Damage Mechanics Problems Research Articles

An extended lumped damage mechanics IGABEM formulation for quasi-brittle material failure

This study proposes a new formulation for the mechanical modeling of quasi-brittle materials. The material degradation due to cracking is addressed through the Extended Lumped Damage Mechanics (XLDM) approach. The model is inserted into an IGABEM formulation, where Non-Uniform Rational B-Splines (NURBS) are the basis functions. A novel nonlinear solution technique has been developed for the numerical implementation. Crack propagation is captured using the initial stress field approach, widely utilized by the BEM community to account for nonlinear material behavior. The XLDM is coupled into an IGABEM formulation by discretizing part of the domain into cells, placed only where damage is expected to grow. Classical benchmark problems are presented to demonstrate the method’s capability and effectiveness. The results show excellent agreement with both experimental and numerical findings from the literature. Damage evolution is assessed through the band thickness opening, leading to material degradation. This method offers a new way of addressing damage mechanics problems within the BEM framework. It could benefit the BEM community, as traditional damage analysis within this numerical method often leads to significant time-consuming and elevated computational costs, which are mitigated by the formulation proposed herein.

A new unified arc-length method for damage mechanics problems

A new unified arc-length method for damage mechanics problems

A new approach for physically nonlinear analysis of continuum damage mechanics problems using the generalized/extended finite element method with global-local enrichment

The Generalized/Extended Finite Element Method (G/XFEM) is a numerical technique suitable to solve a wide range of continuum mechanics problems. It applies hierarchical nodal enrichment strategies within the Finite Element Method framework, allowing more flexibility in the numerical solution of boundary value problems (BVP) and being a powerful mesh-reduced method that takes advantage of the state-of-art of the standard FEM. One of the enrichment mechanisms is the so-called global-local enrichment (G/XFEMGL), in which the solution of a refined local BVP generates enrichment functions for the global domain. In this context, this work presents a new two-scale nonlinear strategy, associated with the G/XFEMGL, able to solve the material nonlinear analysis of continuum damage mechanics problems, in which quasi-brittle media degrade and soften, using a versatile mesh refinement strategy. A comprehensive description of the proposed strategy is registered and the aforementioned computational technique is validated throughout a set of plane stress numerical experiments that employ smeared crack constitutive model formulations, with well-known stress-strain laws. The results indicate that the implemented methodology could be used to solve a reasonable range of problems with considerable flexibility.

On mechanics and material length scales of failure in heterogeneous interfaces using a finite strain high performance solver

Three-dimensional simulations capable of resolving the large range of spatial scales, from the failure-zone thickness up to the size of the representative unit cell, in damage mechanics problems of particle reinforced adhesives are presented. We show that resolving this wide range of scales in complex three-dimensional heterogeneous morphologies is essential in order to apprehend fracture characteristics, such as strength, fracture toughness and shape of the softening profile. Moreover, we show that computations that resolve essential physical length scales capture the particle size-effect in fracture toughness, for example. In the vein of image-based computational materials science, we construct statistically optimal unit cells containing hundreds to thousands of particles. We show that these statistically representative unit cells are capable of capturing the first- and second-order probability functions of a given data-source with better accuracy than traditional inclusion packing techniques. In order to accomplish these large computations, we use a parallel multiscale cohesive formulation and extend it to finite strains including damage mechanics. The high-performance parallel computational framework is executed on up to 1024 processing cores. A mesh convergence and a representative unit cell study are performed. Quantifying the complex damage patterns in simulations consisting of tens of millions of computational cells and millions of highly nonlinear equations requires data-mining the parallel simulations, and we propose two damage metrics to quantify the damage patterns. A detailed study of volume fraction and filler size on the macroscopic traction-separation response of heterogeneous adhesives is presented.

GS0501-214 非連成解析による多層塗膜の動的損傷力学シミュレーション

In this research we use uncoupled analysis to evaluate the impact resistance of multi-layer coatings. We conduct high strain-rate simulation by ANSYS. Then the results of stress and strain are in put to damage analysis program which employs the elasto-viscoplastic damage constitutive equation based on continuum damage mechanics. Both of tensile fracture analysis and drop impact analysis have almost agreed well with the corresponding experimental results. Uncoupled analysis for dynamic damage mechanics problems can be expected to be used as a computational tool for the evaluation and the design of multi-layer coatings.

Damage Effective Functions Described Based on Combination of Macro and Micro Damage Mechanics

The model of Helmholtz free energy serves as the constitutive functional expression for a damaged material, and was expanded into Taylor's series with respect to some state variables εij and Ω, the generalized expressions of isotropic elastic damage constitutive equations and the damage strain energy release rate with a configuration of isotropic damage scale were derived directly from the second law of thermodynamics. From the aspect of relationship between the porosity and damage variable, the different influence to damage effective functions were discussed theoretically and some valuable conclusions were carried out from the variation of material properties. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome, and the method developed in this article can be applied to study different damage problems. It is shown that the applied method and obtained conclusions are useful to study the damage mechanics problems further.

Exploring the applicability of gradient elasticity to certain micro/nano reliability problems

It has long been assessed that continuum mechanics can be used successfully to address a variety of mechanical problems at both macroscopic and microscopic scales. The term “micromechanics”, in particular, has been used in considering elasticity, plasticity, damage, and fracture mechanics problems at the micron scale involving metallic, ceramic and polymeric materials, as well as their composites. Applications to automobile, aerospace, and concrete industries, as well as to chemical and microelectronic technologies have already been documented. The recent developments in the field of nanotechnology have prompted a substantial literature in nanomechanics. While this term was first introduced by the author in the early 90’s to advance a generalized continuum mechanics framework for applications at the nanoscale, it is mainly used today in considering “hybrid” ab-initio/molecular dynamics/finite element simulations, usually based on elasticity theory, to interpret the mechanical response of nano-objects (nanotubes, nanowires, nanoaggregates) and extract information on nano-configurations (dislocation cores, crack tips, interfaces). The modest goal of this article is to show that continuum elasticity can indeed be extended to describe a variety of problems at the micro/nano regime. The resultant micro/nanoelasticity theory includes long-range or nonlocal material point interactions and surface effects in the form of (phenomenological) higher-order stress/strain gradients. Coupled thermo-diffuso-chemo-mechanical processes can also be considered within such a higher-order theory. Size effects on micro/nano holes and micro/nano cracks can conveniently be modeled, and some standard strength of materials formulas routinely used for micro/nano beams can be improved, with potential applications to MEMS/NEMS devices and micro/nano reliability components.

Boundary-only element solutions of 2D and 3D nonlinear and nonhomogeneous elastic problems

This paper presents a robust boundary element method (BEM) that can be used to solve elastic problems with nonlinearly varying material parameters, such as the functionally graded material (FGM) and damage mechanics problems. The main feature of this method is that no internal cells are required to evaluate domain integrals appearing in the conventional integral equations derived for these problems, and very few internal points are needed to improve the computational accuracy. In addition, one of the basic field quantities used in the boundary integral equations is normalized by the material parameter. As a result, no gradients of the field quantities are involved in the integral equations. Another advantage of using the normalized quantities is that no material parameters are included in the boundary integrals, so that a unified equation form can be established for multi-region problems which have different material parameters. This is very efficient for solving composite structural problems.

3D boundary element analysis of creep continuum damage mechanics problems

In this paper, a boundary element formulation of creep damage problems for three-dimensional problems using isoparametric quadratic elements is presented. The Euler method with automatic time-step control scheme is implemented for time integrations. Creep rupture life is predicted using a continuum damage mechanics approach. The proposed formulation is applied to the FE Benchmark problems, uniaxial, perforated plate and Multi-material cross-weld problems.

Continuum Damage Mechanics Theory and Application-Part I: Theory

A systematic formulation for isotropic and anisotropic elasto-plastic analysis of static and dynamic damage mechanics problems based on the principle of thermodynamics is presented in this article. These formulations are developed by the combination of concepts between the internal energy dissipation and the damage elasto-plasticity energy potential in terms of a set of internal state variables for explanation of microstructural changes in damaged materials. The main studies in this article are related to isotropic and anisotropic elasto-plastic damage mechanics problems, as well as dynamics of damaged materials and structures. The theory of damage mechanics has also been extended to study the behaviour of isotropic and anisotropic damaged materials subjected to dynamic loading.

Continuum Damage Mechanics Theory and Application-Part II: Application

The theoretical formulations of continuum damage mechanics theory developed in Part I have been applied into numerical algorithms of the finite element technique for isotropic and anisotropic elasto-plastic analysis of static and dynamic damage mechanics problems. A statistics method to estimate isotropic and anisotropic damage state in materials has been taken into account of finite element analysis. Numerical examples pertaining to a footing on isotropic and anisotropic damaged ground and a thick walled cylinder subjected to internal pressure have been included to illustrate the applicability of the formulations postulated in this study.

A parameter identification procedure for viscoelastic materials

Abstract A parameter identification procedure is presented for visco-elastic materials. The idea of this method is based on the boundary control concept by using the dual properties of traction and displacement, for example, if we give the traction force on a traction boundary and we observe displacement on a part of the same boundary (the observational or control boundary condition), then we may determine the material properties corresponding to the given and observed data. The numerical procedure is then developed on the basis of Newton’s iteration scheme. The method has been shown to be effective for a linear elastic material Ichikawa and Ohkami, Soils and Foundations , 1992, 32 (2), 35–44 and for damage mechanics problems Tsuchiyama et al., Journal of Geotechnical Engineering, Japan Society of Civil Engineer s, 1993, 475/III -24 , 49–58 (in Japanese). In this paper we give an extension to the visco-elastic problem.

A two-field finite element formulation for elasticity coupled to damage

A two-field variational formulation is proposed for continuum damage mechanics problems. This formulation is applied to the numerical solution, via the finite element method, of initial boundary value problems arising in elasticity coupled to damage; the nodal variables are the displacement and damage fields. Simple examples are presented to demonstrate the advantages and limitations of this formulation.

Elasto-plastic analysis of anisotropic damage mechanics problems : Valliappan, S; Wohua, Z Proc International Symposium on Assessment and Prevention of Failure Phenomena in Rock Engineering, Istanbul, 5–7 April 1993P47–51. Publ Rotterdam: A A Balkema, 1993

Elasto-plastic analysis of anisotropic damage mechanics problems : Valliappan, S; Wohua, Z Proc International Symposium on Assessment and Prevention of Failure Phenomena in Rock Engineering, Istanbul, 5–7 April 1993P47–51. Publ Rotterdam: A A Balkema, 1993

Analysis of random anisotropic damage mechanics problems of rock mass. Part 1 - probabilistic simulation : Wohua, Z; Valliappan S Rock Mech Rock EngngV23, N2, April–June 1990, P91–112

Analysis of random anisotropic damage mechanics problems of rock mass. Part 1 - probabilistic simulation : Wohua, Z; Valliappan S Rock Mech Rock EngngV23, N2, April–June 1990, P91–112

Analysis of random anisotropic damage mechanics problems of rock mass

Probabilistic analysis of random anisotropic damage mechanics problems is proposed in Parts of I and II. In Part I, a probabilistic law of damage variables for rock mass was presented as a Beta distribution by using the Monte-Carlo statistical simulation method. In part II, statistical estimation of a damage state and properties of random damaged rock mass are evaluated by Rosenblueth's point estimate method. Two stability problems involving randomly damaged rock mas have been analyzed using the finite element method

Finite element analysis of anisotropic damage mechanics problems

Elastic constitutive relationships for anisotropic damage mechanics have been developed in this paper. Implementation of these constitutive equations in the finite element analysis is explained. Validation of these relations is provided in the form of comparison of numerical results with the available experimental results. The application of these relationships to an anisotropic damaged foundation problem is discussed.

Analysis of random anisotropic damage mechanics problems of rock mass

A probabilistic analysis method of random anisotropic damage mechanics problems is proposed in parts I and II. In part I, based on the measured characteristics of random crack distribution on the surface of a rock specimen, a probabilistic distribution law of damage variables for rock mass is presented as a Beta distribution by using the Monte-Carlo statistical simulation method. In part II, statistical estimation of a damage state and properties of random damaged rock mass are evaluated by Rosenblueth's point estimate method. Combining with the F. E. method, rock mechanics problem for random damaged state have been analyzed.