Elasto-viscoplastic Constitutive Law Research Articles

Modeling and Simulation of Impact Failure Characteristic of Polypropylene by Elastoviscoplastic Constitutive Law

For simulating the final failure of glassy polymers under impact loading, Shizawa's constitutive model was modified by introducing the craze density based softening law in which the phenomenological softening law using the craze density is employed. The material parameter identification procedure in the constitutive law was developed based on the sensitivity analysis. All parameters were identified with the measurement data which were obtained by both the dumbbell-shape tensile test specimen and the notched tensile test specimen. The dart impact test was also conducted. The load displacement curve and damage zone development were compared with those obtained by the finite element analysis using proposed constitutive equations. Both results were in good agreement and the usefulness of the constitutive equations was validated.

Extension of the concept of material objectivity to mixed Eulerian-Lagrangian reference systems

The material objectivity of stress and strain measures forms one of the fundamental physical principles, which have to be taken into account in the formulation of constitutive laws. In the present paper we investigate its form in a mixed Eulerian-Lagrangian (E-L) reference system and show that it covers the well-known versions in the Eulerian (E) and Lagrangian (L) levels of description. The transformation rules for vector and tensor quantities are derived, and the concept of the Lie-derivative for time-dependent quantities is reviewed and generalized. Depending on the underlying formulation, different objective rate tensors for stress and strain, such as the Oldroyd and Truesdell rate, can be derived in a systematic way in the intermediary (E-L) system. This concept is then applied to elasto-viscoplastic and hypoelastic constitutive laws.

Fatigue design of structures under thermomechanical loadings

AbstractThis paper presents a global approach to the design of structures that experience thermomechanical fatigue loading, which has been applied successfully in the case of cast‐‐iron exhaust manifolds. After a presentation of the design context in the automotive industry, the important hypotheses and choices of this approach, based on a thermal 3D computation, an elastoviscoplastic constitutive law and the dissipated energy per cycle as a damage indicator associated with a failure criterion, are first pointed out. Two particular aspects are described in more detail: the viscoplastic constitutive models, which permit a finite element analysis of complex structures and the fatigue criterion based on the dissipated energy per cycle. The FEM results associated with this damage indicator permit the construction of a design curve independent of temperature; an agreement is observed between the predicted durability and the results of isothermal as well as non isothermal tests on specimens and thermomechanical fatigue tests on real components on an engine bench. These results show that thermomechanical fatigue design of complex structures can be performed in an industrial context.

Analysis of Crack Opening Behavior in Amorphous Metal (Comparative Study of Atomistic and Elasto-Viscoplastic Continuum Model)

A large-scale molecular dynamics simulation on an atomistic model and an elasto-viscoplastic finite element analysis on a continuum model are carried out to study deformation field near a crack tip in amorphous metal. The atomistic model, in which Finnis-Sinclair type potential for iron is assumed as interatomic potential, is generated using heating-quenching simulation. The parameters in strain-dependent elasto-viscoplastic constitutive law for the continuum model are determined using a uni-axial tensile test for the atomistic model of amorphous metal. The results for the crack problem using the atomistic model and the continuum model are compared each other. The shape of crack front, strain distribution and stress distribution around the crack tip, increase of crack tip opening displacement and crack growth are examined, and FE results for the continuum model agree with MD results for the atomistic model. However, the continuum model can depict only averaged description of the atomistic model. In the atomistic model, it is observed that the highly deformed region consists of atomistically localized deformation. The atomistic simulation is indispensable to reveal the microscopic structures and deformation mechanisms.

Fatigue design of structures under thermomechanical loadings

ABSTRACTThis paper presents a global approach to the design of structures that experience thermomechanical fatigue loading, which has been applied successfully in the case of cast‐iron exhaust manifolds. After a presentation of the design context in the automotive industry, the important hypotheses and choices of this approach, based on a thermal 3D computation, an elastoviscoplastic constitutive law and the dissipated energy per cycle as a damage indicator associated with a failure criterion, are first pointed out. Two particular aspects are described in more detail: the viscoplastic constitutive models, which permit a finite element analysis of complex structures and the fatigue criterion based on the dissipated energy per cycle. The FEM results associated with this damage indicator permit the construction of a design curve independent of temperature; an agreement is observed between the predicted durability and the results of isothermal as well as non isothermal tests on specimens and thermomechanical fatigue tests on real components on an engine bench. These results show that thermomechanical fatigue design of complex structures can be performed in an industrial context.

Parameter identification for lined tunnels in a viscoplastic medium

AbstractThis paper is dedicated to the identification of constitutive parameters of elasto‐viscoplastic constitutive law from measurements performed on deep underground cavities (typically tunnels). This inverse problem is solved by the minimization of a cost functional of least‐squares type. The exact gradient is computed by the direct differentiation method and the descent is done using the Levenberg–Marquardt algorithm. The method is presented for lined or unlined structures and is applied for an elastoviscoplastic constitutive law of the Perzyna class. Several identification problems are presented in one and two dimensions for different tunnel geometries. The used measurements have been obtained by a preliminary numerical simulation and perturbed with a white noise. The identified responses match the measurements. We also discuss the usage of the sensitivity analysis of the system, provided by the direct differentiation method, for the optimization of in situ monitoring. The sensitivity distribution in space and time assess the location of the measurements points as well as the time of observation needed for reliable identification. Copyright © 2002 John Wiley & Sons, Ltd.

Non-linear dynamic response of a reinforced concrete secondary containment shell subjected to seismic load

The paper presents details of a non-linear dynamic analysis carried out at SERC, Madras on a reinforced concrete (RC) secondary containment shell subjected to seismic load, taking into account the non-linearities of reinforced concrete in the finite element modelling. A 20-noded, three-dimensional, solid isoparametric finite element is used for spatial discretisation. The concrete in compression is modelled using elasto-viscoplastic constitutive laws, which also include the strain-rate sensitivity and progressive strength degradation of concrete in compression. Cracked concrete is modelled by using a smeared approach and the tension-stiffening effect of concrete is considered by a strain-softening rule. The reinforcement is represented by a smeared approach and a classical elasto-viscoplastic material model is adopted for reinforcement steel. The non-linear response of the RC containment shell subjected to seismic loading was studied by considering appropriate values for the concrete's elastic limit and dynamic modulus of elasticity. The influence of these two parameters on the non-linear response and ultimate behaviour of the structure is discussed.

On the identification of elastoviscoplastic constitutive laws from indentation tests

This paper addresses the identification of the parameters of a nonlinear constitutive law from indentation tests. The identification problem is considered as a constrained minimization problem and the gradient is computed using the adjoint state method, in spite of the difficulties of the underlying contact problem. This provides a general framework to perform optimization in some problems involving contact conditions and nonlinear material behaviour. The case of a Maxwell viscoelastic and a Norton-Hoff elastoviscoplastic constitutive law are treated extensively and a series of numerical identification examples are shown.

Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling

Homogenisation methods provide an efficient way to model the mechanical behaviour of heterogeneous materials. In this paper, a homogenisation procedure is adopted that allows to determine apparent properties for Perzyna's elastoviscoplastic constitutive law for arbitrary microstructures. Numerical simulations on a representative volume element (RVE) are performed, from which the volume averaged state variables are acquired, necessary to establish the constitutive equations for the equivalent homogeneous medium. The applicability of mixed and periodic boundary conditions has been assessed. In addition, the difference between uniform and irregular distributions of the microstructural constituents is discussed. To substantiate our findings, a comparison is made between the global response of a heterogeneous and the corresponding homogenised structure.