In this article, we present a variational formulation for coupled problems in thermodynamics the most suitable for long‐term simulations of plastic behavior. We start with three‐field Hu–Washize ...variational formulation and perform regularization to include non‐symmetric stress, we thus recover the formulation that can accommodate any choice of discrete approximation. Such a regularized variational formulation allows us to eliminate the rotation field (as typically less important) and recover the corresponding hybrid stress format for equations of motion and transient heat conduction. The regularized variational formulation is further combined with discrete approximation based upon the Raviart–Thomas vector space for both mechanical and thermal fields, which enforces continuity across element boundaries for stress vector and normal component of heat‐flux. The conservation properties are validated with energy‐conserving scheme for thermoelastic behavior. The time integration of thermo‐viscoplastic behavior is carried out by energy‐decaying scheme to provide superior accuracy for computed stress in a long‐term simulation. The proposed approach offers higher computational robustness and results accuracy than the classical finite elements and time‐integration schemes. Such a performance is illustrated on several numerical simulations in non‐stationary problems for thermo‐viscoplastic behavior.
This work addresses the large strain behaviors of thermoplastic polyurethanes (TPUs) spanning a range of fractions of hard and soft contents in both experiment and theoretical modeling. The key ...mechanical features involve a combination of elasticity and inelasticity, and are quantified experimentally under a broad variety of loading scenarios. A finite deformation constitutive model is then presented to capture the main features of the stress-strain data, which are strongly dependent on fractions of hard and soft contents. The stress-strain behavior of these TPUs is characterized by highly nonlinear rate-dependent hyperelastic-viscoplasticity, in which substantial energy dissipation is accompanied by shape recovery as well as softening. Agreement between the model and the experimental data for the representative TPUs provides physical insight into the underlying deformation mechanisms in this important class of soft materials that exhibit both elastomeric and plastomeric characteristics.
Large strain behavior of thermoplastic polyurethanes spanning a range of fractions of hard and soft segment contents: shape recovery and energy dissipation upon cyclic loading conditions are highly dependent on the fractions of hard and soft contents, spanning the range from glassy to rubbery polymers. Display omitted
•Large strain behavior of thermoplastic polyurethanes is examined under various loading scenarios•Mechanical behavior characterized by nonlinear rate-dependent hyperelastic-viscoplasticity•Finite deformation constitutive model is presented that captures mechanical response•Interpretation of constitute model provides insight into deformation mechanisms
This paper investigates the viscoelastic/viscoplastic/fracture behavior of an epoxy resin. A state-of-the-art pressure-dependent elastoplastic constitutive model (Melro et al. 2013) is expanded to ...include viscoelasticity, viscoplasticity and a modified damage formulation with linear softening and shrinking pressure-dependent fracture surface. A water plasticization model with a single degradation factor is proposed. A set of new quasi-static and fatigue experiments is used to calibrate the model and assess its predictive capabilities. The model correctly represents the rate dependent plasticity and fracture initiation behavior of the studied epoxy. The stiffness and strength degradations after plasticization are also accurately captured. The model is found to be less suitable in reproducing the measured loading-unloading behavior, which displayed strong nonlinearity in combination with limited permanent deformation. Nevertheless, reasonably accurate fatigue life predictions in the low-cycle regime are obtained.
Preconditioning of rock for drilling operations is a potential method to facilitate the mechanical breakage and mitigate the tool wear. This paper numerically investigates one such preconditioning ...technique, namely, the thermal jet assisted rock cutting. For this end, a numerical method for solving the governing thermo‐mechanical problem is developed and validated. The continuum approach is chosen to describe the rock failure, being based on a damage‐viscoplasticity model with the Drucker–Prager yield surface and the modified Rankine surface as the tensile cut‐off. In the damage part, separate scalar damage variables are employed for tension and compression. The cutters are modelled as rigid bodies and their interaction with the rock is modelled by imposing contact constraints by the forward increment Lagrange multiplier method, which is compatible with the chosen explicit time integration scheme. A damage‐based erosion criterion is applied to remove the contact nodes surrounded by heavily damaged elements. The thermal jets are modelled with a moving external heat flux boundary condition. The global thermo‐mechanical problem is solved with a staggered approach explicitly in time while applying mass scaling to increase the critical time step. The novel 3D numerical simulations involving two cutters demonstrate the capabilities of the method with a special emphasis on cutter‐thermal jet configurations. Therefore, the present method provides a potential tool for the bit design in thermal jet assisted drilling.
An experimental study of temperature-dependent mechanical behaviour of Poly-methyl methacrylate (PMMA) was performed at a range of temperatures (20 °C, 40 °C, 60 °C and 80 °C) below its glass ...transition point (108 °C) under uniaxial tension and three-point bending loading conditions. This study was accompanied by simulations aimed at identification of material parameters for two different constitutive material models. Experimental flow curves obtained for PMMA were used in elasto-plastic analysis, while a sim-flow optimization tool was employed for a two-layer viscoplasticity model. The temperature increase significantly affected mechanical behaviour of PMMA, with quasi-brittle fracture at room temperature and super-plastic behaviour (ε>110%) at 80 °C. The two-layer viscoplasticity material model was found to agree better with the experimental data obtained for uniaxial tension than the elasto-plastic description.
•Temperature-dependent mechanical behaviour of PMMA below its Tg point was analyzed.•PMMA showed quasi-brittle behaviour at 20 °C and super-plastic one (ε>110%) at 80 °C.•Parameters of two-layer viscoplasticity and elasto-plastic models were identified.•Experimental data were used to validate parameters of the material models.•Two-layer viscoplasticity model reproduced mechanical behaviour of PMMA better.
Polymeric materials are widely used in structural components and systems, and the accurate prediction of their complex time‐dependent behavior is critical. Several constitutive models are available ...for different types of mechanical behaviors and loading conditions. However, selecting the model and the correct calibration of its parameters is often a challenge. This paper evaluates the applicability of the two‐layer viscoplasticity (TLV) model to predict the viscoplastic behavior of polyvinylidene fluoride (PVDF) in a large range of strain rates and complex states of strain. The setting of parameters and model validation was made by performing experimentally and numerically uniaxial compression tests and relaxation tests. The model parameters were also analyzed in performing microindentation tests. The TLV model using the same set of parameters selected well predicted the PVDF behavior in a wide variety of compressive loading conditions.
Experimental data compression test.
The purpose of the present review article is twofold:
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recall elementary notions as well as the main ingredients and assumptions of developing macroscopic inelastic constitutive equations, mainly ...for metals and low strain cyclic conditions. The explicit models considered have been essentially developed by the author and co-workers, along the past 30 years;
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summarize and discuss a certain number of alternative theoretical frameworks, with some comparisons made with the previous ones, including more recent developments that offer potential new capabilities.
► A systematic thermodynamic framework for rate- and time-dependent materials. ► Coupled viscoelasticity, viscoplasticity, viscodamage, and micro-damage healing. ► A micro-force balance is derived ...for each nonlinear behavior is formulated. ► Only two functions are needed; the free energy and rate of dissipation functions. ► Non-associative plasticity is obtained from the principle of virtual power.
A general thermodynamic-based framework for deriving coupled temperature-dependent viscoelasticity, viscoplasticity, viscodamage, and micro-damage healing constitutive models for constitutive modeling of time- and rate-dependent materials is presented. Principle of virtual power, Clausius–Duhem inequality, and the principle of maximum rate of dissipation are used to construct this general thermodynamic framework. A micro-damage healing natural configuration is introduced to enhance the continuum damage mechanics theories in modeling the healing phenomenon. This healing configuration can be considered as the extension of the well-known Kachanov’s effective (undamaged) configuration (Kachanov, 1958). The viscoplasticity loading condition is defined from the microforce balance derived directly from the principle of virtual power. Moreover, for the first time, viscoelasticity, viscodamage, and micro-damage healing microforce balances are derived directly from the principle of virtual power. It is also shown that the generalized non-associative plasticity/viscoplasticity theories can be a direct consequence of postulating the principle of virtual power. The emphasis in this paper is placed on the decomposition of thermodynamic conjugate forces into energetic and dissipative components. It is shown that this decomposition is necessary for accurate estimation of the rate of energy dissipation. The energetic components are related to the Helmholtz free energy, whereas the dissipative components are related to the rate of energy dissipation. This thermodynamic framework is used for deriving more comprehensive viscoelastic, viscoplastic, and viscodamage, and micro-damage healing constitutive models.
•A constitutive model for combustor liner material Haynes 230 is developed.•A broad set of isothermal low-cycle fatigue and fatigue-creep responses are simulated.•Static recovery feature simulated ...stress relaxation in rate-independent regime.•Simulation of mean stress evolution needs additional modeling feature.•Strain range modeling features are essential to simulate hysteresis loop shapes.
A robust cyclic viscoplasticity model is developed for simulating a broad set of isothermal, low-cycle fatigue and fatigue-creep responses of Haynes 230 (HA 230) under uniaxial loading. High temperature components experiencing thermo-mechanical fatigue failures can be designed considering their failure responses such that their fatigue life is predictable. Hence, design of high temperature components in aerospace, automobile, nuclear power, and chemical industries should be based on viscoplastic nonlinear analysis using a robust constitutive model. A unified viscoplasticity model based on the nonlinear kinematic hardening rule of Chaboche with several added features for strain-range dependence, rate-dependence, static recovery, and mean stress evolution is developed and evaluated against a broad set of HA 230 responses. Robustness of the constitutive model is demonstrated against predicting fatigue and dwell period stress relaxation responses under uniaxial strain-controlled loading for a broad temperature range of 25–982°C and strain rate range of 1.1×10−2 to 2.6×10−5/s. Parameter determination of such an advanced model is discussed showing the importance of a well thought out experimental database and thereby providing physical meaning to model parameters.
Due to favorable properties (cheap price, easy processing, preeminent combination of toughness and strength, clearness, recyclability etc.), amorphous polymers are widely used in windows, sporting ...goods, vehicles, aeronautic equipment, electronics, and health technology. However, their applications may suffer from fatigue, when material fails at significantly lower stress levels than under monotonic loading conditions; fatigue loads result in polymer degradation which can affect horrific accidents (e.g., the air disaster of China Airlines Flight 611) and tremendous financial losses. Despite this motivation, fatigue behavior of amorphous polymers has been scarcely investigated so far. In this study, micro-mechanical characteristics of amorphous structure and their influence on macroscopic deformation behavior (ratcheting) and fatigue life are investigated. It was found (SEM results) that polymer degradation is the process of failure (shear banding affecting micro-cracking and fracture) causing finally breakdown of polymer network. The degradation process was very rate sensitive, and the crack initiation phase before rapid rupture of the material encompassed the majority (even 95 %) of the total fatigue life. Certain fracture surfaces showed sharpened protrusions indicating that the separation of the fracture surfaces from each other occurred precisely on those protrusions. The vein-like, cellular, and rippled patterns of shear bands on fracture surfaces increased fracture toughness and thus, fatigue resistance and life.
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