Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model

We predict macroscopic fracture related material parameters of fully exfoliated clay/epoxy nano- composites based on their fine scale features. Fracture is modeled by a phase field approach which is implemented as user subroutines UEL and UMAT in the commercial finite element software Abaqus. The phase field model replaces the sharp discontinuities with a scalar damage field representing the diffuse crack topology through controlling the amount of diffusion by a regularization parameter. Two different constitutive models for the matrix and the clay platelets are used; the nonlinear coupled system con- sisting of the equilibrium equation and a diffusion-type equation governing the phase field evolution are solved via a NewtoneRaphson approach. In order to predict the tensile strength and fracture toughness of the clay/epoxy composites we evaluated the J integral for different specimens with varying cracks. The effect of different geometry and material parameters, such as the clay weight ratio (wt.%) and the aspect ratio of clay platelets are studied.

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas- ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para- metrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen- tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.