Finite element implementation of the Hoek–Brown material model with general strain softening behavior

2015 ◽  
Vol 78 ◽  
pp. 163-174 ◽  
Author(s):  
E.S. Sørensen ◽  
J. Clausen ◽  
L. Damkilde
Keyword(s):  
Finite Element ◽  
Strain Softening ◽  
Material Model ◽  
Finite Element Implementation ◽  
Softening Behavior ◽  
General Strain

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.

scholarly journals Failure in anisotropic sensitive clays: finite element study of Perniö failure test

2017 ◽  
Vol 54 (7) ◽  
pp. 1013-1033 ◽  
Author(s):  
Marco D’Ignazio ◽  
Tim Tapani Länsivaara ◽  
Hans Petter Jostad
Keyword(s):  
Finite Element ◽  
Strain Softening ◽  
Soft Clay ◽  
Study Data ◽  
Peak Strain ◽  
Railway Network ◽  
Element Analysis ◽  
Softening Behavior ◽  
Rate Dependent ◽  
Laboratory Test Results

The railway network on coastal areas of Finland is predominantly located in soft clay areas. The undrained shear strength of such clays is generally low, highly anisotropic, and rate dependent, and it exhibits post-peak strain softening under undrained conditions. A full-scale failure test was performed by Tampere University of Technology in Perniö, Western Finland, in 2009. A shallow railway embankment built on a soft clay deposit was equipped with a loading structure and loaded to failure in about 30 h. The embankment collapsed 2 h after the last loading step. In this study, data collected from the experiment are used, together with laboratory test results on high-quality samples, to conduct advanced finite element analysis of the Perniö failure test. The NGI-ADPSoft model is used for this purpose, which is capable of simulating the strain-softening behavior of the clay. Even though the observed rate effect is not taken into account in the analyses, the failure load can be predicted reasonably well. Good agreement is also observed for calculated displacements and failure mechanism with experimental observations.

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.

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