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This study aims to develop a new analysis approach devised by incorporating a gradient-enhanced microplane damage model (GeMpDM) into isogeometric analysis (IGA), which shows computational stability and capability in accurately predicting crack propagations in structures with complex geometries.

For the non-local microplane damage modeling, the maximum modified von-Mises equivalent strain among all microplanes is regularized as a representative quantity. This characterization implies that only one additional governing equation is considered, which improves computational efficiency dramatically. By combined use of GeMpDM and IGA, quasi-static and dynamic numerical analyses are conducted to demonstrate the capability in predicting crack paths of complex geometries in comparison to FEM and experimental results.

The implicit scheme with the adopted damage model shows favorable numerical stability and the numerical results exhibit appropriate convergence characteristics concerning the mesh size. The damage evolution is successfully controlled by a tension-compression damage factor. Thanks to the advanced geometric design capability of IGA, the details of crack patterns can be predicted reliably, which are somewhat difficult to be acquired by FEM. Additionally, the damage distribution obtained in the dynamic analysis is in close agreement with experimental results.

The paper originally incorporates GeMpDM into IGA. Especially, only one non-local variable is considered besides the displacement field, which improves the computational efficiency and favorable convergence characteristics within the IGA framework. Also, enjoying the geometric design ability of IGA, the proposed analysis method is capable of accurately predicting crack paths reflecting the complex geometries of target structures.

The purpose of this study is the numerical investigation of densification and molding processes of wood. Providing theoretical and numerical approaches with respect to a consistent multi-physical finite element method framework are further goals of this research.

Constitutive phenomenological descriptions of the thermo-mechanical and moisture-dependent material characteristics of wood are introduced. Special focus is given to a consistent hygro-thermo-mechanical modeling at finite deformations to capture the realistic material behavior of wood, especially when it is subjected to densification and molding processes.

Realistic theoretical formulations of different hygro-thermo-mechanical processes are provided. A successful numerical modeling is demonstrated for beech wood by validation at experimental findings.

The constitutive laws and numerical findings are new, as they govern a multi-physical large deformation framework and are applied to the advanced technology of densification and molding of wood.

This paper aims to introduce a method to couple truss finite elements to the material point method (MPM). It presents modeling reinforced material using MPM and describes how to consider the bond behavior between the reinforcement and the continuum.

The embedded approach is used for coupling reinforcement bars with continuum elements. This description is achieved by coupling continuum elements in the background mesh to the reinforcement bars, which are described using truss- finite elements. The coupling is implemented between the truss elements and the continuum elements in the background mesh through bond elements that allow for freely distributed truss elements independent of the continuum element discretization. The bond elements allow for modeling the bond behavior between the reinforcement and the continuum.

The paper introduces a novel method to include the reinforcement bars in the MPM applications. The reinforcement bars can be modeled without any constraints with a bond-slip constitutive model being considered.

As modeling of reinforced materials is required in a wide range of applications, a method to include the reinforcement into the MPM framework is required. The proposed approach allows for modeling reinforced material within MPM applications.

The purpose of this paper is to propose a path-finding algorithm to solve problems with an arbitrary load-displacement relationship which results from geometrical and material nonlinear models to simulate e.g. timber structures realistically.

A method using combined load and displacement control for the Newton method along with path-characterising measures and sub-incremention is introduced. A path-related stiffness measure is used to identify the situation when it is necessary to select the displacement control and chose the best degree of freedom as a parameter instead of the load factor. The nonlinearity index extracts information about the convergence behaviour during one incremental step. Together with the reduction of the load increments it avoids leaving the equilibrium path.

The method is discussed based on numerical examples with highly nonlinear behaviour. It is capable to solve systems with decreasing load capacity and snap-back effects.

The algorithm combines load and displacement control and adaptively choses the method and the corresponding degree of freedom and cares for reliable path following.

The purpose of this paper is to investigate of interphasial effects, including temperature dependency, within fiber reinforced polymers on the overall composite behavior. Providing theoretical and numerical approaches in terms of a consistent thermomechanical finite element method framework are further goals of this research.

Starting points for achieving the aims of this research are the partial differential equations describing the evolution of the displacements and temperature within a continuum mechanical setting. Based on the continuous formulation of a thermomechanical equilibrium, constitutive equations are derived, accounting for the modeling of fiber reinforced thermosets and thermoplastics, respectively. The numerical solutions of different initial boundary value problems are obtained by a consistent implementation of the proposed formulations into a finite element framework.

The successful theoretical formulation and numerical modeling of the thermoinelastic matrix materials as well as the thermomechanical treatment of the composite interphase (IP) are demonstrated for an epoxy/glass system. The influence of the IP on the overall composite behavior is successfully investigated and concluded as a further aspect.

A thermomechanical material model, suitable for finite thermoinelasticity of thermosets and thermoplastics is introduced and implemented into a novel kinematic framework in context of the inelastic deformation evolution. The gradually changing material properties between the matrix and the fiber of a composite are continuously formulated and numerically processed, in order to achieve an efficient and realistic approach to model fiber reinforced composites.

The purpose of this paper is to evaluate current simulation capabilities for thin film delamination on the basis of real test data as well as a contribution to its extension in order to partly substitute experimental investigations.

The proposed model consists of a formulation that describes the behaviour of the bulk material and an approach that introduces the film's delamination capability. An implicit finite element framework with a cohesive zone implementation is used and described in detail. The numerical results on the basis of the a priori identified material parameters are related to the experimental work. In order to capture the obvious peel speed dependency of these delamination processes, a viscoelastic cohesive formulation is introduced and compared with a pure separation rate dependent cohesive material in the second part of this contribution.

The performed numerical simulations show a good approximation of the experimental peel process. The extension in order to take time‐dependent effects into account is required for the simulation of such problems. In contrast with the pure rate‐dependent model, the presented consistent formulation of the cohesive part is able to cover the whole range of observed material phenomena.

Owing to the absence of suitable experimental single mode investigations of the sealed layer, the used cohesive material parameters are identified in relation to the pre‐existing experimental results. Furthermore, the resultant peel force has a constant value due to the assumed homogeneous cohesive material and therefore gives only a mean approximation of the experimental values at this stage of the investigation.

The numerical representation of such a thin film delamination process in relation to real experimental results shows the additional capabilities and the usability of the implicit finite element method with a cohesive zone implementation in a clear and illustrative way. The first proposed cohesive extension based on a rheological model shows the capability to cover the full range of time‐dependent interface layer behaviour.

Derives a formulation for spatial stress tensors and spatial material tensors of hyperelastic material. Looks at a class of materials with the strain energy function decomposed into a volumetric and a deviatoric part. Separate terms formulate the strain energy with respect to the invariants of the left Cauchy‐Green tensor. Stress and material tensors, which play a crucial role in the solution process of the finite element formulation, are derived solely in the current configuration. Applies the described framework to several different constitutive models based on phenomenologically and physically motivated material descriptions. Proposes a formulation for the finite element implementation of van der Waals material. Compares numerical results with experimental investigations given in the literature. For three‐dimensional finite element computations standard elements and mixed elements, based on a three‐field variational principle where displacements, the hydrostatic pressure and the dilatations are independent variables, are used.

The purpose of this paper is to develop a constitutive model in cyclic viscoplasticity of perfluoroelastomers that accounts for the Mullins effect and to determine adjustable parameters in the stress‐strain relations by fitting observations in mechanical tests.

A perfluoroelastomer with a complicated internal structure is modeled as an equivalent incompressible, permanent, non‐affine network of chains with constrained mobility. Its viscoplastic response at finite strains is treated as sliding of junctions between chains with respect to their reference positions. Damage accumulation is associated with acceleration of plastic flow of junctions driven by growth of free volume. Stress‐strain relations are derived by using the Clausius‐Duhem inequality.

Constitutive equations are developed that correctly describe the mechanical behavior of perfluoroelastomers under cyclic loading with stress‐ and strain‐controlled deformation programs and arbitrary numbers of cycles. Adjustable parameters in the stress‐strain relations are found by matching experimental data in uniaxial tensile tests. Numerical simulation demonstrates that the model adequately predicts characteristic features of the Mullins effect.

A constitutive model is derived that can be applied for description of the viscoplastic response in perfluoroelastomers at cyclic loading with complicated deformation programs and prediction of their time to failure under fatigue conditions.

This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.

The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.

The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.

This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

This paper proposes a unified original general framework, designed to theoretically develop and to extremely easily implement elastoplastic constitutive laws defined in the so called two-invariants space, both in small and finite strain regime.

A general return mapping algorithm is proposed, and particularly a standard procedure is developed to compute the two algorithmic tangent operators, required to solve the Newton–Raphson scheme at the local and global level and thus cast the elastoplastic algorithm within a FEM code.

This work demonstrates that the proposed procedure is fully general and can be applied whatever is the elastic law, the yield surface, the plastic potential function and the hardening law. Several numerical examples are reported, not only to demonstrate the accuracy and robustness of the algorithm, but also explain how to use this general algorithm also in other applications.

The proposed algorithm and its numerical implementation into a FEM code is new and original. The usefulness and the value of the algorithm is twofold: (1) it can be implemented in a small and finite strain simulation FEM code, in order to handle different types of constitutive laws in the same modular way, thus fully leveraging on modern object-oriented coding approach; (2) it can be used as a framework to develop (and then to implement) new constitutive models, since the researcher can simply define the relevant functions (and its main derivatives) and automatically get the numerical algorithm.