatus tendon), a pathologic variation in properties (thoracic aorta containing transmural plaque), and active behavior (contracting cardiac sheet). The routine enables the dissection of samples computationally rather than physically, allowing for the study of small tissues specimens with unknown and irregular inhomogeneity.