Modeling of the Long-Term Behavior of Glassy Polymers

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Sami Holopainen ◽  
Mathias Wallin
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Glassy Polymers ◽  
Integration Scheme ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Plastic Spin ◽  
Backward Euler ◽  
Long Term Behavior

The constitutive model for glassy polymers proposed by Arruda and Boyce (BPA model) is reviewed and compared to experimental data for long-term loading. The BPA model has previously been shown to capture monotonic loading accurately, but for unloading and long-term behavior, the response of the BPA model is found to deviate from experimental data. In the present paper, we suggest an efficient extension that significantly improves the predictive capability of the BPA model during unloading and long-term recovery. The new, extended BPA model (EBPA model) is calibrated to experimental data of polycarbonate (PC) in various loading–unloading situations and deformation states. The numerical treatment of the BPA model associated with the finite element analysis is also discussed. As a consequence of the anisotropic hardening, the plastic spin enters the model. In order to handle the plastic spin in a finite element formulation, an algorithmic plastic spin is introduced. In conjunction with the backward Euler integration scheme use of the algorithmic plastic spin leads to a set of algebraic equations that provides the updated state. Numerical examples reveal that the proposed numerical algorithm is robust and well suited for finite element simulations.

A Finite Element Procedure of a Cyclic Thermoviscoplasticity Model for Solder and Copper Interconnects

1998 ◽  
Vol 120 (1) ◽  
pp. 24-34 ◽  
Author(s):  
C. Fu ◽  
D. L. McDowell ◽  
I. C. Ume
Keyword(s):  
Finite Element ◽  
Electronic Packaging ◽  
Copper Interconnects ◽  
Implicit Time ◽  
Integration Scheme ◽  
Single Element ◽  
Ofhc Copper ◽  
Computation Efficiency ◽  
Backward Euler ◽  
Finite Element Procedure

A finite element procedure using a semi-implicit time-integration scheme has been developed for a cyclic thermoviscoplastic constitutive model for Pb-Sn solder and OFHC copper, two common metallic constituents in electronic packaging applications. The scheme has been implemented in the commercial finite element (FE) code ABAQUS (1995) via the user-defined material subroutine, UMAT. Several single-element simulations are conducted to compare with previous test results, which include monotonic tensile tests, creep tests, and a two-step ratchetting test for 62Sn36Pb2Ag solder; a nonproportional axial-torsional test and a thermomechanical fatigue (TMF) test for OFHC copper. At the constitutive level, we also provide an adaptive time stepping algorithm, which can be used to improve the overall computation efficiency and accuracy especially in large-scale FE analyses. We also compare the computational efforts of fully backward Euler and the proposed methods. The implementation of the FE procedure provides a guideline to apply user-defined material constitutive relations in FE analyses and to perform more sophisticated thermomechanical simulations. Such work can facilitate enhanced understanding thermomechanical reliability issue of solder and copper interconnects in electronic packaging applications.

Multiscale Modeling of Large Deformation Processes in Polycrystalline Metals

2003 ◽  
Author(s):  
Antoinette Maniatty ◽  
Karel Matous ◽  
Jing Lu
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Grain Structure ◽  
Current Work ◽  
Integration Scheme ◽  
Two Dimensional ◽  
Scale Bridging ◽  
Grain Structures ◽  
Backward Euler ◽  
Bulk Response

A mesoscale model for predicting the evolution of the grain structure and the mechanical response of polycrystalline aggregates subject to large deformations, such as arise in bulk metal forming processes, is presented. The gain structures modeled are either experimentally observed or are computer generated and statistically similar to experimentally observed grain structures. In order to capture the inhomogeneous deformations and the resulting grain structure characteristics, a discretized model at the mesoscale is used. This work focuses on Al-Mg-Si alloys. Scale bridging is used to link to the macroscale. Examples involving two-dimensional grain structures and current work on three-dimensional grain structures are presented. The present work provides a framework to model the mesoscopic behavior and interactions between grains during finite strains. The mesoscale is characterized by a statistically representative voluem element (RVE), which contains the grains of a polycrystal. Experimentally observed grain structures are used both as models directly (for two-dimensional cases) and to define statistical characteristics to verify the similarity of computer generated grain structures (for three-dimensional cases). A Monte Carlo method based on the Potts model is used to define three-dimensional grain structures. In order to make the representative grain structure appropriate for scale-bridging, we design them with periodicity. A three-field, updated Lagrangian finite element formulation with a kinematic split of the deformation gradient into volume preserving and volumetric parts is used to create a stable finite element method in the context of nearly incompressible behavior. A fully implicit two-level backward Euler integration scheme is derived for integrating the constitutive equations, and consistent linearization is used in Newton’s method to solve the resulting equations. In addition, the average of the boundary conditions and bulk response must match the macroscopically measured bulk response. To illustrate and verify the proposed model, we analyze examples involving two-dimensional grain structures and compare with results from a Taylor model. Current work on three-dimensional grain structures ara also presented.

scholarly journals Development of a continuum plasticity model for the commercial finite element code ABAQUS

2011 ◽  
Vol 2 (2) ◽  
pp. 275-283
Author(s):  
M. Safaei ◽  
W. De Waele
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Euler Method ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Implicit Integration ◽  
Backward Euler ◽  
User Material Subroutine ◽  
Von Mises ◽  
Future Work

The present work relates to the development of computational material models for sheet metalforming simulations. In this specific study, an implicit scheme with consistent Jacobian is used forintegration of large deformation formulation and plane stress elements. As a privilege to the explicitscheme, the implicit integration scheme is unconditionally stable. The backward Euler method is used toupdate trial stress values lying outside the yield surface by correcting them back to the yield surface atevery time increment. In this study, the implicit integration of isotropic hardening with the von Mises yieldcriterion is discussed in detail. In future work it will be implemented into the commercial finite element codeABAQUS by means of a user material subroutine.

scholarly journals Finite Element Modeling of FRP-Strengthened RC Beam under Sustained Load

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Shiyong Jiang ◽  
Weilai Yao ◽  
Jin Chen ◽  
Tao Cai
Keyword(s):  
Finite Element ◽  
Field Performance ◽  
Adhesive Layer ◽  
Aging Effect ◽  
Time Dependent ◽  
Sustained Load ◽  
Fe Model ◽  
Rc Beam ◽  
Long Term Behavior

External bonding of FRP laminates to the tension soffit of concrete members has become a popular method for flexural strengthening. However, the long-term field performance of FRP-strengthened RC members under service conditions is still a concern, and more work needs to be done. Based on concrete smeared-crack approach, this paper presents a finite-element (FE) model for predicting long-term behavior of FRP-strengthened RC beam, which considers the time-dependent properties of all components including the aging effect of concrete. According to the comparison between theoretical predictions and test results, the validity of the FE model is verified. The interfacial edge stresses in adhesive layer were determined through appropriate mesh refinement near the plate end, and their time-dependent characteristics were investigated. The results show that creep of concrete and epoxy resin cause significant variations of the edge stresses with time. According to the research in this paper, the FE approach is found to be able to properly simulate the long-term behavior of the FRP-strengthened beam and help us better understand the complex changes in the stress state occurring over time.

Long-Term Design of Composite Pipes and Tanks

2013 ◽  
Author(s):  
Hugo Faria ◽  
Rui M. Guedes ◽  
A. Torres Marques
Keyword(s):  
Experimental Data ◽  
Industrial Applications ◽  
Design Criterion ◽  
Manufacturing Processes ◽  
Wide Range ◽  
Predictive Approach ◽  
Different Types ◽  
Composite Pipes ◽  
Long Term Behavior

In order to improve the reliability and confidence of composite solutions for piping and tanks in the several industrial applications they serve, deeper knowledge on the long-term behavior is needed. In this work a practical predictive approach for the long-term properties of these structures was established. It is based on experimental data previously obtained in comprehensive experimental programs for different types of GFRP pipes, thus covering a wide range of laminate constructions and manufacturing processes. In this paper, the principles, applicability and validation of the design criterion developed are presented and discussed.

scholarly journals Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

2021 ◽  
Vol 5 (3) ◽  
pp. 132
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Algebraic Equations ◽  
State Representation ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Infinite State

In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.

scholarly journals An Interface Model Including Cracks and Roughness Applied to Masonry

2014 ◽  
Vol 8 (1) ◽  
pp. 263-271 ◽  
Author(s):  
Fazia Fouchal ◽  
Frédéric Lebonb ◽  
Maria L. Raffa ◽  
Giuseppe Vairo
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Numerical Analysis ◽  
Numerical Procedure ◽  
Element Formulation ◽  
Interface Model ◽  
Shear Tests ◽  
Micro Cracks ◽  
Homogenization Approach ◽  
Asymptotic Analyses

In this paper an interface model accounting for roughness and micro-cracks is presented and applied to masonry-like structures. The model is consistently derived by coupling a homogenization approach and arguments of asymptotic analyses. A numerical procedure is introduced and numerical results, based on a finite element formulation, are successfully compared with experimental data , obtained on masonry samples undergoing to shear tests. Finally, a parametric numerical analysis is proposed, highlighting the influence of the roughness features on the interface response.

Quasi Exact Solutions for Some Elastodynamics Problems

1999 ◽  
Author(s):  
André Barraco ◽  
Marguerite Gilbert
Keyword(s):  
Finite Element ◽  
Small Strain ◽  
Integration Scheme ◽  
Element Formulation ◽  
Kutta Method ◽  
Finite Rotation ◽  
Large Rotation ◽  
Runge Kutta Method ◽  
Method Integration ◽  
Actual Configuration

Abstract In this paper we develop the formulation for large displacement, large rotation, but small strain, for Timoshenko beam. The so-called “finite rotation vector” is used. Rather to use a finite element formulation we solve the exact semi-local differential equations, written in the actual configuration, using a space (finite difference method) and time (Runge Kutta method) integration scheme. This method is restricted to geometrically simple structures but is developed to validate FEM codes. We present a static and dynamic example.

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