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.

Finite-strain laminates: Bending-enhanced hexahedron and delamination

With a new finite strain anisotropic framework, we introduce a unified approach for constitutive model- ing and delamination of composites. We describe a finite-strain semi-implicit integration algorithm and the application to assumed-strain hexahedra. In a laminate composite, the laminae are modeled by an anisotropic Kirchhoff/Saint-Venant material and the interfaces are modeled by the exponential cohesive law with intrinsic characteristic length and the criterion by Benzeggagh and Kenane for the equivalent fracture toughness. For the element formulation, a weighted least-squares algorithm is used to calculate the mixed strain. Löwdin frames are used to model orthotropic materials without the added task of per- forming a polar decomposition or empirical frames. To assess the validity of our proposals and inspect step and mesh size dependence, a least-squares based hexahedral element is implemented and tested in depth in both deformation and delamination examples.

Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame

Two novelties are introduced: (i) a finite-strain semi-implicit integration algorithm compatible with current element technologies and (ii) the application to assumed-strain hexahedra. The Löwdin algo- rithm is adopted to obtain evolving frames applicable to finite strain anisotropy and a weighted least- squares algorithm is used to determine the mixed strain. Löwdin frames are very convenient to model anisotropic materials. Weighted least-squares circumvent the use of internal degrees-of-freedom. Het- erogeneity of element technologies introduce apparently incompatible constitutive requirements. Assumed-strain and enhanced strain elements can be either formulated in terms of the deformation gradient or the Green–Lagrange strain, many of the high-performance shell formulations are corotational and constitutive constraints (such as incompressibility, plane stress and zero normal stress in shells) also depend on specific element formulations. We propose a unified integration algorithm compatible with possibly all element technologies. To assess its validity, a least-squares based hexahedral element is implemented and tested in depth. Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy.

Quantification of free auxins in semi-hardwood plant cuttings and microshoots by dispersive liquid–liquid microextraction/microwave derivatization and GC/MS analysis

Several studies have suggested that differences in the natural rooting ability of plant cuttings could be attributed to differences in endogenous auxin levels. Hence, during rooting experiments, it is important to be able to routinely monitor the evolution of endogenous levels of plant hormones. This work reports the development of a new method for the quantification of free auxins in auxin-treated Olea europaea (L.) explants, using dispersive liquid–liquid microextraction (DLLME) and microwave assisted derivatization (MAD) followed by gas chromatography/mass spectrometry (GC/MS) analysis. Linear ranges of 0.5–500 ng mL 1 and 1–500 mg mL 1 were used for the quantification of indole-3-acetic acid (IAA) and indole-3-butyric acid (IBA), respectively. Determined by serial dilutions, the limits of detection (LOD) and quantification (LOQ) were 0.05 ng mL 1 and 0.25 ng mL 1, respectively for both compounds. When using the calibration curve for determination, the LOQ corresponded to 0.5 ng mL 1 (IAA) and 0.5 mg mL 1 (IBA). The proposed method proved to be substantially faster than other alternatives, and allowed free auxin quantification in real samples of semi-hardwood cuttings and microshoots of two olive cultivars. The concentrations found in the analyzed samples are in the range of 0.131–0.342 mg g 1 (IAA) and 20–264 mg g 1 (IBA).