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.     

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.     

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.     

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.     

An efficient sparse matrix‐vector multiplication on CUDA‐enabled graphic processing units for finite element method simulations

Finite element method (FEM) is a well‐developed method to solve real‐world problems that can be modeled with differential equations. As the available computational power increases, complex and large‐size problems can be solved using FEM, which typically involves multiple degrees of freedom (DOF) per node, high order of elements, and an iterative solver requiring several sparse matrix‐vector multiplication operations. In this work, a new storage scheme is proposed for sparse matrices arising from FEM simulations with multiple DOF per node. A sparse matrix‐vector multiplication kernel and its variants using the proposed scheme are also given for CUDA‐enabled GPUs. The proposed scheme and the kernels rely on the mesh connectivity data from FEM discretization and the number of DOF per node. The proposed kernel performance was evaluated on seven test matrices for double‐precision floating point operations. The performance analysis showed that the proposed GPU kernel outperforms the ELLPACK (ELL) and CUSPARSE Hybrid (HYB) format GPU kernels by an average of 42% and 32%, respectively, on a Tesla K20c card. Copyright © 2016 John Wiley & Sons, Ltd.     

A stochastic second‐order and two‐scale thermo‐mechanical model for strength prediction of concrete materials

A stochastic thermo‐mechanical model for strength prediction of concrete is developed, based on the two‐scale asymptotic expressions, which involves both the macroscale and the mesoscale of concrete materials. The mesoscale of concrete is characterized by a periodic layout of unit cells of matrix‐aggregate composite materials, consisting of randomly distributed aggregate grains and cement matrix. The stochastic second‐order and two‐scale computational formulae are proposed in detail, and the maximum normal stress is assumed as the strength criterion for the aggregates, and the cement paste, in view of their brittle characteristics. Numerical results for the strength of concrete obtained from the proposed model are compared with those from known experiments. The comparison shows that the proposed method is validated for strength prediction of concrete. The proposed thermo‐mechanical model is also employed to investigate the influence of different volume fraction of the aggregates on the strength of concrete. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental and computational study on thermo‐mechanical fatigue life of aluminium alloy piston

To assess the life of a new diesel aluminium alloy piston under thermal shock loads, thermo‐mechanical fatigue (TMF) testing was conducted to characterise the TMF properties of the piston alloy, and an empirical model based on the constraint ratio concept was proposed to predict the TMF life of the piston. Considering that the empirical model required expensive experimental support, a platform with high‐frequency induction heating was established to simulate the force on the piston under thermal shock loads to calculate the piston life using the thermal shock test. Additionally, a finite element method was developed to compute the distributions of temperature, strain, and stress during this process. The characteristics of crack initiation and propagation in TMF test rods and piston mock‐ups were also investigated. The results showed that the TMF test rod suffered brittle fracture with brittle quasi‐cleavage features. The microcracks mainly occurred in primary Si particles due to stress concentration around the primary Si particles induced by the difference between the thermal expansion coefficients of Si and Al. From a macro perspective, the piston initially cracked at the rim above the pinhole, where the stress is larger than that along other directions. From a micro perspective, the protrusions of various sizes on the piston rim were induced by the compression stresses at high temperature. The piston cracks usually initiate around primary Si particles, propagate along the edge of primary Si in a straight line, bifurcate and then stop at a certain depth. If the piston was only heated, cracks or plastic deformations were not produced. The piston life can be assessed using the proposed empirical model based on the constraint ratio concept or thermal shock testing based on the developed platform. The difference between the predicted and experimental life was not greater than 7%.     

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.     

An energy momentum consistent integration scheme using a polyconvexity‐based framework for nonlinear thermo‐elastodynamics

The present contribution provides a new approach to the design of energy momentum consistent integration schemes in the field of nonlinear thermo‐elastodynamics. The method is inspired by the structure of polyconvex energy density functions and benefits from a tensor cross product that greatly simplifies the algebra. Furthermore, a temperature‐based weak form is used, which facilitates the design of a structure‐preserving time‐stepping scheme for coupled thermoelastic problems. This approach is motivated by the general equation for nonequilibrium reversible‐irreversible coupling (GENERIC) framework for open systems. In contrast to complex projection‐based discrete derivatives, a new form of an algorithmic stress formula is proposed. The spatial discretization relies on finite element interpolations for the displacements and the temperature. The superior performance of the proposed formulation is shown within representative quasi‐static and fully transient numerical examples.     

Low cycle thermo‐mechanical fatigue: damage operator approach

The strain‐life approach is standardized and widely accepted for determining fatigue damage under strain‐controlled low cycle fatigue (LCF) loading. It was first extended to non‐isothermal cases by introducing an equivalent temperature approach (ETA). The paper presents its extension that is the damage operator approach (DOA) enabling online continuous damage calculation for isothermal and non‐isothermal loading with mean stress correction. The cycle closure point, cycle equivalent temperature, threshold temperature and separate rainflow counting obligatory for the ETA are not necessary for the DOA any more. Both approaches are equivalent for the second and subsequent runs of block loading if temperature is constant. However, for non‐isothermal cases, the DOA is within the worst and the best case scenarios of the ETA. The approaches are compared to the simple stress histories and several thermo‐mechanical fatigue (TMF) cycle types.     

ANN approach to sorption hysteresis within a coupled hygro‐thermo‐mechanical FE analysis

Non‐linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An artificial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN‐FE code has been developed and tested for 1‐D and 2‐D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative effect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary‐porous materials. The most distinct differences are observed for the saturation and displacement solutions. The ANN‐FE approach seems to be an efficient way to take into account the influence of hysteresis during analysis of hygro‐thermal behaviour of capillary‐porous materials. Copyright © 2001 John Wiley & Sons, Ltd.     

Experimental and theoretical studies on thermo‐mechanical fatigue test for aluminium cast alloy

Evaluation of the thermo‐mechanical behaviour and prediction of the service life of cast aluminium alloys are important for the design of automobile engine cylinder heads. In this study, cast Al alloy specimens are extracted from cylinder heads and subjected to in‐phase thermo‐mechanical cyclic loading. The hysteresis curves related to stress and strain were recorded under the individual thermo‐mechanical loading conditions. The number cycles to failure corresponding to multiple mechanical strain and temperature ranges were obtained. It is found that the cyclic stress amplitude decreases and the cyclic softening rate increases with increasing maximum temperature rise. A modified fatigue‐creep model based on energy conservation has been developed for prediction of the fatigue life of cylinder heads. The proposed method shows good agreement with the well‐established Ostergren model and low standard deviations. In summary, the proposed method described in this study provides an option for prediction of the thermo‐mechanical behaviour of metals.     

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 frontal solver tuned for fully coupled non‐linear hygro‐thermo‐mechanical problems

Solving fully coupled non‐linear hygro‐thermo‐mechanical problems relative to the behaviour of concrete at high temperatures using monolithic models is nowadays a very interesting and challenging computational problem. These models require an extensive use of computational resources, such as main memory and computational time, due to the great number of variables and the numerical characteristics of the coefficients of the linear systems involved. In this paper, a number of different variants of a frontal solver used within HITECOSP, an application developed within the BRITE Euram III ‘HITECO’ EU project, to solve multiphase porous media problems, are presented and evaluated with respect to their numerical accuracy and performance. When developing the variants, several optimization techniques have been adopted, such as data structure, cache and branches optimizations. Specifically, numerical accuracy has been evaluated using a modified componentwise backward error analysis. The main result of this work is a new solver which is both much faster and more accurate than the original one. Specifically, the code runs over five times faster and numerical errors are reduced by up to three orders of magnitude. Copyright © 2003 John Wiley & Sons, Ltd.     

Improved fatigue resistance of pseudo‐elastic NiTi alloys by thermo‐mechanical treatment

Shape memory alloys are susceptible to two types of fatigue in addition to classical fatigue: 1. Pseudo‐elastic fatigue leads to an increase in the slope of the pseudo‐elastic plateau and final loss of pseudo‐elasticity 2. A change in transformation temperature. Usually the martensite temperature is lowered with the number of cycles until final loss of transformability. This paper describes measures to improve stability against both types of fatigue. Such methods are simple ageing in order to achieve precipitation in austenite, and thermo‐mechanical treatments such as ausforming that introduce lattice defects into austenite, which transforms subsequently into martensite. Another method consists in the introduction of defects into martensite by marforming plus subsequent ageing. This ageing treatment has two purposes. It increases the classical strength and restores the β‐phase from residual martensite and consequently it recreates transformability. It is shown that the last mentioned method leads to the greatest effect in respect to stabilisation against both types of fatigue. An additional effect of these treatments is a transition of localised to more homogeneous strain. Its relevance for fatigue resistance is still under investigation.     

Fully coupled non‐linear analysis of piezoelectric solids involving domain switching

Domain switching is the cause of significant non‐linearity in the response of piezoelectric materials to mechanical and electrical effects. In this paper, the response of piezoelectric solids is formulated by coupling thermal, electrical, and mechanical effects. The constitutive equations are non‐linear. Moreover, due to the domain switching phenomenon, the resulting governing equations become highly non‐linear. The corresponding non‐linear finite element equations are derived and solved by using an incremental technique. The developed formulation is first verified against a number of benchmark problems for which a closed‐form solution exists. Next, a cantilever beam made of PZT‐4 is studied to evaluate the effect of domain switching on the overall force–displacement response of the beam. A number of interesting observations are made with respect to the extent of non‐linearity and its progressive spread as the load on the beam increases. Copyright © 2002 John Wiley & Sons, Ltd.