Effect of Laminar Orthotropic Myofiber Architecture on Regional Stress and Strain in the Canine Left Ventricle

Recent morphological studies have demonstrated a laminar (sheet) organization of ventricular myofibers. Multiaxial measurements of orthotropic myocardial constitutive properties have not been reported, but regional distributions of three-dimensional diastolic and systolic strains relative to fiber and sheet axes have recently been measured in the dog heart by Takayama et al. [30]. A three-dimensional finite-deformation, finite element model was used to investigate the effects of material orthotropy on regional mechanics in the canine left ventricular wall at end-diastole and end-systole. The prolate spheroidal model incorporated measured transmural distributions of fiber and sheet angles at the base and apex. Compared with transverse isotropy, the orthotropic model of passive myocardial properties yielded improved agreement with measured end-diastolic strains when: (1) normal stiffness transverse to the muscle fibers was increased tangent to the sheets and decreased normal to them; (2) shear coefficients were increased within sheet planes and decreased transverse to them. For end-systole, orthotropic passive properties had little effect, but three-dimensional systolic shear strain distributions were more accurately predicted by a model in which significant active systolic stresses were developed in directions transverse to the mean fiber axis as well as axial to them. Thus the ventricular laminar architecture may give rise to anisotropic material properties transverse to the fibers with greater resting stiffness within than between myocardial laminae. There is also evidence that intact ventricular muscle develops significant transverse stress during systole, though it remains to be seen if active stress is also orthotropic with respect to the laminar architecture. This revised version was published online in July 2006 with corrections to the Cover Date.     

A cell-based constitutive model for embryonic epithelia and other planar aggregates of biological cells

Embryonic epithelia are shown to have in common with plastic materials a number of key characteristics, including fabric evolution, “yielding”, “particle” (cell) rearrangement, energy dissipation, dependence of stress on fabric and irreversibility of deformation. The strains apparent at the tissue level can be large (several hundred percent over the course of 5–10 h), and are possible because of in-plane cell rearrangement. We propose a cell-based constitutive model, the first of its kind, to relate in-plane stresses, tissue deformations, evolution of cellular fabric (cell size, shape and orientation), mitosis and cell rearrangement. The governing equations are based on results from finite element models, statistical mechanics analyses and experiments. The constitutive model overcomes drawbacks of existing finite element models where cells are modeled using multiple elements, and it confirms that tissue fabric is a primary determinant of stress and deformation. Fabric predictions made using the model are as good as the available data, even when strain histories are complex or multiple biological processes are active simultaneously. The model provides insights into the mechanics of embryonic epithelia and other labile biological tissues, and it sets the stage for future computational studies of whole embryos.     

THIRD ORDER SHEAR DEFORMATION MODEL FOR LAMINATED SHELLS WITH FINITE ROTATIONS： FORMULATION AND CONSISTENT LINEARIZATION

The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates, are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.     

正交各向异性弹塑性摩擦接触问题的数值求解

采用正交各向异性摩擦定律对三维弹塑性摩擦接触问题进行分析,基于参变量变分原理,经过有限元离散,将问题化为线性互补问题模型,之后给出一个求解互补问题的非内点光滑化算法．对三维接触问题,滑动方向的确定一直是个难点,为此,该文采用作者提出的组合规划法和迭代法对各向异性摩擦本构模型进行分析,数值结果说明了模型与算法的正确性。     

On the modeling of a prestressed thermoelectroelastic half-space with a coating

The constitutive equations of nonlinear mechanics of a prestressed electrothermoelastic continuum are linearized in the framework of the theory of small strains imposed on finite strains. Simple and convenient-to-operate formulas of linearized constitutive equations and equations of motion of the mediumare obtained. A model of electrothermoelastic half-space with inhomogeneous coating, which is a structure of functionally graded layers, is proposed. It is assumed that each of the medium components is under the action of initial mechanical strains and initial temperature, and the materials of the medium components are orthotropic pyroelectric materials of hexagonal crystal system of class 6 mm. The integral representation of the mediumwave field is constructed by a hybrid numerical-analytical method based on a combination of analytical solutions and numerical schemes used to reconstruct the Green function for the inhomogeneous components of the coating and the matrix approach used to satisfy the boundary conditions.     

Determining the stress state of flexible orthotropic shells of revolution in magnetic field

A two-dimensional nonlinear magnetoelastic model of a current-carrying orthotropic shell of revolution is constructed taking into account finite orthotropic conductivity, permeability, and permittivity. It is assumed that the principal axes of orthotropy are aligned with the coordinate axes and that the orthotropic body is magnetically and electrically linear. The coupled nonlinear differential equations derived describe the stress-strain state of flexible current-carrying orthotropic shells of revolution that have an arbitrarily shaped meridian and orthotropic conductivity and are in nonstationary mechanical and electromagnetic fields. A method to solve this class of problems is proposed Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 64–76, August 2008.     

Thermally induced wrinkling in orthotropic layered plates with irregular delaminations

Delaminated regions figure prominently among potential threats to the structural integrity of layered plate configurations. Under a certain thermal loading threshold, geometrically nonlinear local instabilities in the form of buckling or wrinkling across the delaminated region crop up, giving rise to markedly amplified distributions of contour peeling stresses. The present paper aims to shed light on and quantify the manifold aspects and implications of the delamination-thermal-wrinkling trio. The paper faces the challenges of handling the nature of the layered configuration, the inherent geometrical irregularity of delaminated regions, the discontinuous interfacial conditions, the 3D stress state along the delamination contour, and the nonlinear evolution of local instabilities across an orthotropic delamination. For that purpose, a specially tailored 2D multi layered plate model and a corresponding triangular finite element are derived. The original contribution of the proposed model is in its ability to capture the thermally-driven, nonlinear small scale phenomena related to geometrically nonlinear response of the layered structure, using a 2D multi-layered plate theory solved with efficient 2D multi-layered triangular finite elements, as opposed to computationally expensive 3D finite element analysis. This is accomplished via the integration and synergy of methodologies that include: multi-layered high order plate theory to account for the layered layout, geometrically nonlinear strain-displacement relations to account for geometrical nonlinearities, orthotropic and thermo-elastic constitutive laws to account for thermal loads, and interlayer interface modelling which, combined with a the shear-locking free triangular FE, allows accounting for arbitrarily shaped delaminations. The model is validated against a 1D closed form solution and a 3D continuum based finite element analysis and is then used for a numerical study. In the study, the onset and the evolution of local instabilities in an adhesively bonded orthotropic layer across an irregular delamination are looked into. Special attention is given to the significant influence of material orthotropy and the relative directionality of the delamination on the threshold thermal load, the nonlinear wrinkling patterns, and the peeling traction distribution.     

A ferroelectric and ferroelastic 3D hexahedral curvilinear finite element

An isoparametric 3D electromechanical hexahedral finite element integrating a 3D phenomenological ferroelectric and ferroelastic constitutive law for domain switching effects is proposed. The model presents two internal variables which are the ferroelectric polarization (related to the electric field) and the ferroelastic strain (related to the mechanical stress). An implicit integration technique of the constitutive equations based on the return-mapping algorithm is developed. The mechanical strain tensor and the electric field vector are expressed in a curvilinear coordinate system in order to handle the transverse isotropy behavior of ferroelectric ceramics. The hexahedral finite element is implemented into the commercial finite element code Abaqus® via the subroutine user element. Some linear (piezoelectric) and non linear (ferroelectric and ferroelastic) benchmarks are considered as validation tests.     

Parametric variational principle and quadratic programming method for van der Waals force simulation of parallel and cross nanotubes

A parametric variational principle for van der Waals force simulation between any two adjacent nonbonded atoms and the corresponding improved quadratic programming method for numerical simulation of mechanical behaviors of carbon nanotubes are developed. Carbon nanotubes are modeled and computed based on molecular structural mechanics model. van der Waals force is simulated by the network of bars (called bar network) with a special nonlinear mechanical constitutive law (called generalized parametric constitutive law) in the finite element analysis. Compared with conventional numerical methods, the proposed method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the model and method developed present very good convergence behavior in computation and provide accurate predictions of the mechanical behaviors and displacement distributions in the nanotubes. Numerical results demonstrate the validity and the efficiency of the proposed method.     

A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales

Plastic flow in crystal at submicron-to-nanometer scales involves many new interesting problems. In this paper, a unified computational model which directly combines 3D discrete dislocation dynamics (DDD) and continuum mechanics is developed to investigate the plastic behaviors at these scales. In this model, the discrete dislocation plasticity in a finite crystal is solved under a completed continuum mechanics framework: (1) an initial internal stress field is introduced to represent the preexisting stationary dislocations in the crystal; (2) the external boundary condition is handled by finite element method spontaneously; and (3) the constitutive relationship is based on the finite deformation theory of crystal plasticity, but the discrete plastic strains induced by the slip of the newly nucleated or propagating dislocations are calculated by dislocation dynamics methodology instead of phenomenological evolution equations used in conventional crystal plasticity. These discrete plastic strains are then localized to the continuum material points by a Burgers vector density function proposed by us. Various processes, such as loop dislocation evolution, dislocation junction formation etc., are simulated to verify the reliability of this computational model. Specifically, a uniaxial compression test for micro-pillars of Cu is simulated by this model to investigate the ‘dislocation starvation hardening’ observed in the recent experiment.