Parameter identification for finite deformation elasto-plasticity in principal directions

1997 ◽  
Vol 147 (1-2) ◽  
pp. 17-39 ◽  
Author(s):  
Rolf Mahnken ◽  
Erwin Stein
Keyword(s):  
Parameter Identification ◽  
Finite Deformation ◽  
Elasto Plasticity ◽  
Principal Directions

Effects of ventricular pacing on finite deformation in canine left ventricles

1987 ◽  
Vol 252 (5) ◽  
pp. H1023-H1030 ◽  
Author(s):  
L. K. Waldman ◽  
J. W. Covell
Keyword(s):  
Left Ventricle ◽  
Finite Deformation ◽  
Repeated Measures ◽  
Three Dimensional ◽  
Radial Strain ◽  
Tangent Plane ◽  
Ventricular Pacing ◽  
Anesthetized Dogs ◽  
Principal Directions ◽  
Heart Wall

Despite the fact that myofibers would be expected to shorten only along their axes, there is now evidence for substantial deformation away from the local myofiber direction in the left ventricle. To determine if the principal directions of deformation could be altered by a physiological stimulus, we examined local three-dimensional finite deformation in the anterior free wall of the left ventricle during normal atrial activation (AA) and, subsequently, during epicardial ventricular pacing (VP) at the site of deformation measurement in open-chest anesthetized dogs. An analysis of variance by repeated measures revealed the following significant changes (P less than or equal to 0.05) in the overall (average of epicardial and endocardial data) strain variables at end systole. Circumferential strain increased from -0.07 (AA) to 0.14 (VP), radial strain decreased from 0.16 (AA) to 0.01 (VP), shear in the tangent plane of the local epicardium decreased from 0.04 (AA) to -0.02 (VP), shear in the plane of the longitudinal and radial coordinates decreased from 0.03 (AA) to -0.03 (VP). Neither the first (greatest shortening) nor the third (greatest lengthening) principal strain changed significantly, but the direction of the first principal axis of deformation projected on the epicardial tangent plane changed from -51 degrees (AA) to -80 degrees (VP) from circumferential. In addition, substantial tipping of the plane of principal shortening away from the epicardial tangent plane was observed, particularly with ventricular pacing. These data indicate that the principal directions of deformation can be altered substantially by changing the activation sequence. In conjunction with the observed shearing deformations, particularly near the endocardium, they support the concept that locally the heart wall deforms as a unit with significant transmural tethering.

A Presentation and Comparison of Two Large Deformation Viscoelasticity Models

1997 ◽  
Vol 119 (3) ◽  
pp. 251-255 ◽  
Author(s):  
Sanjay Govindjee ◽  
Stefanie Reese
Keyword(s):  
Large Deformation ◽  
Plane Strain ◽  
Finite Deformation ◽  
Strain Relaxation ◽  
Elastic Equilibrium ◽  
Alternative Formulation ◽  
Small Perturbations ◽  
Elasto Plasticity

In this paper we present a theory of finite deformation viscoelasticity. The presentation is not restricted to small perturbations from the elastic equilibrium in contrast to many viscoelasticity theories. The fundamental hypothesis of our model is the multiplicative viscoelastic decomposition of Sidoroff (1974). This hypothesis is combined with the assumption of a viscoelastic potential to give a model that is formally similar to finite associative elasto-plasticity. Examples are given to compare the present proposal to an alternative formulation in the literature for the cases of uniaxial plane strain relaxation and creep.

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