Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials （FGMs）. First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest＇s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

Finite Element Simulation of Flexible Roll Forming with Supplemented Material Data and the Experimental Verification

Flexible roll forming is a promising manufacturing method for the production of variable cross section products. Considering the large plastic strain in this forming process which is much larger than that of uniform deformation phase of uniaxial tensile test, the widely adopted method of simulating the forming processes with non-supplemented material data from uniaxial tensile test will certainly lead to large error. To reduce this error, the material data is supplemented based on three constitutive models. Then a finite element model of a six passes flexible roll forming process is established based on the supplemented material data and the original material data from the uniaxial tensile test. The flexible roll forming experiment of a B pillar reinforcing plate is carried out to verify the proposed method. Final cross section shapes of the experimental and the simulated results are compared. It is shown that the simulation calculated with supplemented material data based on Swift model agrees well with the experimental results, while the simulation based on original material data could not predict the actual deformation accurately. The results indicate that this material supplement method is reliable and indispensible, and the simulation model can well reflect the real metal forming process. Detailed analysis of the distribution and history of plastic strain at different positions are performed. A new material data supplement method is proposed to tackle the problem which is ignored in other roll forming simulations, and thus the forming process simulation accuracy can be greatly improved.

Non-linear Constitutive Model for the Oligocarbonate Polyurethane Material

The polyurethane, which was the subject of the constitutive research presented in the paper, was based on oligocarbonate diols Desmophen C2100 produced by Bayer？. The constitutive modelling was performed with a view to applying the material as the inlay of intervertebral disc prostheses. The polyurethane was assumed to be non-linearly viscohyperelastic, isotropic and incompressible. The constitutive equation was derived from the postulated strain energy function. The elastic and rheological constants were identified on the basis of experimental tests, i.e. relaxation tests and monotonic uniaxial tests at two different strain rates, i.e. λ= 0.1 min-1 and λ= 1.0 min-1. The stiffness tensor was derived and introduced to Abaqus？finite element（FE） software in order to numerically validate the constitutive model. The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyurethane material.