Multiscale technique for nonlinear analysis of elastoplastic and viscoplastic composites
TL;DR: In this article, the authors developed an efficient multiscale procedure for studying the mechanical response of structural elements made of elastoplastic or viscoplastic composite materials, where the micro and the macro scales are considered separated.
Abstract: Aim of the present paper is to develop an efficient multiscale procedure for studying the mechanical response of structural elements made of elastoplastic or viscoplastic composite materials. The micro and the macro scales are considered separated. At the microscale a PieceWise Uniform Transformation Field Analysis (PWUTFA) homogenization technique is adopted to derive the overall response of a periodic composite. Thus, a Unit Cell (UC) containing all the properties of the heterogeneous material is analyzed and divided in subsets; in each one the inelastic strain is considered uniform, i.e. constant, and represents the history variable of the analysis. Elastoplastic and elasto-viscoplastic models with isotropic hardening are adopted in order to describe the nonlinear response of the constituents. A new numerical procedure is developed in order to solve the evolutive problem in all the subsets simultaneously adopting a predictor-corrector technique. The corrector phase is solved by means of a modified Newton-Raphson iterative procedure. Furthermore, the tangent consistent with the algorithm is computed and adopted in the multiscale computations. Numerical applications are carried out in order to assess the efficiency of the proposed multiscale approach.
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TL;DR: Two different multiscale modeling approaches are presented for the analysis of microstructural instability-induced failure in locally periodic fiber-reinforced composite materials subjected to general loading conditions involving large deformations.
42 citations
Cites methods from "Multiscale technique for nonlinear ..."
...Furthermore, to circumvent the computational effort related to nested calculations in FE2 methods, other approaches have been introduced for the homogenization of heterogeneous materials with timedependent or nonlinear behaviors, for instance, recently a multiscale approach for the analysis of elastoplastic and viscoplastic composites employing a PieceWise Uniform TFA was proposed in [20]....
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TL;DR: In this article, the authors developed a two-scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semi-analytical homogenization of a bi-layer microstructure.
Abstract: Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic---specifically, transversely isotropic---and closely linked to the layered composite structure at the microscale. In this work, we develop a two-scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semi-analytical homogenization of a bi-layer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic Modified Cam-Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time-dependent borehole closure in a shale formation with different bedding plane directions.
18 citations
Cites methods from "Multiscale technique for nonlinear ..."
...Specific assumptions such as piecewise uniform [57] or non-uniform [58] distribution of the strain field in each phase were used to accommodate viscoplasticity within the transformation field analysis framework [59–61]....
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TL;DR: In this paper, the dynamic elastoplastic response of carbon nanotube (CNT) fiber/polymer multiscale laminated composite (CNTFPC) doubly curved shell subjected to low-velocity impact of the projectile is investigated.
15 citations
TL;DR: In this article, a step-by-step numerical homogenization procedure is introduced to calibrate a homogenized viscoelastic-viscoplastic (VE-VP) model with the same formulation as the VE-VP model used for describing the polymer behavior in the RVE model.
13 citations
TL;DR: The application of a multiscale strategy, employing a reduced order method at the Gauss point level for the analysis of 3D-printed structural elements, could represent a good compromise in terms of accuracy of the results and computational efficiency.
10 citations
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TL;DR: The fundamental assumption of all theories of plasticity, that of time independence of the equations of state, makes simultaneous description of the plastic and rheologic properties of a material impossible as mentioned in this paper.
Abstract: Publisher Summary The fundamental assumption of all theories of plasticity—that of time independence of the equations of state—makes simultaneous description of the plastic and rheologic properties of a material impossible. I t is well-known that in many practical problems, the actual behaviour of a material is governed by plastic as well as by rheologic effects. It can even be said that for many important structural materials, rheologic effects are more pronounced after the plastic state has been reached. Every material shows more or less pronounced viscous properties. In some problems, the influence of viscous properties of the material may be negligible, while in others, it may be essential. Both sciences—plasticity and rheology—are concerned with the description of important mechanical properties of structural materials. Each of them has created its own methods of investigation and has developed within the framework of certain assumptions which, unfortunately, cannot always be satisfied in reality. The results of rheology are confined to cases where plastic strain is of no decisive importance.
1,672 citations
Book•
01 Jan 2008
TL;DR: In this article, the authors present a general numerical integration algorithm for elastoplastic constitutive equations, based on the von Mises model, which is used for the integration of the isotropically hardening deformation.
Abstract: Part One Basic concepts 1 Introduction 1.1 Aims and scope 1.2 Layout 1.3 General scheme of notation 2 ELEMENTS OF TENSOR ANALYSIS 2.1 Vectors 2.2 Second-order tensors 2.3 Higher-order tensors 2.4 Isotropic tensors 2.5 Differentiation 2.6 Linearisation of nonlinear problems 3 THERMODYNAMICS 3.1 Kinematics of deformation 3.2 Infinitesimal deformations 3.3 Forces. Stress Measures 3.4 Fundamental laws of thermodynamics 3.5 Constitutive theory 3.6 Weak equilibrium. The principle of virtual work 3.7 The quasi-static initial boundary value problem 4 The finite element method in quasi-static nonlinear solid mechanics 4.1 Displacement-based finite elements 4.2 Path-dependent materials. The incremental finite element procedure 4.3 Large strain formulation 4.4 Unstable equilibrium. The arc-length method 5 Overview of the program structure 5.1 Introduction 5.2 The main program 5.3 Data input and initialisation 5.4 The load incrementation loop. Overview 5.5 Material and element modularity 5.6 Elements. Implementation and management 5.7 Material models: implementation and management Part Two Small strains 6 The mathematical theory of plasticity 6.1 Phenomenological aspects 6.2 One-dimensional constitutive model 6.3 General elastoplastic constitutive model 6.4 Classical yield criteria 6.5 Plastic flow rules 6.6 Hardening laws 7 Finite elements in small-strain plasticity problems 7.1 Preliminary implementation aspects 7.2 General numerical integration algorithm for elastoplastic constitutive equations 7.3 Application: integration algorithm for the isotropically hardening von Mises model 7.4 The consistent tangent modulus 7.5 Numerical examples with the von Mises model 7.6 Further application: the von Mises model with nonlinear mixed hardening 8 Computations with other basic plasticity models 8.1 The Tresca model 8.2 The Mohr-Coulomb model 8.3 The Drucker-Prager model 8.4 Examples 9 Plane stress plasticity 9.1 The basic plane stress plasticity problem 9.2 Plane stress constraint at the Gauss point level 9.3 Plane stress constraint at the structural level 9.4 Plane stress-projected plasticity models 9.5 Numerical examples 9.6 Other stress-constrained states 10 Advanced plasticity models 10.1 A modified Cam-Clay model for soils 10.2 A capped Drucker-Prager model for geomaterials 10.3 Anisotropic plasticity: the Hill, Hoffman and Barlat-Lian models 11 Viscoplasticity 11.1 Viscoplasticity: phenomenological aspects 11.2 One-dimensional viscoplasticity model 11.3 A von Mises-based multidimensional model 11.4 General viscoplastic constitutive model 11.5 General numerical framework 11.6 Application: computational implementation of a von Mises-based model 11.7 Examples 12 Damage mechanics 12.1 Physical aspects of internal damage in solids 12.2 Continuum damage mechanics 12.3 Lemaitre's elastoplastic damage theory 12.4 A simplified version of Lemaitre's model 12.5 Gurson's void growth model 12.6 Further issues in damage modelling Part Three Large strains 13 Finite strain hyperelasticity 13.1 Hyperelasticity: basic concepts 13.2 Some particular models 13.3 Isotropic finite hyperelasticity in plane stress 13.4 Tangent moduli: the elasticity tensors 13.5 Application: Ogden material implementation 13.6 Numerical examples 13.7 Hyperelasticity with damage: the Mullins effect 14 Finite strain elastoplasticity 14.1 Finite strain elastoplasticity: a brief review 14.2 One-dimensional finite plasticity model 14.3 General hyperelastic-based multiplicative plasticity model 14.4 The general elastic predictor/return-mapping algorithm 14.5 The consistent spatial tangent modulus 14.6 Principal stress space-based implementation 14.7 Finite plasticity in plane stress 14.8 Finite viscoplasticity 14.9 Examples 14.10 Rate forms: hypoelastic-based plasticity models 14.11 Finite plasticity with kinematic hardening 15 Finite elements for large-strain incompressibility 15.1 The F-bar methodology 15.2 Enhanced assumed strain methods 15.3 Mixed u/p formulations 16 Anisotropic finite plasticity: Single crystals 16.1 Physical aspects 16.2 Plastic slip and the Schmid resolved shear stress 16.3 Single crystal simulation: a brief review 16.4 A general continuum model of single crystals 16.5 A general integration algorithm 16.6 An algorithm for a planar double-slip model 16.7 The consistent spatial tangent modulus 16.8 Numerical examples 16.9 Viscoplastic single crystals Appendices A Isotropic functions of a symmetric tensor A.1 Isotropic scalar-valued functions A.1.1 Representation A.1.2 The derivative of anisotropic scalar function A.2 Isotropic tensor-valued functions A.2.1 Representation A.2.2 The derivative of anisotropic tensor function A.3 The two-dimensional case A.3.1 Tensor function derivative A.3.2 Plane strain and axisymmetric problems A.4 The three-dimensional case A.4.1 Function computation A.4.2 Computation of the function derivative A.5 A particular class of isotropic tensor functions A.5.1 Two dimensions A.5.2 Three dimensions A.6 Alternative procedures B The tensor exponential B.1 The tensor exponential function B.1.1 Some properties of the tensor exponential function B.1.2 Computation of the tensor exponential function B.2 The tensor exponential derivative B.2.1 Computer implementation B.3 Exponential map integrators B.3.1 The generalised exponential map midpoint rule C Linearisation of the virtual work C.1 Infinitesimal deformations C.2 Finite strains and deformations C.2.1 Material description C.2.2 Spatial description D Array notation for computations with tensors D.1 Second-order tensors D.2 Fourth-order tensors D.2.1 Operations with non-symmetric tensors References Index
1,077 citations
TL;DR: In this paper, a multiscale behaviour model based on a multilevel finite element (FE2) approach is used to take into account heterogeneities in the behaviour between the fibre and matrix.
1,056 citations
TL;DR: In this article, a new method is proposed for evaluation of local fields and overall properties of composite materials subjected to incremental thermomechanical loads and to transformation strains in the phases.
Abstract: A new method is proposed for evaluation of local fields and overall properties of composite materials subjected to incremental thermomechanical loads and to transformation strains in the phases. The composite aggregate may consist of many perfectly bonded inelastic phases of arbitrary geometry and elastic material symmetry. In principle, any inviscid or time-dependent inelastic constitutive relation that complies with the additive decomposition of total strains can be admitted in the analysis. The governing system of equations is derived from the representation of local stress and strain fields by novel transformation influence functions and concentration factor tensors, as discussed in the preceding paper by G. J. Dvorak and Y. Benveniste. The concentration factors depend on local and overall thermoelastic moduli, and can be evaluated with a selected micromechanical model. Applications to elastic-plastic, viscoelastic, and viscoplastic systems are discussed. The new approach is contrasted with some presently accepted procedures based on the self-consistent and Mori-Tanaka approximations, which are shown to violate exact relations between local and overall inelastic strains.
476 citations
TL;DR: In this article, a decomposition of the microscopic anelastic strain field on a finite set of transformation fields is proposed to describe the overall behavior of composites with nonlinear dissipative phases.
342 citations