Finite deformation formulation

The proposed model consists of a biphasic mechanical description of the tissue engineered construct. The resulting fluid velocity and displacement fields are used for evaluating solute transport. Solute concentrations determine biosynthetic behavior. A finite deformation biphasic displacement-velocity-pressure (u-v-p) formulation is implemented [12, 7], Compared to the more standard u-p element the mixed treatment of the Darcy problem enables an increased accuracy for the fluid velocity field which is of primary interest here. The system to be solved increases however considerably and for multidimensional flow the use of either stabilized methods or Raviart-Thomas type elements is required [15, 10]. To model solute transport the input features of a standard convection-diffusion element for compressible flows are employed [20], For flexibility (non-linear) solute uptake is included using Strang operator splitting, decoupling the transport equations [9],... 

Based on this understanding, a mechanism based constitutive model incorporating the nonlinear structural relaxation model into the continuum finite-deformation thermoviscoelastic framework was developed as follows. The aim of this effort was to estabUsh a quantitative understanding of the shape memory behavior of the thermally responsive thermoset SMP programmed at temperamres below Tg. To simplify the formulation, several basic assumptions were made in this study ... 

Chen CJ, Kwak BM, Rim K, Falsetti HL (1980) A model for an active left ventricle deformation -formulation of a nonlinear quasi-steady finite-element analysis for orthotropic, three-dimensional myocardium. Int Conf Finite Elements in Biomechanics 2 639-655 Feit TS (1979) Diastolic pressure-volume relations and distribution of pressure and fiber extension across the wall of a model left ventricle. Biophys J 28 143-166 Ghista ND, Sandler HD (1968) An elastic viscoelastic model for the shape and the forces in the left ventricle. J Biomechanics 2 35-47... 

Compaction, consolidation, and subsidence. A formal approach to modeling compaction, consolidation, and subsidence requires the use of well-defined constitutive equations that describe both fluid and solid phases of matter. At the same time, these would be applied to a general Lagrangian dynamical formulation written to host the deforming meshes, whose exact time histories must be determined as part of the overall solution. These nonlinear deformations are often plastic in nature, and not elastic, as in linear analyses usually employed in structural mechanics. This finite deformation approach, usually adopted in more rigorous academic researches into compressible porous media, is well known in soil mechanics and civil engineering. However, it is computationally intensive and not practical for routine use. This is particularly true when order-of-magnitude effects and qualitative trends only are examined. 

The numeric simulation by finite element methods is based on two different approaches the Euler formulation and the Lagrange formulation. In the Euler formulation, the knots are fixed therefore, only stationary processes can be described. In the Lagrange formulation, the net flows and deforms with the work material. The net in front of the cutting tool is extremely... 

The QC method which presents a relationship between the deformations of a continuum with that of its crystal lattice uses the classical Cau-chy-Bom rule and representative atoms. The quasi-continuum method mixes atomistic-continuum formulation and is based on a finite element discretization of a continuum mechanics variation principle. 

A major limitation of the model in the formulation of [71] is the prediction of stress and strain in dependency of temperature for only small unidirectional deformations of about 10%. As principal extension to large finite strains, the same authors published an improved 3-D, thermoviscoelastic approach to a phenomenological temperature dependence of the viscosity [87]. It allowed successful reanalysis of the experimental data of [71]. 

In the case of materials which can undergo non-reversible deformations the plasticity model formulated in the material configuration is used for predicting their mechanical response. Assuming small elastic, finite plastic deformations, an adequate form of the free energy density and analogous procedures as those for the damage model we have... 

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