Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

The flow of homogeneous fluids through porous media: analogies with other physical problems

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FEAP - - A Finite Element Analysis Program

Object composition offers significant advantages over class inheritance to develop a flexible software architecture for finite-element analysis. Using this approach, separate classes encapsulate fu...

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Nonlinear Finite-Element Analysis Software Architecture Using Object Composition

Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.

Multiscale Methods for Composites: A Review

General Problems in solid mechanics and non-linearity Galerkin method of approximation - irreducible and mixed forms Solution of non-linear algebraic equations Inelastic and non-linear materials Geometrically non-linear problems - finite deformation Material constitution for finite deformation Treatment of Constraints - contact and tied interfaces Pseudo-Rigid & Rigid-Flexible Bodies Discrete element methods Structural Mechanics Problems in One Dimension - rods Plate Bending Approximation Thick Reissner-Mindlin Plates -Irreducible & Mixed Formulations Shells as an assembly of flat elements Curved rods and axisymmetric shells Shells as a special case of three-dimensional analysis Semi-analytical finite element processes Non-linear structural processes - large displacement and instability Multiscale modelling Computer procedures for finite element analysis Appendices

The Finite Element Method for Solid and Structural Mechanics

In this chapter we consider modeling of the interaction between one or more bodies that come into contact with each other. Such contact problems are among the most difficult to model by finite elements and we summarize here only some of the approaches which have proved successful in practice. The chapter includes description of solution techniques based on penalty, augmented Lagrangian, and Lagrange multiplier methods. These are first described for node-to-node contacts and subsequently extended to treat node-to-surface and surface-to-surface treatments. Basic forms start from a frictionless treatment and some are extended to treat friction.

Chapter 8 – Treatment of Constraints: Contact and Tied Interfaces

In this chapter we review the general equations for analysis of solids in which deformations remain “small” but material behavior includes effects of a nonlinear kind. We present the theory in both an indicial (or tensorial) form as well as in the matrix form commonly used in finite element developments. We also reformulate the equations of solids in a variational (Galerkin) form. The chapter also presents the notation and the methodology which we shall adopt throughout this book. The reader will note how simply the transition between forms for linear and nonlinear problems occurs.

Chapter 1 – General Problems in Solid Mechanics and Nonlinearity

This chapter presents the modeling of the interaction between one or more bodies that come into contact with each other Such contact problems are among the most difficult to model by finite elements This chapter summarizes only some of the approaches that have proved successful in practice In general, the finite element discretization process itself leads to surfaces that are not smooth and therefore, when large sliding occurs, the transition from one element to the next leads to discontinuities in the response and in transient applications can induce non-physical inertial discontinuities as well For quasi-static response, such discontinuity leads to difficulties in defining a unique solution and here methods of multi-surface plasticity prove useful This chapter also includes some illustrations of performance for many of the formulations and problem classes discussed

Treatment of Constraints: Contact and Tied Interfaces

This appendix includes a summary of shape functions in parametric form for use in an isoparametric finite element formulation. Shape functions for quadrilateral and brick shapes are expressed in parametric form using Lagrange interpolation. This yields the Lagrange family of elements. For triangular and tetrahedral shapes barycentric coordinates are used. Expressions for derivatives with respect to global coordinates are described using the chain rule and derivatives with respect to parent coordinates.

David Fox

Papers

The Finite Element Method for Solid and Structural Mechanics

Chapter 8 – Treatment of Constraints: Contact and Tied Interfaces

Chapter 1 – General Problems in Solid Mechanics and Nonlinearity

Treatment of Constraints: Contact and Tied Interfaces

Isoparametric Finite Element Approximations