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.     

Mixed finite element method for coupled thermo‐hydro‐mechanical process in poro‐elasto‐plastic media at large strains

A mixed finite element for coupled thermo‐hydro‐mechanical (THM) analysis in unsaturated porous media is proposed. Displacements, strains, the net stresses for the solid phase; pressures, pressure gradients, Darcy velocities for pore water and pore air phases; temperature, temperature gradients, the total heat flux are interpolated as independent variables. The weak form of the governing equations of coupled THM problems in porous media within the element is given on the basis of the Hu–Washizu three‐filed variational principle. The proposed mixed finite element formulation is derived. The non‐linear version of the element formulation is further derived with particular consideration of the THM constitutive model for unsaturated porous media based on the CAP model. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elasto‐plastic tangent modulus matrix and the element tangent stiffness matrix are developed. For geometrical non‐linearity, the co‐rotational formulation approach is utilized. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization and the softening behaviours caused by thermal and chemical effects. Copyright © 2005 John Wiley & Sons, Ltd.     

Sensitivity analysis and shape optimization for preform design in thermo‐mechanical coupled analysis

In complex forging processes, it is essential to find the optimal deformation path and the optimal preform shape that will lead to the desired final shape and service properties. A sensitivity analysis and optimization for preform billet shape in thermo‐mechanical coupled simulation is developed in this work. Non‐linear sensitivity analysis of temperatures, flow‐stresses, strains and strain‐rates are presented with respect to design variables. Both analytical and finite‐difference gradients are employed to validate the effectiveness of sensitivity analysis developed in this work. Numerous iterations of coupled thermo‐mechanical analysis are performed to determine an optimum preform shape based on a given criterion of minimizing the objective function on effective strain variance within the final forging. The design constraints are imposed on die underfill, material scrap, folding defects and temperatures. In addition, a method for material data processing is given in order to determine the flow stress and its derivatives. The shape optimization scheme is demonstrated with the preform designs of an axisymmetric disk and a plane strain problem. Copyright © 1999 John Wiley & Sons, Ltd.     

Finite element formulation for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems

A finite element algorithm has been developed for the efficient analysis of smart composite structures with piezoelectric polymer sensors or/and actuators based on piezoelectro‐hygro‐thermo‐viscoelasticity. Variational principles for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems have also been proposed in this study. As illustrative studies, dynamic responses in laminated composite beams and plates with PVDF sensors and actuators are obtained as functions of time using the present finite element procedures. The voltage feedback control scheme is utilized. The proposed numerical method can be used for analysing problems in the design of smart structures as well as smart sensors and actuators. Copyright © 1999 John Wiley & Sons, Ltd.     

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

This paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows:

• A unified treatment for the analysis and implicit time integration of thermo‐elasto‐viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework.
• An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated.
• An operator split‐based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo‐elasto‐viscoplastic problem.
• The possibility to couple any hardening law, including rate‐dependent models, with any damage model that fits into the present framework.

All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact and metal‐forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS‐MN ²L, University of Liège, Belgium) named Metafor.Copyright © 2013 John Wiley & Sons, Ltd.     

A continuum sensitivity method for finite thermo‐inelastic deformations with applications to the design of hot forming processes

A computational framework is presented to evaluate the shape as well as non‐shape (parameter) sensitivity of finite thermo‐inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for the large thermo‐mechanical deformation of hyperelastic thermo‐viscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are defined in a rigorous sense and the sensitivity analysis is performed in an infinite‐dimensional continuum framework. The effects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity fields. The direct deformation and sensitivity deformation problems are solved using the finite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by finite difference approximations (i.e. using the solution of a deformation problem with perturbed design variables). The effectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes. Copyright © 2002 John Wiley & Sons, Ltd.     

Time and temperature dependent mechanical characterization of polymer‐based materials in electronic packaging applications

Abstract

The thermo‐mechanical testing of high performance polyimide films Type HPPST supplied by Dupont^® was conducted at different strain rates and in different temperature environments. The stress‐strain behavior of materials was investigated, and the dependence of Young's modulus on temperature and strain rate is reported. In view of the uncertainty of the Young's modulus determination, the specimens were tested with unloading‐reloading to verify the test results. Constant strain rate uniaxial tensile tests and long‐time creep tests at various temperatures were performed to characterize the time‐temperature‐dependent mechanical property precisely. Cyclic loading tests were also implemented on specimens to investigate cyclic stress‐strain behaviors. This research is expected to enhance finite‐element‐modeling accuracy and characterize material properties precisely.     

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.     

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.     

Local Measurement of Stress–Strain Behaviour of Ductile Materials at Elevated Temperatures in a Split‐Hopkinson Tension Bar System

A split‐Hopkinson tension bar system is modified to allow for measuring the stress–strain behaviour of ductile materials at large strains, high strain rates and elevated temperatures. The specimen is heated by induction, and a pyrometer provides a laser‐based temperature measurement that controls the testing temperature in a feed‐back loop. A high‐speed digital camera system and an edge detection algorithm are used to obtain local measures of strain after necking of the axisymmetric specimens. Using the local strain measurements and Bridgman's analytical formulas, it is feasible to find the equivalent stress–strain curve to fracture for different levels of strain rate and temperature. Thermal and thermo‐mechanical finite element simulations of the test set‐up are used to evaluate the validity of the proposed experimental method.     

Thermo‐hydro‐mechanical modeling of fluid geological storage by Godunov‐mixed methods

The efficient solution to the coupled system of PDEs governing the mass and the energy balance in deformable porous media requires advanced numerical algorithms. A combination of mixed/Galerkin finite elements and finite volumes along with a staggered method are employed. Fluid flow and heat transfer are addressed iteratively by a fully coupled approach and the medium deformation by an explicitly coupled scheme, at each time step. Such formulation allows for stable numerical solutions, element‐wise conservative velocity fields and accurate prediction of sharp temperature convective fronts. The proposed model is experimented with in realistic applications of a deep aquifer fluid injection. Copyright © 2012 John Wiley & Sons, Ltd.     

Consistent coupling of beam and shell models for thermo‐elastic analysis

In this paper, the finite element formulation of a transition element for consistent coupling between shell and beam finite element models of thin‐walled beam‐like structures in thermo‐elastic problems is presented. Thin‐walled beam‐like structures modelled only with beam elements cannot be used to study local stress concentrations or to provide local mechanical or thermal boundary conditions. For this purpose, the structure has to be modelled using shell elements. However, computations using shell elements are a lot more expensive as compared to beam elements. The finite element model can be more efficient when the shell elements are used only in regions where the local effects are to be studied or local boundary conditions have to be provided. The remaining part of the structure can be modelled with beam elements. To couple these two models (i.e. shell and beam models) at transitional cross‐sections, transition elements are derived here for thermo‐elastic problems. The formulation encloses large displacement and rotational behaviour, which is important in case of thin‐walled beam‐like structures. Copyright © 2004 John Wiley & Sons, Ltd.     

A constitutive model for saturated compacted soils under undrained shear condition

Abstract

In this paper, elasto‐plastic constitutive equations extended from theory of plasticity and based on laws of thermo‐dynamics were derived to predict the mechanical behavior of saturated geological media. Besides, these equations can also be adapted to form the stiffness matrix for finite element analysis on deformation and stress distribution in geotechnical engineering practice. The test data were obtained from compacted crushed mudstone under consolidated un‐drained triaxial tests with pore water pressure measurement. The preparation of the specimen was different from those which had usually been adopted. Hence, it is hoped that this study will throw some light on the constitutive equations applied on compacted geological media.     

热释电材料层合板柱形弯曲解析解

由热机电耦合微分方程出发, 用富里叶级数展开方法, 探讨了含有热释电材料铺层的复合材料层合板的柱形弯曲问题。由于不作任何简化, 所得结果为精确解且适用于任何厚跨比的层合板分析。用复指数形式, 使公式推导简洁统一且极大方便了程序实施。分析中考虑了各种可能的热学、力学和静电学边界条件, 对各种耦合元素相互关系和各自特点进行了分析, 发现结构对热载荷与电载荷的响应有明显的不同。      

Finite element modelling of fibre reinforced polymer sandwich panels exposed to heat

A finite element model that predicts temperature distribution in a composite panel exposed to a heat source, such as fire, is described. The panel is assumed to be composed of skins consisting of polymer matrix reinforced with fibres and a lightweight core (the paper concentrates on the crucial aspect of the problem, i.e. the behaviour of the ‘hot’ skin of the panel. The core is assumed not to decompose, and the ‘cold’ skin is treated exactly as the ‘hot’ skin.) It is assumed that the polymer matrix undergoes chemical decomposition. Such a model results in a set of coupled non‐linear transient partial differential equations. A Galerkin finite element framework is formulated to yield a fully implicit time stepping scheme. The crucial input parameters for the model are carefully identified for subsequent experimental determination. Copyright © 2004 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.     

Object‐oriented finite element analysis of thermo‐hydro‐mechanical (THM) problems in porous media

The design, implementation and application of a concept for object‐oriented in finite element analysis of multi‐field problems is presented in this paper. The basic idea of this concept is that the underlying governing equations of porous media mechanics can be classified into different types of partial differential equations (PDEs). In principle, similar types of PDEs for diverse physical problems differ only in material coefficients. Local element matrices and vectors arising from the finite element discretization of the PDEs are categorized into several types, regardless of which physical problem they belong to (i.e. fluid flow, mass and heat transport or deformation processes). Element (ELE) objects are introduced to carry out the local assembly of the algebraic equations. The object‐orientation includes a strict encapsulation of geometrical (GEO), topological (MSH), process‐related (FEM) data and methods of element objects. Geometric entities of an element such as nodes, edges, faces and neighbours are abstracted into corresponding geometric element objects (ELE–GEO). The relationships among these geometric entities form the topology of element meshes (ELE–MSH). Finite element objects (ELE–FEM) are presented for the local element calculations, in which each classification type of the matrices and vectors is computed by a unique function. These element functions are able to deal with different element types (lines, triangles, quadrilaterals, tetrahedra, prisms, hexahedra) by automatically choosing the related element interpolation functions. For each process of a multi‐field problem, only a single instance of the finite element object is required. The element objects provide a flexible coding environment for multi‐field problems with different element types. Here, the C++ implementations of the objects are given and described in detail. The efficiency of the new element objects is demonstrated by several test cases dealing with thermo‐hydro‐mechanical (THM) coupled problems for geotechnical applications. Copyright © 2006 John Wiley & Sons, Ltd.     

Three‐dimensional coupled heat,moisture, and air transfer in a deformable unsaturated soil

A three‐dimensional numerical model is presented for three‐phase flow (moisture, air, and heat) in a deformable partly saturated soil with deformation calculated via a non‐linear elastic theory. The present work is an extension of a two‐dimensional analysis presented by Thomas and He. The objective of this work is the solution of problems of greater geometric complexity. The mathematical formulation of this coupled problem consists of four governing equations, developed from the principles of mass and energy conservations as well as the stress equilibrium equation. Darcy's flow law is used to describe the motion of liquid and air in the porous medium, and a Philip and de Vries type vapour flow approach is employed in the formulation. A Galerkin finite element method coupled with a finite difference recurrence relationship is used to obtain simultaneous solutions to the governing equations where pore liquid, pore air pressures, temperature and displacements are the primary variables. The method allows the non‐linear nature of the soil parameters to be modelled. Three‐dimensional 20‐noded isoparametric elements are used to simulate different types of cases for the verification of the work. Results are presented of the application of the new model to four problems, two of which are isothermal and two heating simulations. The three‐dimensional nature of the results achieved is highlighted. Copyright © 1999 John Wiley & Sons, Ltd.     

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

In this paper, the non‐isothermal elasto‐plastic behaviour of multiphase geomaterials in dynamics is investigated with a thermo‐hydro‐mechanical model of porous media. The supporting mathematical model is based on averaging procedures within the hybrid mixture theory. A computationally efficient reduced formulation of the macroscopic balance equations that neglects the relative acceleration of the fluids, and the convective terms is adopted. The modified effective stress state is limited by the Drucker–Prager yield surface. Small strains and dynamic loading conditions are assumed. The standard Galerkin procedure of the finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non‐linear set of equations is solved by the Newton method with a monolithic approach. Coupled dynamic analyses of strain localization in globally undrained samples of dense and medium dense sands are presented as examples. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A numerical study of the regularization properties of the finite element model is shown and discussed. A non‐isothermal case of incipient strain localization induced by temperature increase where evaporation takes place is also analysed. Copyright © 2016 John Wiley & Sons, Ltd.     

Two‐phase thermo‐mechanical and macrosegregation modelling of binary alloys solidification with emphasis on the secondary cooling stage of steel slab continuous casting processes

As an approach towards a better modelling of solidification problems, we introduce a thermo‐mechanical and macrosegregation model that considers a solidifying alloy as a binary mixture made of a liquid and a solid phase. Macroscopic conservation laws for mass, momentum and solute are obtained by spatial averaging of the respective microscopic conservation equations. Assuming local thermal equilibrium, a single equation for the conservation of the mixture energy is then written. A single equation can be obtained for the solute as well by invoking a proper microsegregation rule. The numerical implementation in a two‐dimensional finite element code is then detailed. Lastly, some examples of simulations of academic tests as well as industrial applications for continuous casting of steel slabs are discussed. They particularly enlighten the ability of the formulation to describe the formation of central macrosegregation during the secondary cooling of slab continuous casting processes. Copyright © 2006 John Wiley & Sons, Ltd.