A stabilized finite element formulation for monolithic thermo‐hydro‐mechanical simulations at finite strain

An adaptively stabilized monolithic finite element model is proposed to simulate the fully coupled thermo‐hydro‐mechanical behavior of porous media undergoing large deformation. We first formulate a finite‐deformation thermo‐hydro‐mechanics field theory for non‐isothermal porous media. Projection‐based stabilization procedure is derived to eliminate spurious pore pressure and temperature modes due to the lack of the two‐fold inf‐sup condition of the equal‐order finite element. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for non‐isothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this thermo‐hydro‐mechanical model. Copyright © 2015 John Wiley & Sons, Ltd.     

A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks

A coupled thermo-mechanical bond-based peridynamical (TM-BB-PD) method is developed to simulate thermal cracking processes in rocks. The coupled thermo-mechanical model consists of two parts. In the first part, temperature distribution of the system is modeled based on the heat conduction equation. In the second part, the mechanical deformation caused by temperature change is calculated to investigate thermal fracture problems. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. Two benchmark examples, i.e., steady-state heat conduction and transient heat conduction with deformation problem, are performed to illustrate the correctness and accuracy of the proposed coupled numerical method in dealing with thermo-mechanical problems. Moreover, two kinds of numerical convergence for peridynamics, i.e., m- and \(\delta \)-convergences, are tested. The thermal cracking behaviors in rocks are also investigated using the proposed coupled numerical method. The present numerical results are in good agreement with the previous numerical and experimental data. Effects of PD material point distributions and nonlocal ratios on thermal cracking patterns are also studied. It can be found from the numerical results that thermal crack growth paths do not increases with changes of PD material point spacing when the nonlocal ratio is larger than 4. The present numerical results also indicate that thermal crack growth paths are slightly affected by the arrangements of PD material points. Moreover, influences of thermal expansion coefficients and inhomogeneous properties on thermal cracking patterns are investigated, and the corresponding thermal fracture mechanism is analyzed in simulations. Finally, a LdB granite specimen with a borehole in the heated experiment is taken as an application example to examine applicability and usefulness of the proposed numerical method. Numerical results are in good agreement with the previous experimental and numerical results. Meanwhile, it can be found from the numerical results that the coupled TM-BB-PD has the capacity to capture phenomena of temperature jumps across cracks, which cannot be captured in the previous numerical simulations.     

Analysis of the plastic zone near the crack tips under the uniaxial tension using ordinary state‐based peridynamics

In this paper, the plastic model of ordinary state‐based peridynamics is established. The size and shape of plastic zone around crack tips with the different inclination angles are simulated using ordinary state‐based peridynamics. Comparison of the size and shape of plastic zone around the crack tips obtained from peridynamic solution and analytic solution is made. It is found that the relative errors between the analytical and peridynamic solution are very little. Therefore, it is feasible to predict the plastic zone around crack tips using ordinary state‐based peridynamics.     

Modelling of reinforced polymer composites subject to thermo‐mechanical loading

A coupled finite element model is developed to analyse the thermo‐mechanical behaviour of a widely used polymer composite panel subject to high temperatures at service conditions. Thermo‐chemical and thermo‐mechanical models of previous researchers have been extended to study the thermo‐chemical decomposition, internal heat and mass transfer, deformation and the stress state of the material. The phenomena of heat and mass transfer and thermo‐mechanical deformation are simulated using three sets of governing equations, i.e. energy, gas mass diffusion and deformation equations. These equations are then assembled into a coupled matrix equation using the Bubnov–Galerkin finite element formulation and then solved simultaneously at each time interval. An experimentally tested 1.09 cm thick glass‐fibre woven‐roving/polyester resin composite panel is analysed using the numerical model. Results are presented in the form of temperature, pore pressure, deformation, strain and stress profiles and discussed. The maximum normal stress failure criterion is used in order to establish the load‐bearing capability of the composite panel. Significant pore gas pressure build‐ups (to 0.8 MPa and higher) have been perceived at high thermo‐chemical decomposition rates where the material experiences a complex expansion/contraction phenomenon. It is found that the composite panel experiences structural instability at elevated temperatures up to 300°C but retains its integrity even under moderate external loading. Copyright © 2005 John Wiley & Sons, Ltd.     

Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heat

This paper focuses on the non‐linear responses in thin cylindrical structures subjected to combined mechanical and thermal loads. The coupling effects of mechanical deformation and temperature in the material are considered through the development of a thermo‐elasto‐viscoplastic constitutive model at finite strain. A meshfree Galerkin approach is used to discretize the weak forms of the energy and momentum equations. Due to the different time scales involved in thermal conduction and failure development, an explicit–implicit time integration scheme is developed to link the time scale differences between the two key mechanisms. We apply the developed approach to the analysis of the failure of cylindrical shell subjected to both heat sources and internal pressure. The numerical results show four different failure modes: dynamic fragmentation, single crack with branch, thermally induced cracks and cracks due to the combined effects of pressure and temperature. These results illustrate the important roles of thermal and mechanical loads with different time scales. Copyright © 2008 John Wiley & Sons, Ltd.     

A computational model for the finite element analysis of thermoplasticity coupled with ductile damage at finite strains

An updated Lagrangian implicit FEM model for the analysis of large thermo‐mechanically coupled hyperelastic‐viscoplastic deformations of isotropic porous materials is considered. An appropriate framework for constitutive modelling is introduced that includes a stress‐free thermally expanded configuration and a plastically deformed unstressed damaged configuration. A two‐level iterative scheme is employed at each time increment to solve the field equations governing the conservation of momentum (mechanical step) and the conservation of energy (thermal step) for the coupled thermo‐mechanical problem. Exact linearizations for the calculation of the tangent stiffness are performed in each of these solution steps. A fully implicit, thermo‐mechanically coupled and incrementally objective Euler‐backward radial return based map is developed for the time integration of the constitutive equations. The present model is used to analyse a number of benchmark examples including metal forming processes wherein temperature and the accumulated damage play an important role in influencing the deformation mechanism and the nature of the deformed workpiece. Copyright © 1999 John Wiley & Sons, Ltd.     

Viscoplasticity using peridynamics

Peridynamics is a continuum reformulation of the standard theory of solid mechanics. Unlike the partial differential equations of the standard theory, the basic equations of peridynamics are applicable even when cracks and other singularities appear in the deformation field. The assumptions in the original peridynamic theory resulted in severe restrictions on the types of material response that could be modeled, including a limitation on the Poisson ratio. Recent theoretical developments have shown promise for overcoming these limitations, but have not previously incorporated rate dependence and have not been demonstrated in realistic applications. In this paper, a new method for implementing a rate‐dependent plastic material within a peridynamic numerical model is proposed and demonstrated. The resulting material model implementation is fitted to rate‐dependent test data on 6061‐T6 aluminum alloy. It is shown that with this material model, the peridynamic method accurately reproduces the experimental results for Taylor impact tests over a wide range of impact velocities. The resulting model retains the advantages of the peridynamic formulation regarding discontinuities while allowing greater generality in material response than was previously possible. Copyright © 2009 John Wiley & Sons, Ltd.     

基于改进型近场动力学方法的多裂纹扩展分析

在非局部键型近场动力学理论基础上,提出了能够反映混凝土、岩石类材料力学特性和非局部长程力尺寸效应的改进型近场动力学微极模型,弥补常规微观弹脆性（Prototype Microelastic Brittle,PMB）键型近场动力学本构模型的应用范围限制和定量计算误差大等缺陷,并构建了相应的适合于模拟脆性多裂纹扩展问题的近场动力学算法体系。通过对不同核函数修正项对应的近场动力学定量计算结果进行比较,验证了改进型近场动力学模型和数值算法的计算精度并确定了精度最高的核函数修正项;模拟双裂纹脆性板受压和随机多裂纹脆性板受拉的裂纹扩展全过程并与已有结果对比,进一步验证了模型和算法在模拟多裂纹扩展问题时的可靠性。分析了含多裂纹三点弯梁的起裂和裂纹失稳扩展过程,并研究了裂纹初始倾角、初始长度等因素对构件破坏形式和破坏荷载的影响规律。     

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

The most common technique for the numerical implementation of peridynamic theory is the uniform discretization together with constant horizon. However, unlike the nonuniform discretization and varying horizons, it is not a natural and intrinsic component of the adaptive refinement analysis and multiscale modeling. Besides, it encounters discretization difficulty in analyzing irregular structures. Therefore, to analyze problems with nonuniform discretization and varying horizons and solve the resulting problems of ghost forces and spurious wave reflection, the dual‐horizon peridynamics based on uniform discretization is extended to the nonuniform discretization based on Voronoi diagrams, for which we call it Voronoi‐based peridynamics. We redefine the damage definition as well. Next, an adaptive refinement analysis method based on the proposed Voronoi‐based peridynamics and its numerical implementation is introduced. Finally, the traditional bond‐based peridynamics and the Voronoi‐based peridynamics with or without refinement are used to simulate 4 benchmark problems. The examples of 2‐D quasi‐static elastic deformation, 2‐D wave propagation, 2‐D dynamic crack growth, and 3‐D simulation of the Kalthoff‐Winkler experiment demonstrate the efficiency and effectivity of the proposed Voronoi‐based peridynamics. Further, the adaptive refinement analysis can be used to obtain reasonable crack path and crack propagation speed with reduced computational burden.     

Numerical aspects of finite element simulations of residual stresses in metal matrix composites

When a metal matrix composite (MMC) is cooled down from the fabrication or annealing temperature to room temperature, residual stresses are induced in the composite due to the mismatch of the thermal expansion coefficients of the matrix and reinforcement. A thermomechanical model describing these processes is presented considering that the reinforcement component has a thermo‐elastic behaviour and that the matrix material exhibits a thermo‐elastoviscoplastic behaviour. The model is implemented with a semi‐implicit forward gradient finite element method algorithm and the resulting code is used to perform numerical simulations and calculate thermally induced residual stress fields in MMCs. Several tests are performed on a continuously reinforced MMC and a short cylindrical particle MMC in order to optimize the algorithm and define its governing parameters. Good agreement was obtained with results from other authors. Copyright © 2001 John Wiley & Sons, Ltd.     

Two‐scale diffusion–deformation coupling model for material deterioration involving micro‐crack propagation

In this paper, we introduce a two‐scale diffusion–deformation coupled model that represents the aging material deterioration of two‐phase materials involving micro‐crack propagations. The mathematical homogenization method is applied to relate the micro‐ and macroscopic field variables, and a weak coupling solution method is employed to solve the two‐way coupling phenomena between the diffusion of scalar fields and the deformation of quasi‐brittle solids. The macroscopic mechanical behavior represented by the derived two‐scale two‐way coupled model reveals material nonlinearity due to micro‐scale cracking induced by the scalar‐field‐induced deformation, which can be simulated by the finite cover method. After verifying the fundamental validity of the proposed model and the analysis method, we perform a simple numerical example to demonstrate their ability to predict aging material deterioration. Copyright © 2010 John Wiley & Sons, Ltd.     

Studies on the potential risk of liquid metal assisted cracking (LMAC) in normal‐temperature and high‐temperature hot‐dip galvanizing of high strength bolts of dimensions greater M24

Liquid metal assisted cracking (LMAC) mainly occurs due to an unfavorable interaction of three factors: a susceptible material condition, presence of a liquid metal and sufficient tensile stress. Hot‐dip galvanizing of high‐strength bolts induces high thermal loads in bolts made of tempered steel in the presence of a zinc melt and thus, provides the boundary conditions for the above mentioned critical factors to interact. The focus of this study is on investigating thermally‐induced stresses in large diameter bolts and their impact on the formation of liquid metal assisted cracking (LMAC). In order to calculate the thermal loads in hot‐dip galvanizing, simulations were carried out regarding the thermo‐mechanical behavior of bolts during the hot‐dip galvanizing process. The simulations illustrate that cracks are most likely to occur in the first thread turn. This prediction is confirmed by experimental observations.     

基于非局部微分算子的近场动力学及固体材料应力数值模拟

在经典近场动力学模型的基础上引入非局部微分算子求解理论,建立近场动力学微弹性应力分析模型。在近场动力学模型物质点处进行泰勒级数展开,利用正交非局部函数构建微分算子的数值积分方程并且根据矩阵正交性求解函数未知系数,最终由平衡方程等价性建立近场动力学应力求解模型。采用所提出的方法对固体材料变形破坏过程中的应力进行模拟,并将计算结果与理论解对比以验证方法有效性,同时对粒子离散间距、泰勒项数及权函数的数值收敛性进行分析。结果表明:该文提出的方法可以较准确的反映完整及非完整固体脆性材料在荷载作用下的应力分布,并且离散间距及权函数对数值收敛结果具有显著影响,可为使用近场动力学方法模拟变形破坏时提供新的应力分析思路,有着较为广泛的应用前景。     

Dual‐horizon peridynamics

In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH‐PD. All three peridynamic formulations, namely, bond‐based, ordinary state‐based, and non‐ordinary state‐based peridynamics, can be implemented within the DH‐PD framework. Our DH‐PD formulation allows for h‐adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two‐dimensional and three‐dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Thermal fatigue failure induced by delamination in thermal barrier coating

The paper presents the experimental and theoretical investigation on the thermal fatigue failure induced by delamination in thermal barrier coating system. Laser heating method was used to simulate the operating state of TBC (thermal barrier coating) system. The non-destructive evaluation such as acoustic emission (AE) detect was used to study the evolution of TBC system damage. Micro-observation and AE detect both revealed that fatigue crack was in two forms: surface crack and interface delamination. It was found that interface delamination took place in the period of cooling or heating. Heating or cooling rate and temperature gradient had an important effect on interface delamination cracking propagation. A theoretical model on interface delamination cracking in TBC system at operating state is proposed. In the model, a membrane stress P and a bending moment M are designated the thermal loads of the thermal stress and temperature gradient in TBC system. In this case, the coupled effect of plastic deformation, creep of ceramic coating as well as thermal growth oxidation (TGO) and temperature gradient in TBC system was considered in the model. The thermal stress intensity factors (TSIFs) in non-FGM (functional gradient material) thermal barrier coating system is analytical obtained. The numerical results of TSIFs reveal some same results as obtained in experimental test. The model is based on fracture mechanics theory about heterogeneous materials and it gives a rigorous explanation of delaminations in TBC system loaded by thermal fatigue. Both theoretical analysis and experimental observation reveal an important fact: delaminations are fatigue cracks which grow during thermal shocks due to compressive stresses in the loading, this loads the delaminations cracks in mixed I and II mode.     

Multi‐scale modeling of surface effects in nano‐materials with temperature‐related Cauchy‐Born hypothesis via the modified boundary Cauchy‐Born model

In nano‐structures, the influence of surface effects on the properties of material is highly important because the ratio of surface to volume at the nano‐scale level is much higher than that of the macro‐scale level. In this paper, a novel temperature‐dependent multi‐scale model is presented based on the modified boundary Cauchy‐Born (MBCB) technique to model the surface, edge, and corner effects in nano‐scale materials. The Lagrangian finite element formulation is incorporated into the heat transfer analysis to develop the thermo‐mechanical finite element model. The temperature‐related Cauchy‐Born hypothesis is implemented by using the Helmholtz free energy to evaluate the temperature effect in the atomistic level. The thermo‐mechanical multi‐scale model is applied to determine the temperature related characteristics at the nano‐scale level. The first and second derivatives of free energy density are computed using the first Piola‐Kirchhoff stress and tangential stiffness tensor at the macro‐scale level. The concept of MBCB is introduced to capture the surface, edge, and corner effects. The salient point of MBCB model is the definition of radial quadrature used at the surface, edge, and corner elements as an indicator of material behavior. The characteristics of quadrature are derived by interpolating the data from the atomic level laid in a circular support around the quadrature in a least‐square approach. Finally, numerical examples are modeled using the proposed computational algorithm, and the results are compared with the fully atomistic model to illustrate the performance of MBCB multi‐scale model in the thermo‐mechanical analysis of metallic nano‐scale devices. Copyright © 2013 John Wiley & Sons, Ltd.     

A peridynamic Reissner-Mindlin shell theory

In this work, we have developed a state-based peridynamics theory for nonlinear Reissener-Mindlin shells to model and predict large deformation of shell structures with thick wall. The nonlocal peridynamic theory of solids offers an integral formulation that is an alternative to traditional local continuum mechanics models based on partial differential equations. This formulation is applicable for solving the material failure problems involved in discontinuous displacement fields. The governing equations of the state-based peridynamic shell theory are derived based on the nonlocal balance laws by adopting the kinematic assumption of the Reissner and Mindlin plate and shell theories. In the numerical calculations, the stress points are employed to ensure the numerical stability. Several numerical examples are conducted to validate the nonlocal structure mechanics model and to verify the accuracy as well as the convergence of the proposed shell theory.     

Variational approach to the analysis of steady‐state thermo‐elastic wear regimes

A transient wear process on frictional interface of two thermo‐elastic bodies in a relative steady sliding motion induces shape evolution of contact interface and tends to a steady state for which the wear process occurs at fixed contact stress and strain distribution. The temperature field generated by frictional and wear dissipation on the contact surface is assumed to reach a steady state. This state is assumed to correspond to minimum of the wear dissipation power and the temperature field corresponds to maximum of the heat entropy production. The stationarity conditions of the response functionals provide the contact pressure distribution and the corresponding temperature field. The present approach extends the authors previous analyses of optimal or steady‐state contact shapes by accounting for coupled wear and thermal distortion effects. The wear rule is assumed as a non‐linear relation of wear rate to shear stress and relative sliding velocity. The analysis of disk and drum brakes is presented with account for thermal distortion effect. It is shown that the contact shape in a steady thermo‐elastic state essentially differs from that specified for mechanical loading with neglect of thermal effects. The thermal instability regimes are not considered in the paper. Copyright © 2009 John Wiley & Sons, Ltd.     

Multiscale analysis method for thermo‐mechanical performance of periodic porous materials with interior surface radiation

This study develops a novel multiscale analysis method to predict thermo‐mechanical performance of periodic porous materials with interior surface radiation. In these materials, thermal radiation effect at microscale has an important impact on the macroscopic temperature and stress field, which is our particular interest in this paper. Firstly, the multiscale asymptotic expansions for computing the dynamic thermo‐mechanical coupling problem, which considers the mutual interaction between temperature and displacement field, are given successively. Then, the corresponding numerical algorithm based on the finite element‐difference method is brought forward in details. Finally, some numerical results are presented to verify the validity and relevancy of the proposed method by comparing it with a direct finite element analysis with detailed numerical models. The comparison shows that the new method is effective and valid for predicting the thermo‐mechanical performance and can capture the microstructure behavior of periodic porous materials exactly.s Copyright © 2015 John Wiley & Sons, Ltd.