Integrity basis of polyconvex invariants for modelling hyperelastic orthotropic materials — Application to the mechanical response of passive ventricular myocardium

2011 ◽

Vol 421 ◽

pp. 312-315

Author(s):

Somsak Siwadamrongpong ◽

Usanee Kitkamthorn ◽

Chaiyapak Sajjawattana

Keyword(s):

Stainless Steel ◽

Material Properties ◽

Mechanical Response ◽

Thin Sheet ◽

Disk Drive ◽

Simple Calculation ◽

Orthotropic Materials ◽

Mechanical Bending ◽

Orthotropic Properties ◽

Good Agreement

The most important factors in hard disk drive suspension manufacturing is the suspension preload, so call “gram load”. The suspensions were generally made from cold rolled stainless steel (SUS304). The suspensions were formed by mechanical forming and gram load was adjusted by mechanical bending until reached a specification. The material properties in mechanical bending simulation of thin stainless steel were usually as isotropic for simple calculation. But the properties of thin stainless steel should be defined as orthotropic materials. Therefore, this work aimed to study gram load results of using isotropic and orthotropic properties. The thin stainless sheet was cut and test for mechanical properties in rolling and transverse directions. The properties of the thin sheet were applied to simulation model. It was found that orthotropic material properties shows a good agreement with the experimental results more than using isotropic material properties. Therefore, the results of this work could be used to explain and predict the mechanical response on the suspension manufacturing.

Download Full-text

A Bimodular Polyconvex Anisotropic Strain Energy Function for Articular Cartilage

Journal of Biomechanical Engineering ◽

10.1115/1.2486225 ◽

2006 ◽

Vol 129 (2) ◽

pp. 250-258 ◽

Cited By ~ 10

Author(s):

Stephen M. Klisch

Keyword(s):

Articular Cartilage ◽

Strong Interaction ◽

Energy Function ◽

Strain Energy ◽

Mechanical Response ◽

Deformation Gradient ◽

Strain Energy Function ◽

Finite Deformations ◽

Orthotropic Materials ◽

Interaction Terms

A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex “strong interaction terms” for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson’s ratios, as well as axial stress–axial strain responses, in tension and compression for finite deformations.

Download Full-text

Constitutive modelling of passive myocardium: a structurally based framework for material characterization

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0091 ◽

2009 ◽

Vol 367 (1902) ◽

pp. 3445-3475 ◽

Cited By ~ 394

Author(s):

Gerhard A. Holzapfel ◽

Ray W. Ogden

Keyword(s):

Mechanical Response ◽

Constitutive Models ◽

Ventricular Myocardium ◽

Incompressible Material ◽

Left Ventricular ◽

Constitutive Modelling ◽

Left Ventricular Myocardium ◽

Fibre Direction ◽

Biaxial Tests ◽

Nonlinearly Elastic

In this paper, we first of all review the morphology and structure of the myocardium and discuss the main features of the mechanical response of passive myocardium tissue, which is an orthotropic material. Locally within the architecture of the myocardium three mutually orthogonal directions can be identified, forming planes with distinct material responses. We treat the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develop a general theoretical framework based on invariants associated with the three directions. Within this framework we review existing constitutive models and then develop a structurally based model that accounts for the muscle fibre direction and the myocyte sheet structure. The model is applied to simple shear and biaxial deformations and a specific form fitted to the existing (and somewhat limited) experimental data, emphasizing the orthotropy and the limitations of biaxial tests. The need for additional data is highlighted. A brief discussion of issues of convexity of the model and related matters concludes the paper.

Download Full-text

Finite Element Modeling of Composites System in Aerospace Application

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.245.316 ◽

2012 ◽

Vol 245 ◽

pp. 316-322

Author(s):

Ramadan A. Al-Madani ◽

M. Jarnaz ◽

K. Alkharmaji ◽

M. Essuri

Keyword(s):

Finite Element ◽

Composite Structure ◽

Composite Laminates ◽

Composite Structures ◽

Mechanical Response ◽

Laminated Composite ◽

Orthotropic Materials ◽

Laminate Structure ◽

Metallic Structures ◽

Modeling And Analysis

The characteristics of composite materials are of high importance to engineering applications; therefore the increasing use as a substitute for conventional materials, especially in the field of aircraft and space industries. It is a known fact that researchers use finite element programs for the design and analysis of composite structures, use of symmetrical conditions especially in complicated structures, in the modeling and analysis phase of the design, to reduce processing time, memory size required, and simplifying complicated calculations, as well as considering the response of composite structures to different loading conditions to be identical to that of metallic structures. Finite element methods are a popular method used to analyze composite laminate structures. The design of laminated composite structures includes phases that do not exist in the design of traditional metallic structures, for instance, the choice of possible material combinations is huge and the mechanical properties of a composite structure, which are anisotropic by nature, are created in the design phase with the choice of the appropriate fiber orientations and stacking sequence. The use of finite element programs (conventional analysis usually applied in the case of orthotropic materials) to analysis composite structures especially those manufactured using angle ply laminate techniques or a combination of cross and angle ply techniques, as well considering the loading response of the composite structure to be identical to that of structures made of traditional materials, has made the use of, and the results obtained by using such analysis techniques and conditions questionable. Hence, the main objective of this paper is to highlight and present the results obtained when analyzing and modeling symmetrical conditions as applied to commercial materials and that applied to composite laminates. A comparison case study is carried out using cross-ply and angle-ply laminates which concluded that, if the composition of laminate structure is pure cross-ply, the FEA is well suited for predicting the mechanical response of composite structure using principle of symmetry condition. On the other hand that is not the case for angle-ply or mixed-ply laminate structure.

Download Full-text

Comparison of Substructures Between Uniaxial and Biaxial Deformation in 1100-0 Aluminum

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096989 ◽

1981 ◽

Vol 39 ◽

pp. 52-53

Author(s):

D. L. Rohr ◽

S. S. Hecker

Keyword(s):

Plastic Strain ◽

Cell Walls ◽

Room Temperature ◽

Mechanical Response ◽

Biaxial Tension ◽

Initial Deformation ◽

Uniaxial Deformation ◽

Biaxial Deformation ◽

Stress States ◽

Comprehensive Study

As part of a comprehensive study of microstructural and mechanical response of metals to uniaxial and biaxial deformations, the development of substructure in 1100 A1 has been studied over a range of plastic strain for two stress states.Specimens of 1100 aluminum annealed at 350 C were tested in uniaxial (UT) and balanced biaxial tension (BBT) at room temperature to different strain levels. The biaxial specimens were produced by the in-plane punch stretching technique. Areas of known strain levels were prepared for TEM by lapping followed by jet electropolishing. All specimens were examined in a JEOL 200B run at 150 and 200 kV within 24 to 36 hours after testing.The development of the substructure with deformation is shown in Fig. 1 for both stress states. Initial deformation produces dislocation tangles, which form cell walls by 10% uniaxial deformation, and start to recover to form subgrains by 25%. The results of several hundred measurements of cell/subgrain sizes by a linear intercept technique are presented in Table I.

Download Full-text

Construction of plastic contact deformation maps on ceramics: a case study on aluminum nitride

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100165641 ◽

1996 ◽

Vol 54 ◽

pp. 636-637

Author(s):

D. L. Callahan

Keyword(s):

Plastic Deformation ◽

Aluminum Nitride ◽

Mechanical Response ◽

Three Dimensional ◽

Bright Field Image ◽

Perfectly Plastic ◽

Contrast Analysis ◽

Deformation Patterns

Modern polishing, precision machining and microindentation techniques allow the processing and mechanical characterization of ceramics at nanometric scales and within entirely plastic deformation regimes. The mechanical response of most ceramics to such highly constrained contact is not predictable from macroscopic properties and the microstructural deformation patterns have proven difficult to characterize by the application of any individual technique. In this study, TEM techniques of contrast analysis and CBED are combined with stereographic analysis to construct a three-dimensional microstructure deformation map of the surface of a perfectly plastic microindentation on macroscopically brittle aluminum nitride.The bright field image in Figure 1 shows a lg Vickers microindentation contained within a single AlN grain far from any boundaries. High densities of dislocations are evident, particularly near facet edges but are not individually resolvable. The prominent bend contours also indicate the severity of plastic deformation. Figure 2 is a selected area diffraction pattern covering the entire indentation area.

Download Full-text