Inverse identification of constitutive parameters from heat source fields: A local approach applied to hyperelasticity

Abstract

In this paper, a new inverse identification method of constitutive parameters is developed from full kinematic and thermal field measurements. It consists in reconstructing the heat source field from two different approaches by using the heat diffusion equation. The first one requires the temperature field measurement and the value of the thermophysical parameters. The second one is based on the kinematic field measurement and the choice of a thermo‐hyperelastic model that contains the parameters to be identified. The identification is carried out at the local scale, ie, at any point of the heat source field, without using the boundary conditions. In the present work, the method is applied to the challenging case of hyperelasticity from a heterogeneous test. Due to large deformations undergone by the rubber specimen tested, a motion compensation technique is developed to plot the kinematic and the thermal fields at the same points before reconstructing the heterogeneous heat source field. In the present case, the constitutive parameter of the Neo‐Hookean model has been identified, and its distribution has been characterized with respect to the strain state at the surface of a cross‐shaped specimen.

Thermomechanical Behaviour and Interface of Overmoulded Soft Thermoplastic Vulcanizate Elastomers

“…Fused Deposition Modelling (FDM) printed rolls of 6 mm in diameter were glued (Loctite 406, Henkel, Düsseldorf, Germany) to the ends of the specimen. Such rolls prevent the specimens from slipping into the jaws, which shape has been designed accordingly [ 26 , 27 ].…”

“…As explained in [ 27 ], the components of the deformation gradient tensor are determined at the centre of the square elements, which are composed of four Zones Of Interest (ZOI). Each corner of the square element corresponds to a ZOI centre defined in the undeformed DIC grid.…”

“…The emissivity of the material was set at 0.94. The emissivity has been identified from the calibration procedure detailed in [ 27 ]. The infrared camera was trigged at the same acquisition frequency as the optical camera one, i.e., 10 Hz.…”

“…A calibration test pattern was placed in one of the grips. The reader can refer to [ 27 ] for further information about the calibration procedure. This approach has been successfully applied for rubber [ 42 , 43 , 44 , 45 , 46 , 47 , 48 ], for Poly(methyl methacrylate) [ 49 ] and for metallic materials [ 50 , 51 , 52 , 53 , 54 , 55 ].…”

The Parameters Identification of High-Temperature Constitutive Model Based on Inverse Optimization Method and 3D Processing Map of Cr8 Alloy Steel

“…Giovanni B. Broggiato [ 13 ] used the inverse method to accurately determine the parameters of the damage model. Sylvain Charles [ 14 ] proposed a new method for determining constitutive antithesis parameters based on total kinematics and thermal field measurements. It could be seen that there was a smaller parameter error and higher prediction accuracy in the constitutive model obtained by the inverse optimization algorithm.…”