Behaviour up to rupture of woven ply laminate structures under static loading conditions

A general model based on continuum damage mechanics (CDM) and a non-local ply scale criterion were developed to describe the failure of carbon woven ply laminated structures. This non-local criterion is based on mean quantities over a fracture characteristic volume (FCV) corresponding to a cylinder with a circular area and a given ply thickness. The nonlinear behaviour and the non-local criterion were implemented in the finite element code ABAQUS. This paper presents new comparisons between the results of experimental data and simulations performed on plates with notches and saw cuts. The results show the efficiency of this approach, even for structures with very high stress gradients. A simplified approach based on the FCV and the Tsai criterion is also presented here and the results obtained with this method are then compared with the experimental data.     

Non-local regularization for FE simulation of damage in ductile materials

The paper presents an application of the non-local regularization to the finite element modelling of ductile damage and tearing. In order to model the damage growth in ductile materials of structural components, integral limiters have been introduced. These integral limiters, which are spatial averaging operators, can prevent the problem of mesh-sensitivity of the finite element computations. Hence, it was important to establish the characteristic length l_c for spatial averaging operators of the non-local regularization. More formally, the in-plane distance l_c and the out-of-plane FE dimension have been specified, characterizing the volume over which averaging of stress and strain was carried out to ensure that the continuum theory can represent the physical process of damage.

In order to check the reliability and transferability of the method, FE simulations of various testing examples have been carried out, namely ductile fracture in notched tensile specimens, ductile crack growth in C(T) specimens and application to the pipe-bending test.     

The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture

We introduce a framework that adapts local and non-local continuum models to simulate static fracture problems. Non-local models based on the peridynamic theory are promising for the simulation of fracture, as they allow discontinuities in the displacement field. However, they remain computationally expensive. As an alternative, we develop an adaptive coupling technique based on the morphing method to restrict the non-local model adaptively during the evolution of the fracture. The rest of the structure is described by local continuum mechanics. We conduct all simulations in three dimensions, using the relevant discretization scheme in each domain, i.e., the discontinuous Galerkin finite element method in the peridynamic domain and the continuous finite element method in the local continuum mechanics domain.     

动态镦粗过程的动力显式有限元分析

为了研究金属的三维动态锤锻成形过程,基于连续介质力学及有限变形理论,建立了一种有限元模型.采用动力分析方法,在运动方程中加入惯性力项考虑锤锻中显著的惯性效应;根据设备的工作原理按照能量守恒定律计算变形期间的锤头速度;同时,将变形视为一个绝热过程计算变形期间试样内部的温度升高.基于建立的模型开发了动力显式有限元分析程序,模拟了铅块试样在落锤打击下的动态镦粗过程,给出了试样内部的位移、等效应变、等效应力和温度分布规律.将变形后试样几何形状、成形载荷-时间曲线和锤头速度-时间曲线的计算结果与实验结果相对比,表明了开发程序计算结果的准确性.     

MESH INDEPENDENT CELL MODELS FOR CONTINUUM DAMAGE THEORY

Abstract— The conventional use of continuum ductile damage mechanics in finite element analyses identifies the "cell" in which damage occurs with the finite elements in which the distribution of stress and strain is modelled. Since the cell size is a fixed, metallurgically-defined, property of the material being analysed, this methodology forces a minimum size for the finite element mesh. Mesh refinement is thereby disallowed. This paper presents one way of avoiding the problem by developing a mesh-independent cell model which, with a fixed cell size, allows the finite element mesh to be refined to any degree within the cells. Procedures which average some state variables within the cells are introduced to prevent the localisation of damage after a certain critical stage is reached. The method has been tested in numerical simulations of (a) the deformation of a notched tensile bar, (b) a 35 mm compact tension specimen and (c) the first of the AEA spinning cylinder tests. There is a reasonable agreement between the results of the computer simulations and those of the experiments.     

Non-local yield limit degradation

Presented is a new type of a non-local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit. The key idea, which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation, is to apply the non-local concept only to those parameters which cause the degradation while keeping the definition of the strains local. Compared to the previously advanced fully non-local continuum formulation, the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions. The new formulation exhibits no zero-energy periodic modes, imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient. Two-dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy. The formulation is applied to tunnel excavation in a soil stabilized by cement grouting, with the objective of preventing cave-in (burst) of the tunnel sides due to compression softening.     

A numerical study on the impact resistance of composite shells using an energy based failure model

This paper presents a numerical study on the impact resistance of composite shells laminates using an energy based failure model. The damage model formulation is based on a methodology that combines stress based, continuum damage mechanics (CDM) and fracture mechanics approaches within a unified procedure by using a smeared cracking formulation. The damage model has been implemented as a user-defined material model in ABAQUS FE code within shell elements. Experimental results obtained from previous works were used to validate the damage model. Finite element models were developed in order to investigate the pressure and curvature effects on the impact response of laminated composite shells.     

Continuum damage mechanics approach to composite laminated shallow cylindrical/conical panels under static loading

Static response characteristics and failure load of laminated composite shallow cylindrical and conical panels subjected to internal/external lateral pressure are investigated using continuum damage mechanics approach considering geometric nonlinearity and damage evolution. The damage model is based on a generalized macroscopic continuum theory within the framework of irreversible thermodynamics and enables to predict the progressive damage and failure load. Damage variables are introduced for the phenomenological treatment of the state of defects and its implications on the degradation of the stiffness properties. The analysis is carried out using finite element method based on the first order shear deformation theory. The nonlinear governing equations are solved using Newton–Raphson iterative technique coupled with the adaptive displacement control method to efficiently trace the equilibrium path. The detailed parametric study is carried out to investigate the influences of geometric nonlinearity, evolving damage, span-to-thickness ratio, lamination scheme and semi-cone angle on the static response and failure load of laminated cylindrical/conical panels. It is revealed that the membrane forces due to geometric nonlinearity significantly influence the damage distribution and failure load.     

On the numerical prediction of the ductile fracture in metal forming

In this paper, fully coupled constitutive equations accounting for combined isotropic and kinematic hardening as well as the isotropic ductile damage are implemented into the general purpose finite element code for metal forming simulation. The associated numerical aspects concerning both the local integration of the coupled constitutive equations as well as the global (equilibrium) integration schemes are presented. Various 2D and 3D examples are given in order to show the capability of the proposed numerical methodology to predict the ductile fracture initiation and growth during metal forming processes.     

Computational modelling of static indentation-induced damage in glass

The present paper is focused on the numerical simulation of a glass plate subjected to static indentation by a spherical indenter. For this purpose, a combined approach of continuum damage mechanics (CDM) and fracture mechanics is performed. Results provided by an axisymmetric finite element model were compared with analytical solutions. A CDM based constitutive model with an anisotropic damage tensor was selected and implemented into a finite element code to study the damage of glass. The numerical results were analysed through the framework of the stress and damage distribution. Various regions with critical damage values were therefore predicted in good agreement with the experimental observations in the literature. In these regions, the directions of crack propagation, including both cracks initiating on the surface as well as in the bulk, were predicted using the strain energy density factor. Predicted directions were found in good agreement with those experimentally obtained in the literature results.     

3-D shape optimal design and automatic finite element regridding

A unified method for continuum shape design sensitivity analysis and optimal design of mechanical components is developed. A domain method of shape design sensitivity analysis that uses the material derivative concept of continuum mechanics is employed. For numerical implementation of shape optimal design, parameterization of the boundary shape of mechanical components is defined and illustrated using a Bezier surface. In shape design problems, nodal points of the finite element model move as the shape changes. A method of automatic regridding to account for shape change has been developed using a design velocity field in the physical domain that obeys the governing equilibrium equations of the elastic solid. For numerical implementation of the continuum shape design sensitivity analysis and automatic regridding, an established finite element analysis code is used. To demonstrate the feasibility of the method developed, shape design optimization of a main engine bearing cap is carried out as an example.     

Numerical aspects of non-local modeling of the damage evolution in elastic–plastic materials

The design of mechanical systems in modern industrial plants requires reliable and efficient methods to predict the behavior of structural materials. For complex loading conditions, the behavior of the structural materials is determined by damage evolution, strain rate and temperature. The subject of the article is the modeling of the damage evolution in elastic–plastic materials of structural components, which are utilized at various temperatures. To achieve this goal, a hybrid model of steel cracking is applied. The hybrid model uses a finite element simulation combined with an experimental test realized in the macroscale. By using the hybrid model, the modeling of the damage evolution affords possibilities of determining macroscopic effects of the steel micro-defects. An essence of solving the predicting behavior of structural materials with micro-defects consists in time integration procedures for constitutive equations. In the article a semi-implicit time integration procedure is presented. The semi-implicit time integration procedure is suitable for the inelastic materials (compressible or incompressible) with the combined kinematic–isotropic hardening behavior. Its numerical solutions are stable, namely without the oscillatory behavior. By spatial averaging over a representative volume (RV), the homogenization technique (HT) is used for the defining of non-local variables in the constitutive equations. Evolutionary algorithms (EAs) based on local selections are applied to perform the homogenization technique. Within the framework of the large strain theory, the non-local continuum satisfies the objectivity requirements. Limitations on applicability of the -integral approach to construct crack growth resistance curves are also presented.     

The small length scale effect for a non-local cantilever beam: a paradox solved

Non-local continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with microstructures or nanostructures. This paper presents some simplified non-local elastic beam models, for the bending analyses of small scale rods. Integral-type or gradient non-local models abandon the classical assumption of locality, and admit that stress depends not only on the strain value at that point but also on the strain values of all points on the body. There is a paradox still unresolved at this stage: some bending solutions of integral-based non-local elastic beams have been found to be identical to the classical (local) solution, i.e.?the small scale effect is not present at all. One example is the Euler-Bernoulli cantilever nanobeam model with a point load which has application in microelectromechanical systems and nanoelectromechanical systems as an actuator. In this paper, it will be shown that this paradox may be overcome with a gradient elastic model as well as an integral non-local elastic model that is based on combining the local and the non-local curvatures in the constitutive elastic relation. The latter model comprises the classical gradient model and Eringen's integral model, and its application produces small length scale terms in the non-local elastic cantilever beam solution.     

A finite element analysis of damage propagation during metal forming process

In this paper damage propagation during metal forming process is investigated with the concept of continuum damage mechanics. An isotropic damage model based on the theory of materials of type N is adopted to describe the damage process of a ductile material with large elasto-viscoplastic deformation. To solve the finite elasto-viscoplasticity problem, a reasonable kinematic strain measure for largely deformed solids is used and the damage constitutive equations based on thermodynamical framework are developed. The stiffness degradation of the loaded material is chosen as a damage measure. An extended interior penalty method is used to impose the contact condition on the boundary. The highly nonlinear equilibrium equations are reduced to the incremental weak form and approximated by the total Lagrangian finite element method. The displacement control method along with the modified Riks' continuation technique based on displacement parameter is used to solve the incremental iterative equations. As numerical examples, upsetting, backward extrusion and punch problems are simulated and the results of damage propagation and J₂ stress contours with and without damage are presented. For punch problems, spring back and residual stresses are also presented.     

A computational continuum damage mechanics model for predicting transverse cracking and splitting evolution in open hole cross‐ply composite laminates

The present study focuses on a computational constitutive model which predicts the matrix cracking evolution and fibre breakage in cross‐ply composite laminates with open hole under in‐plane loading. To consider the effects of matrix cracking on the nonlinear response of laminates, a simplified crack density based model is applied which evaluates the representative damage parameters of matrix cracking. Furthermore, a developed subroutine based on continuum damage mechanics concepts is applied in ANSYS code which is capable to consider the transverse cracking/splitting evolution and predict the final failure load of mentioned laminate under monotonic loading in a progressive damage analyses. It is shown that the obtained stress–strain behaviours and the damage evaluation of considered laminates are in good agreement with the available experimental results.     

Real-time inference of stochastic damage in composite materials

This study describes a control system designed for real-time monitoring of damage in materials that employs methods and models that account for uncertainties in experimental data and parameters in continuum damage mechanics models. The methodology involves (1) developing an experimental set-up for direct and indirect measurements of damage in materials; (2) modeling damage mechanics based constitutive equations for continuum models; and (3) implementation of a Bayesian framework for statistical calibration of model with quantification of uncertainties. To provide information for real-time monitoring of damage, indirect measurement of damage is made feasible using an embedded carbon nanotube (CNT) network to perform as sensor for detecting the local damage. A software infrastructure is developed and implemented in order to integrate the various constituents, such as finite element approximation of the continuum damage models, generated experimental data, and Bayesian-based methods for model calibration and validation. The outcomes of the statistical calibration and dynamic validation of damage models are presented. The experimental program designed to provide observational data is discussed.     

Optimisation of process parameters in flanging operation in order to minimise stresses and Lemaitre’s damage

The objective of this work is modelling and optimisation of sheet bending process by means of numerical simulation. One of the problems to be solved in the sheet metal forming processes of thin sheets is the taking into account of the effects of technological process parameters so that the part takes the desired mechanical characteristics. Accordingly, it has been a crucial research subject for designing bending tools guaranteeing an optimal performance of products in terms of mechanical properties and good rigidity. In this paper, we propose a numerical procedure allowing the definition of the optimal values of process parameters in flanging operation, which minimises the residual stresses and the material damage at the end of the bending phase. The concept of continuum damage mechanics fully coupled with elasto-plasticity has been retained to describe the progressive damage accumulation into the sheet metal. According to parametric investigation on the maximum stress and calculated damage values, it has been found that the punch-die clearance and the die radius have significant effects on mechanical behaviour of parts. An application of design of experiments was developed as a preliminary step for the optimisation of the process parameters by using response surface methodology. This model allows the identification of the influential parameters of an optimisation problem and the reduction of the number of evaluations of the objective function.     

Simulation of progressive damage development in braided composite tubes under axial compression

A continuum damage mechanics based model for composite materials (CODAM), which has been implemented as a user material model in an explicit finite element code (LS-DYNA), is used to capture the complete tensile and compressive response of a braided composite material. Model parameters are related to experimentally observed behaviour to ensure a physical basis to the model and a crack band scaling approach is used to minimize mesh sensitivity (or lack of objectivity) of the numerical results. The predictive capability of the model is validated against the results from dynamic tube crush experiments. The damage propagation, failure morphology and energy absorption predictions correlate well with the experimental results.     

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

In general, non‐linear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two non‐linear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, whereas the second one is a non‐linear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex non‐linear problems, a computation technique based on automatic differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher‐order derivatives of these constitutive laws and thereafter to define the Taylor series that are the basis of the continuation technique called asymptotic numerical method. The algorithm is about the same with an explicit or implicit constitutive relation. In the modelling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code: the user is only required to define the tool geometry and the computer is able to obtain the higher‐order derivatives. Copyright © 2013 John Wiley & Sons, Ltd.     

Improvement of Progressive Damage Model to Predicting Crashworthy Composite Corrugated Plate

To predict the crashworthy composite corrugated plate, different single and stacked shell models are evaluated and compared, and a stacked shell progressive damage model combined with continuum damage mechanics is proposed and investigated. To simulate and predict the failure behavior, both of the intra- and inter- laminar failure behavior are considered. The tiebreak contact method, 1D spot weld element and cohesive element are adopted in stacked shell model, and a surface-based cohesive behavior is used to capture delamination in the proposed model. The impact load and failure behavior of purposed and conventional progressive damage models are demonstrated. Results show that the single shell could simulate the impact load curve without the delamination simulation ability. The general stacked shell model could simulate the interlaminar failure behavior. The improved stacked shell model with continuum damage mechanics and cohesive element not only agree well with the impact load, but also capture the fiber, matrix debonding, and interlaminar failure of composite structure.