Finite Element Implementation of Anisotropic Quasi-Linear Viscoelasticity Using a Discrete Spectrum Approximation

1998 ◽  
Vol 120 (1) ◽  
pp. 62-70 ◽  
Author(s):  
M. A. Puso ◽  
J. A. Weiss
Keyword(s):  
Finite Element ◽  
Discrete Spectrum ◽  
Soft Tissues ◽  
Transversely Isotropic ◽  
Material Model ◽  
Material Behavior ◽  
Elastic Response ◽  
Test Problems ◽  
Finite Element Program ◽  
Finite Element Implementation

The objective of this work was to develop a theoretical and computational framework to apply the finite element method to anisotropic, viscoelastic soft tissues. The quasi-linear viscoelastic (QLV) theory provided the basis for the development. To allow efficient and easy computational implementation, a discrete spectrum approximation was developed for the QLV relaxation function. This approximation provided a graphic means to fit experimental data with an exponential series. A transversely isotropic hyperelastic material model developed for ligaments and tendons was used for the elastic response. The viscoelastic material model was implemented in a general-purpose, nonlinear finite element program. Test problems were analyzed to assess the performance of the discrete spectrum approximation and the accuracy of the finite element implementation. Results indicated that the formulation can reproduce the anisotropy and time-dependent material behavior observed in soft tissues. Application of the formulation to the analysis of the human femur-medial collateral ligament–tibia complex demonstrated the ability of the formulation to analyze large three-dimensional problems in the mechanics of biological joints.

Implementation of the Nonlocal Microplane Concrete Model Within an Explicit Dynamic Finite Element Program

1992 ◽  
Vol 45 (3S) ◽  
pp. S132-S139 ◽  
Author(s):  
William F. Cofer
Keyword(s):  
Finite Element ◽  
Strain Tensor ◽  
Material Model ◽  
Material Behavior ◽  
Concrete Material ◽  
Finite Element Program ◽  
Dynamic Finite Element ◽  
Weighted Integral ◽  
Element Program ◽  
Explicit Dynamic

The microplane concrete material model is based upon assumptions regarding the behavior of the material components. At any point, the response to the strain tensor on arbitrarily oriented surfaces is considered. Simple, softening stress-strain relationships are assumed in directions perpendicular and parallel to the surfaces. The macroscopic material behavior is then composed of the sum of the effects. The implementation of this model into the explicit, nonlinear, dynamic finite element program, DYNA3D, is described. To avoid the spurious mesh sensitivity that accompanies material failure, a weighted integral strain averaging approach is used to ensure that softening is nonlocal. This method is shown to be effective for limiting the failure zone in a concrete rod subjected to an impulse loading.

A Study of the Dynamic Behavior of Elastomeric Materials Using Finite Elements

1996 ◽  
Vol 118 (4) ◽  
pp. 503-508 ◽  
Author(s):  
G. E. Vallee ◽  
Arun Shukla
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Split Hopkinson Pressure Bar ◽  
Material Model ◽  
Element Model ◽  
Material Behavior ◽  
Hopkinson Pressure Bar ◽  
Material Models ◽  
Finite Element Program ◽  
Elastomeric Materials

A numerical method is described for determining a dynamic finite element material model for elastomeric materials loaded primarily in compression. The method employs data obtained using the Split Hopkinson Pressure Bar (SHPB) technique to define a molecular constitutive model for elastomers. The molecular theory is then used to predict dynamic material behavior in several additional deformation modes used by the ABAQUS/Explicit (Hibbitt, Karlsson, and Sorenson, 1993a) commercial finite element program to define hyperelastic material behavior. The resulting dynamic material models are used to create a finite element model of the SHPB system, yielding insights into both the accuracy of the material models and the SHPB technique itself when used to determine the dynamic behavior of elastomeric materials. Impact loading of larger elastomeric specimens whose size prohibits examination by the SHPB technique are examined and compared to the results of dynamic load-deflection experiments to further verify the dynamic material models.

A Sub-Domain Inverse Finite Element Characterization of Hyperelastic Membranes Including Soft Tissues

2003 ◽  
Vol 125 (3) ◽  
pp. 363-371 ◽  
Author(s):  
Padmanabhan Seshaiyer ◽  
Jay D. Humphrey
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soft Tissues ◽  
Nonlinear Behavior ◽  
Local Stress ◽  
Biological Tissues ◽  
Material Behavior ◽  
Inverse Finite Element Method ◽  
Complicated Geometry ◽  
Element Method

Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.

Hyperelastic Muscle Simulation

2007 ◽  
Vol 345-346 ◽  
pp. 1241-1244 ◽  
Author(s):  
Mohd. Zahid Ansari ◽  
Sang Kyo Lee ◽  
Chong Du Cho
Keyword(s):  
Skeletal Muscle ◽  
Silicone Rubber ◽  
Soft Tissues ◽  
Material Model ◽  
Incompressible Material ◽  
Material Behavior ◽  
Rubber Tube ◽  
Stress Strain ◽  
Element Analysis ◽  
Strain Behavior

Biological soft tissues like muscles and cartilages are anisotropic, inhomogeneous, and nearly incompressible. The incompressible material behavior may lead to some difficulties in numerical simulation, such as volumetric locking and solution divergence. Mixed u-P formulations can be used to overcome incompressible material problems. The hyperelastic materials can be used to describe the biological skeletal muscle behavior. In this study, experiments are conducted to obtain the stress-strain behavior of a solid silicone rubber tube. It is used to emulate the skeletal muscle tensile behavior. The stress-strain behavior of silicone is compared with that of muscles. A commercial finite element analysis package ABAQUS is used to simulate the stress-strain behavior of silicone rubber. Results show that mixed u-P formulations with hyperelastic material model can be used to successfully simulate the muscle material behavior. Such an analysis can be used to simulate and analyze other soft tissues that show similar behavior.

scholarly journals A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Min Kyoo Kang ◽  
Rui Huang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Numerical Simulations ◽  
Variational Approach ◽  
Chemical Potential ◽  
Polymer Network ◽  
Material Model ◽  
Geometric Constraints ◽  
Free Energy Function ◽  
Finite Element Implementation

A hydrogel consists of a cross-linked polymer network and solvent molecules. Depending on its chemical and mechanical environment, the polymer network may undergo enormous volume change. The present work develops a general formulation based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions along with proper boundary conditions. A specific material model is employed in a finite element implementation, for which the nonlinear constitutive behavior is derived from a free energy function, with explicit formula for the true stress and tangent modulus at the current state of deformation and chemical potential. Such implementation enables numerical simulations of hydrogels swelling under various constraints. Several examples are presented, with both homogeneous and inhomogeneous swelling deformation. In particular, the effect of geometric constraint is emphasized for the inhomogeneous swelling of surface-attached hydrogel lines of rectangular cross sections, which depends on the width-to-height aspect ratio of the line. The present numerical simulations show that, beyond a critical aspect ratio, creaselike surface instability occurs upon swelling.

Nonlinear Finite Element Analysis for Thermoplastic Pipes

1998 ◽  
Vol 1624 (1) ◽  
pp. 225-230 ◽  
Author(s):  
Chuntao Zhang ◽  
Ian D. Moore
Keyword(s):  
Finite Element ◽  
Geometrical Nonlinearity ◽  
Constitutive Models ◽  
Material Behavior ◽  
Pipe Material ◽  
Limit States ◽  
Element Analysis ◽  
Finite Element Program ◽  
Highly Nonlinear ◽  
Nonlinear Constitutive Models

Thermoplastic pipes are being used increasingly for water supply lines, storm sewers, and leachate collection systems in landfills. To facilitate limit states design for buried polymer pipes, nonlinear constitutive models have recently been developed to characterize the highly nonlinear and time-dependent material behavior of high-density polyethylene (HDPE). These models have been implemented in a finite element program to permit structural analysis for buried HDPE pipes and to provide information regarding performance limits of the structures. Predictions of HDPE pipe response under parallel plate loading and hoop compression in a soil cell are reported and compared with pipe response measured in laboratory tests. Effects on the structural performance of pipe material nonlinearity, geometrical nonlinearity, and backfill soil properties were investigated. Good correlations were found between the finite element predictions and the experimental measurements. The models can be used to predict pipe response under many different load histories (not just relaxation or creep). Work is ongoing to develop nonlinear constitutive models for polyvinylchloride and polypropylene to extend the predictive capability of the finite element model to these materials.

A Consistent Implicit Formulation for Nonlinear Finite Element Modeling With Contact and Friction: Part I—Theory

1991 ◽  
Vol 58 (2) ◽  
pp. 499-506 ◽  
Author(s):  
M. J. Saran ◽  
R. H. Wagoner
Keyword(s):  
Finite Element ◽  
Nonlinear Problems ◽  
Material Model ◽  
Test Problems ◽  
Large Strains ◽  
Numerical Verification ◽  
Viscoplastic Material ◽  
Highly Nonlinear ◽  
Complex Boundary ◽  
Consistent Tangent Operator

A formulation for finite element simulation of highly nonlinear problems including friction and contact with arbitrarily shaped rigid surfaces is proposed (CFS approach), prompted by difficulties in robust and accurate simulations of industrial forming processes. Nonlinearities are caused by large strains, plastic flow, and complex boundary conditions with frictional contact. In Part I the theoretical basis is described and the appropriate numerical algorithm is derived. The complete set of the governing relations, comprising equilibrium and interfacial equations, is appropriately linearized; resulting in a consistent tangent operator of the Newton-Raphson algorithm. In Part II, as a numerical verification, plane-strain sheet-forming processes are analyzed using a rigid-viscoplastic material model. Results are presented and discussed for test problems and for complex simulation of reverse drawing by concave tools.

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Leslee W. Brown ◽  
Lorenzo M. Smith
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Material Model ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Material Tests

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

The role of material model in the finite element simulation of high-speed machining of Ti6Al4V

2016 ◽  
Vol 230 (17) ◽  
pp. 2959-2967 ◽  
Author(s):  
Chong-Yang Gao ◽  
Liang-Chi Zhang ◽  
Peng-Hui Liu
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
High Speed ◽  
Material Model ◽  
Machining Process ◽  
High Speed Machining ◽  
Serrated Chip ◽  
Finite Element Program ◽  
Element Simulation ◽  
Improved Model

This paper provides a comprehensive assessment on some commonly used thermo-viscoplastic constitutive models of metallic materials during severe plastic deformation at high-strain rates. An hcp model previously established by us was improved in this paper to enhance its predictability by incorporating the key saturation characteristic of strain hardening. A compensation-based stress-updating algorithm was also developed to introduce the new hcp model into a finite element program. The improved model with the developed algorithm was then applied in finite element simulation to investigate the high-speed machining of Ti6Al4V. It was found that by using different material models, the simulated results of cutting forces, serrated chip morphologies, and residual stresses can be different too and that the improved model proposed in this paper can be applied to simulate the titanium alloy machining process more reliably due to its physical basis when compared with some other empirical Johnson–Cook models.

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