High Performance Algorithm Development For Materials With Different Moduli In Tension And Compression And Its Applications

Materials possessing tension-compression asymmetry behavior can be simulated by a bi-modulus constitutive relation, which assumes the materials have different moduli in tension and compression. Significant error will be introduced if classical elastic theory is used to analysis this kind of material. Traditional iteration methods struggle for the convergence difficulty and it’s even harder for the application in large scale complex structure mechanical analysis, though the constitutive theory of bi-modulus has been studied for a long time. The lack of such kind of material constitutive model in commercial finite element software also gives impetus to the development of efficient and stable computational methods.In this paper, a new computational framework is proposed, the fundamental reason for the convergence difficulties of traditional iteration methods is also revealed both theoretically and numerically. A more efficient tangent stiffness matrix calculation method which have asymptotically quadratic rate of convergence is established. Solution technic which is suitable for bi-modulus truss element, plane stress and three dimensional solid element, have also been proposed and implemented in ABAQUS with UMAT.Numerical examples show that the proposed bi-modulus material subroutine presented efficient converge rate under both small and finite deformations. The proposed computational framework can also be applied to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena.