Homogenization of heterogeneous, fibre structured materials

This contribution presents a multi-scale homogenization method to model fibre structured materials. On the macroscopic level textiles are characterized by a large area-to-thickness ratio, such that a discretization with shell elements is numerically efficient. The material behavior is strongly influenced by the heterogeneous micro structure. To capture the contact on the micro level, the RVE is explicitly modelled by means of a volumetric micro sample and a shell specific homogenization scheme is applied to transfer the microscopic response to the macro level. Theoretical aspects are discussed and a numerical example for contact behavior of a periodic knitted structure is give

Two-scale parameter identification for heterogeneous elastoplastic materials

The aim of this paper is to describe a method for identifying micro material parameters using only macroscopic experimental data. The FE2 method is used to model the behavior of the complex materials with heterogeneous micro-structure. The resulting least squares problem, with the difference of the simulated and the measured macroscopic data in the objective function, is minimized using gradient-based optimization algorithms with respect to the microscopic material parameters. The gradient information is derived analytically within the discretized scheme

On the numerical integration of isogeometric interface elements

Zero-thickness interface elements are commonly used in computational mechanics to model material interfaces or to introduce discontinuities. The latter class requires the existence of a non-compliant interface prior to the onset of fracture initiation. This is accomplished by assigning a high dummy stiffness to the interface prior to cracking. This dummy stiffness is known to introduce oscillations in the traction profile when using Gauss quadrature for the interface elements, but these oscillations are removed when resorting to a Newton-Cotes integration scheme 1. The traction oscillations are aggravated for interface elements that use B-splines or non-uniform rational B-splines as basis functions (isogeometric interface elements), and worse, do not disappear when using Newton-Cotes quadrature. An analysis is presented of this phenomenon, including eigenvalue analyses, and it appears that the use of lumped integration (at the control points) is the only way to avoid the oscillations in isogeometric interface elements. New findings have also been obtained for standard interface elements, for example that oscillations occur in the relative displacements at the interface irrespective of the value of the dummy stiffness

A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities

In the present contribution a discontinuous finite element method for the computational modelling of strong and weak discontinuities in geometrically nonlinear elasticity is introduced. The location of the interface is independent of the mesh structure and therefore discontinuous elements are introduced, to capture the jump in the deformation map or its gradient respectively. To model strong discontinuities the cohesive crack concept is adopted. The inelastic material behaviour is covered by a cohesive constitutive law, which associates the cohesive tractions, acting on the crack surfaces, with the jump in the deformation map. In the case of weak discontinuities an extended Nitsche's method is applied, which ensures the continuity of the deformation map in a weak sense. The applicability of the proposed method is highlighted by means of numerical examples, dealing with both crack propagation and material interfaces

A FE Approach for the Computation of Strong and Weak Discontinuities at Finite Strains

A discontinuous finite element method for the computational modelling of strong and weak discontinuities at finite strains is introduced. The location of the interface is independent of the mesh structure and therefore discontinuous elements are introduced, to capture the jump in the deformation map and its gradient, respectively

Phenomenological modelling of self-healing polymers based on integrated healing agents

The present contribution introduces a phenomenological model for self-healing polymers. Self-healing polymers are a promising class of materials which mimic nature by their capability to autonomously heal micro-cracks. This self-healing is accomplished by the integration of microcapsules containing a healing agent and a dispersed catalyst into the matrix material. Propagating microcracks may then break the capsules which releases the healing agent into the microcracks where it polymerizes with the catalyst, closes the crack and 'heals' the material. The present modelling approach treats these processes at the macroscopic scale, the microscopic details of crack propagation and healing are thus described by means of continuous damage and healing variables. The formulation of the healing model accounts for the fact that healing is directly associated with the curing process of healing agent and catalyst. The model is implemented and its capabilities are studied by means of numerical examples

A finite element method for the computational modelling of cohesive cracks

The present contribution is concerned with the computational modelling of cohesive cracks in quasibrittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage-type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concer ning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method

Two-scale elastic parameter identification from noisy macroscopic data

A two-scale parameter identification procedure to identify microscopic elastic parameters from macroscopic data is introduced and thoroughly analyzed. The macroscopic material behavior of microscopically linear elastic heterogeneous materials is described by means of numerical homogenization. The microscopic material parameters are assumed to be unknown and are identified from noisy macroscopic displacement data. Various examples of microscopically heterogeneous materials—with regularly distributed pores, particles, or layers—are considered, and their parameters are identified from different macroscopic experiments by means of a gradient-based optimization procedure. The reliability of the identified parameters is analyzed by their standard deviations and correlation matrices. It was found that the two-scale parameter identification works well for cellular materials, but has to be designed carefully for layered materials. If the homogenized macroscopic material behavior can be described by less material parameters than the microscopic material behavior, as, e.g., for regularly distributed particles, the identification of all microscopic parameters from macroscopic experiments is not possible

Computational Homogenization of One-dimensional Textile Structures

In this contribution a computational homogenization method for one-dimensional technical textiles, i.e. ropes or cables, is developed. Regarding the large length-tothickness ratio that characterizes rope-like textiles on the macro level, a discretization with beam elements is numerically efficient. The homogeneous macro level is influenced by the heterogeneous micro structure involving contact between the fibers. Therefore, the fibers are modeled explicitly a representative volume element to capture the contact within interactions. For the connection of the two scales a specific homogenization method is introduced involving theoretical aspects and numerical examples for periodic rope-like structures