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Finite element analysis of incompressible viscous flows by the penalty function formulation
 J. Comput. Phys
, 1979
"... A review of recent work and new developments are presented for the penaltyfunction, finite element formulation of incompressible viscous flows. Basic features of the penalty method are described in the context of the steady and unsteady NavierStokes equations. Galerkin and “upwind ” treatments of ..."
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Cited by 17 (1 self)
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A review of recent work and new developments are presented for the penaltyfunction, finite element formulation of incompressible viscous flows. Basic features of the penalty method are described in the context of the steady and unsteady NavierStokes equations. Galerkin and “upwind ” treatments of convection terms are discussed. Numerical results indicate the versatility and effectiveness of the new methods. 1. TNTR~DUCTI~N The finite element method (FEM) is an established numerical technique which now enjoys widespread use in solid and structural mechanics. The main attributes of the FEM are its ease in handling very complex geometries and the ability to “naturally ” incorporate differentialtype boundary conditions. In addition, the method possesses a rich mathematical structure and, in many cases, it can be shown that “optimal ” error estimates hold (see, for example, Strang and Fix [82]). More recently, the FEM has been used increasingly for problems of fluid mechanics (see, for example, [lo, 23, 24, 26, 711). Nevertheless, in convection dominated situations, and in particular for the NavierStokes equations, the FEM has not
Diffusion in PoroElastic Media
 Jour. Math. Anal. Appl
, 1998
"... . Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of se ..."
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Cited by 11 (7 self)
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. Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasistatic system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasistatic assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...
Cellular traction as an inverse problem
 SIAM J. Appl. Math
, 2006
"... Abstract. The evaluation of the traction exerted by a cell on a planar substrate is here considered as an inverse problem: shear stress is calculated on the basis of the measurement of the deformation of the underlying gel layer. The adjoint problem of the direct twodimensional plain stress operato ..."
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Cited by 6 (4 self)
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Abstract. The evaluation of the traction exerted by a cell on a planar substrate is here considered as an inverse problem: shear stress is calculated on the basis of the measurement of the deformation of the underlying gel layer. The adjoint problem of the direct twodimensional plain stress operator is derived by a suitable minimization requirement. The resulting coupled systems of elliptic partial differential equations (the direct and the adjoint problem) are solved by a finite element method and tested vs. experimental measures of displacement induced by a fibroblast cell traction. Introduction. The study of the basic mechanisms of cell migration has received a tremendous increment in the last few years. Cell locomotion occurs through a very complex interaction that involves, among others, actin polymerization, matrix degradation, chemical signaling, adhesion and pulling on substrate and fibers [12]. All these ingredients concur not only in single cell migration but also in collective
MultiMultiplier AmbientSpace Formulations of Constrained Dynamical Systems: The Case of Linearized Incompressible Elastodynamics
, 1999
"... Various formulations of the equations of motion for both finiteand infinitedimensional constrained Lagrangian dynamical systems are studied. The different formulations correspond to different ways of enforcing constraints through multiplier fields. All the formulations considered are posed on ambie ..."
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Cited by 6 (3 self)
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Various formulations of the equations of motion for both finiteand infinitedimensional constrained Lagrangian dynamical systems are studied. The different formulations correspond to different ways of enforcing constraints through multiplier fields. All the formulations considered are posed on ambient spaces whose members are not restricted to satisfy constraint equations, but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied. The stability properties of the invariant set within its ambient space differ in each of the cases. For the model problem of linearized incompressible elastodynamics, we study three formulations and establish the wellposedness of one formulation corresponding to a homogeneous, isotropic material body with a specified traction on its boundary. 1 Introduction In this article we study formulations of the equations of motion for Lagrangian dynamical systems whose configuration space can b...
Exact Energy and Momentum Conserving Algorithms for General Models in Nonlinear Elasticity
, 1999
"... Implicit time integration schemes that inherit the conservation laws of total energy, linear and angular momentum are considered for initial boundaryvalue problems in finitedeformation elastodynamics. Conserving schemes are constructed for general hyperelastic material models, both compressible an ..."
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Cited by 5 (0 self)
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Implicit time integration schemes that inherit the conservation laws of total energy, linear and angular momentum are considered for initial boundaryvalue problems in finitedeformation elastodynamics. Conserving schemes are constructed for general hyperelastic material models, both compressible and incompressible, and are formulated in a way that is independent of spatial discretization. Three numerical examples for Ogdentype material models, implemented using a finite element discretization in space, are given to illustrate the performance of the proposed schemes. These examples show that, relative to the standard implicit midpoint rule, the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy. Key words: numerical integration, nonlinear elastodynamics, incompressible elasticity, integral preservation 1 Introduction In this article we consider energy and momentum conserving time discretization schemes for general initial boundaryvalu...
Traction patterns of tumor cells
 J. Math. Biol
"... Abstract The traction exerted by a cell on a planar deformable substrate can be indirectly obtained on the basis of the displacement field of the underlying layer. The usual methodology used to address this inverse problem is based on the exploitation of the Green tensor of the linear elasticity pro ..."
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Cited by 4 (0 self)
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Abstract The traction exerted by a cell on a planar deformable substrate can be indirectly obtained on the basis of the displacement field of the underlying layer. The usual methodology used to address this inverse problem is based on the exploitation of the Green tensor of the linear elasticity problem in a half space (Boussinesq problem), coupled with a minimization algorithm under force penalization. A possible alternative strategy is to exploit an adjoint equation, obtained on the basis of a suitable minimization requirement. The resulting system of coupled elliptic partial differential equations is applied here to determine the force field per unit surface generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field and is a promising tool to investigate the spatial pattern of force per unit surface generated in cell motion, particularly in the case of such cancer cells.
Asymptotic expansion of the solution of Maxwell’s equations in polygonal plane domains
"... apport de recherche N 02496399Asymptotic expansion of the solution of Maxwell’s equations in polygonal plane domains ..."
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apport de recherche N 02496399Asymptotic expansion of the solution of Maxwell’s equations in polygonal plane domains
AUTHOR’S DECLARATION FOR ELECTRONIC SUBMISSION
"... the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Problems involving mechanical behavior of materials with microstructure are receiving an increasing amount of attention in the literatur ..."
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the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Problems involving mechanical behavior of materials with microstructure are receiving an increasing amount of attention in the literature. First of all, it can be attributed to the fact that a number of recent experiments shows asignificant discrepancy between results of the classical theory of elasticity and the actual behavior of materials for which microstructure is known to be significant (e.g. synthetic polymers, human bones). Second, materials, for which microstructure contributes significantly in the overall deformation of a whole body, are becoming more and more important for applications in different areas of modern day mechanics, physics and engineering. Since the classical theory is not adequate for modeling the elastic behavior
FUNDAMENTAL INEQUALITIES ON FIRMLY STRATIFIED SETS AND SOME APPLICATIONS
, 2002
"... ABSTRACT. We establish different fundamental inequalities on a class of multistructures, more precisely Poincaré’s inequality for second and fourth order (scalar) operators as well as Korn’s inequality for the elasticity systems. Some consequences to the corresponding variational problems are deduce ..."
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ABSTRACT. We establish different fundamental inequalities on a class of multistructures, more precisely Poincaré’s inequality for second and fourth order (scalar) operators as well as Korn’s inequality for the elasticity systems. Some consequences to the corresponding variational problems are deduced.