Jurica Sorić

The modelling of fibre reorientation in soft tissue

In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation is defined by a structural tensor, while the current orientation is described by a time-dependent structural tensor, which results from the initial one by a rotational transformation. The rotation tensor is obtained via an integration process of a rate tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential map algorithm, where it is shown that the rotation is necessarily a two-parametric one. Efficiency of the proposed formulation is demonstrated using some numerical examples.

Stability analysis of a torispherical shell subjected to internal pressure

Abstract A geometrically nonlinear stability analysis of a torispherical shell subjected to internal pressure was performed, using doubly curved finite elements which provide an exact description of the middle surface. The critical pressure and the corresponding buckling mode were calculated. Internal pressurenodal displacement curves were obtained for the pre- and postbuckling regions for the computation model. The buckling modes in bifurcation points were calculated and the changes of the deflection shape on the postbuckling paths analyzed. The effect of geometric imperfections on the critical pressure was studied. Imperfection shapes affine to buckling modes in bifurcation points were investigated and critical pressure-imperfection amplitude curves obtained.

An efficient formulation of integration algorithms for elastoplastic shell analysis based on layered finite element approach

For geometrically and physically nonlinear analyses of shell structures a computational model employing a Reissner-Mindlin type kinematic assumption, a layered finite element approach and a closest-point projection return mapping algorithm, completely formulated in tensor notation is presented. As a result of a consistent linearization, a tangent modulus is derived, expressed also in tensor components. The applied constitutive model includes a von Mises yield criterion and linear isotropic as well as kinematic hardening. All stress deviator components are employed in the formulation. The material model is implemented into a four-noded isoparametric assumed strain finite element, which permits the simulation of geometric nonlinear responses considering finite rotations. The proposed numerical concept is unconditionally stable and allows large time steps, as the numerical examples illustrate. Further, the numerical simulations demonstrate the expected quadratic convergence in a global iterative technique.

Elastic-plastic analysis of internally pressurized torispherical shells

The constitutive equation for an elastic-plastic material model was derived using the von Mises yield criterion and assuming isotropic strain hardening. A layered finite element permitting geometrically linear and geometrically nonlinear elastic-plastic analysis of thin shell structures is presented. The effect of linear strain hardening on the size of plastic regions and the distribution of internal forces in an internally pressurized torispherical shell was analyzed. At sufficiently high pressures a significant difference in the distribution of internal forces was observed between elastic, perfectly plastic and strain hardening material. The effect of the size of plastic regions on the difference in the magnitude of internal forces obtained by geometrically linear and geometrically nonlinear computations of the torispherical shell was studied. An increase in the size of the plastic region was found to produce greater differences in the computation of meridional bending moments than in the computation of hoop stress resultants.

On a numerical implementation of a formulation of anisotropic continuum elastoplasticity at finite strains

In a recent theoretical study [see C. Sansour, I. Karsaj, J. Soric, A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: Modelling, International Journal of Plasticity 22 (2006) 2346-2365], a constitutive model for anisotropic elastoplasticity at finite strains has been developed. The model is based on the multiplicative decomposition of the deformation gradient. The stored energy function as well as the flow rule has been considered as quadratic functions of their arguments. In both cases, the list of arguments is extended to include structural tensors which describe the anisotropy of the material response at hand. Non-linear isotropic hardening is considered as well. In this paper, the integration of the constitutive law is presented. The associative flow rule is integrated using the exponential map which preserves the plastic incompressibility condition. The numerical treatment of the problem is fully developed and expressions related to the local iteration and the consistent tangent operator are considered in detail. It is shown that while the consistent linearisation of the model is quite complicated, it still can be achieved if various intriguing implicit dependencies are identified and correctly dealt with. Various numerical examples of three-dimensional deformations of whole structural components are presented. The examples clearly illustrate the influence of anisotropy on finite elastoplastic deformations.

Increasing solution stability for finite-element modeling of elasto-plastic shell response

Abstract The present article introduces a highly efficient numerical simulation strategy for the analysis of elasto-plastic shell structures. An isoparametric Finite Element, based on a Finite Rotation Reissner–Mindlin shell theory in isoparametric formulation, is enhanced by a Layered Approach for a realistic simulation of nonlinear material behaviour. A general material model including isotropic hardening effects is embedded into each material point. A new, highly accurate integration scheme is combined with consistently linearized constitutive relations in order to achieve quadratic rate of convergence. A global Riks–Wempner–Wessels iteration scheme enhanced by a linear Line-Search procedure was used to trace arbitrary deformation paths. Numerical examples show the efficiency of the present concept.

On nonisothermal elastoplastic analysis of shell components employing realistic hardening responses

Abstract In the present paper, efficient numerical algorithms for elastoplastic analysis of shell-like structural components will be proposed employing nonisothermal, realistic, highly nonlinear hardening responses. The closest point projection integration algorithm is presented using a Reissner–Mindlin type kinematic shell model, completely formulated in tensor notation. Further, a consistent elastoplastic tangent modulus is derived, which ensures high convergence rates in the global iteration approach. The integration algorithm has been implemented into a layered assumed strain isoparametric finite element, which also enables geometrical nonlinearities including finite rotations. The nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed. Under the assumption of an adiabatic process, the increase in temperature is computed during elastoplastic deformation. Robustness and numerical stability of the proposed algorithms are demonstrated.

Homogenized Elastic Properties of Graphene for Small Deformations

In this paper, we provide the quantification of the linear and non-linear elastic mechanical properties of graphene based upon the judicious combination of molecular mechanics simulation results and homogenization methods. We clarify the influence on computed results by the main model features, such as specimen size, chirality of microstructure, the effect of chosen boundary conditions (imposed displacement versus force) and the corresponding plane stress transformation. The proposed approach is capable of explaining the scatter of the results for computed stresses, energy and stiffness and provides the bounds on graphene elastic properties, which are quite important in modeling and simulation of the virtual experiments on graphene-based devices.

On the increase of computational algorithm efficiency for elasto‐plastic shell analysis

Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the a...

C1 continuity finite element formulation in second-order computational homogenization scheme

The paper describes a second-order two-scale computational homogenization procedure for modeling of heterogeneous materials at small strains. The Aifantis theory of linear elasticity has been described and implemented into the two dimensional C1 continuity triangular finite element formulation. The element has been verified on several patch tests and the computational efficiency of numerical integration of the element stiffness matrix has been tested as well. Furthermore, the C1 two dimensional triangular finite element based on full second gradient continuum is formulated and used for the macrolevel discretization in the frame of a multiscale scheme, where the RVE is discretized by the C0 quadrilateral finite element. The application of generalized periodic boundary conditions and the microfluctuation integral condition on RVE has been investigated. The presented numerical algorithms have been implemented into FE software ABAQUS via user subroutines and verified on a pure bending problem. The comparability of RVE size to the length scale parameter of gradient elasticity has been proved, and elastoplastic behavior of heterogeneous material has been also considered. The results obtained show good numerical efficiency of the proposed algorithms.