A displacement-based finite element formulation for incompressible and nearly-incompressible cardiac mechanics

被引:30
|
作者
Hadjicharalambous, Myrianthi [1 ]
Lee, Jack [1 ]
Smith, Nicolas P. [1 ]
Nordsletten, David A. [1 ]
机构
[1] St Thomas Hosp, Kings Coll London, Dept Biomed Engn, London SEI 7EH, England
基金
英国惠康基金;
关键词
Cardiac mechanics; Solid mechanics; Incompressibility; Near incompressibility; Perturbed Lagrangian; Finite element method; PERTURBED LAGRANGIAN FORMULATION; SADDLE-POINT PROBLEMS; VENTRICULAR-FUNCTION; PASSIVE MYOCARDIUM; HEART; ELASTICITY; STRAIN; STRESS; MODEL; HYPERELASTICITY;
D O I
10.1016/j.cma.2014.02.009
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The Lagrange Multiplier (LM) and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics. In this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed Perturbed Lagrangian formulation, which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of LM techniques. A modified Shamanskii-Newton-Raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and, exploiting its equivalence, modifications are developed for the penalty form. Focusing on accuracy, we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics. Our results illustrate the well-known influence of locking phenomena on the penalty approach (particularly for lower order schemes) and its effect on accuracy for whole-cycle mechanics. Additionally, we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable. Combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics, the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics. (C) 2014 The Authors. Published by Elsevier B.V.
引用
收藏
页码:213 / 236
页数:24
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