A variational framework for mathematically nonsmooth problems in solid and structure mechanics

Chen, Pinlei

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https://hdl.handle.net/2142/101813 Copy

Description

Title

A variational framework for mathematically nonsmooth problems in solid and structure mechanics

Author(s)

Chen, Pinlei

Issue Date

2018-07-11

Director of Research (if dissertation) or Advisor (if thesis)

Masud, Arif

Doctoral Committee Chair(s)

Masud, Arif

Committee Member(s)

• Duarte, Armando C.
• Lopez-Pamies, Oscar
• Geubelle, Philippe H.

Department of Study

Civil & Environmental Eng

Discipline

Civil Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Variational Multiscale framework
• Interfaces
• Damage
• Thermomechanical coupled framework
• Stabilized methods
• Finite strains
• Discontinuous Galerkin method
• Multi-constituents
• Debonding
• Fatigue

Abstract

This dissertation presents a new paradigm for addressing multi-physics problems with interfaces in the field of Additive Manufacturing and the modeling of fibrous composite materials. The unique process of adding the material layer by layer in the AM techniques raises the issue about the stability of the interfaces between the layers and along the boundaries of multi-constituent materials. A stabilized interface formulation is developed to model debonding in monotonic loading, fatigue effects in cyclic loading, and thermal effects at interfaces which severely impact the functional life of those materials and structures. The formulation is based on embedding Discontinuous Galkerin (DG) ideas in a Continuous Galerkin (CG) framework. Starting from a mixed method incorporating the Lagrange multiplier along the interface, a pure displacement formulation is derived using the Variational Multiscale Method (VMS). From a mathematical and computational perspective, the key factor influencing the accuracy and robustness of the interface formulation is the design of the numerical flux and the penalty or stability terms. Analytical expressions that are free from user-defined parameters are naturally derived for the numerical flux and stability tensor which are functions of the evolving geometric and material nonlinearity. The proposed framework is extended for debonding at finite strains across general bimaterial interfaces. An interfacial gap function is introduced that evolves subject to constraints imposed by opening and/or sliding interfaces. An internal variable formalism is derived together with the notion of irreversibility of damage results in a set of evolution equations for the gap function that seamlessly tracks interface debonding by treating damage and friction in a unified way. Tension debonding, compression damage, and frictional sliding are accommodated, and return mapping algorithms in the presence of evolving strong discontinuities are developed. This derivation variationally embeds the interfacial kinematic models that are crucial to capturing the physical and mathematical properties involving large strains and damage. The framework is extended for monolithic coupling of thermomechanical fields in the class of problems that have embedded weak and strong discontinuities in the mechanical and thermal fields. Since the derived expressions are a function of the mechanical and thermal fields, the resulting stabilized formulation contains numerical flux and stability tensors that provide an avenue to variationally embed interfacial kinetic and kinematic models for more robust representation of interfacial physics. Representative numerical tests involving large strains and rotations, damage phenomena, and thermal effects are performed to confirm the robustness and accuracy of the method. Comparison of the results with both experimental and numerical results from literature are presented.

Graduation Semester

2018-08

Type of Resource

text

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http://hdl.handle.net/2142/101813

Copyright and License Information

Copyright 2018 Pinlei Chen

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