The virtual element method (VEM) was developed not too long ago, starting with the paper
2
related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of ...different elements; however, it has so far not applied to one-dimensional structures like trusses and beams. Here we study several VEM elements suitable for trusses and beams and show that the virtual element methodology produces elements that are equivalent to well-known finite elements but also elements that are different, especially for higher-order ansatz functions. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns as finite beam elements. Furthermore, the formulation allows to compute nonlinear structural problems undergoing large deflections and rotations.
The virtual element method has been developed over the last decade and applied to problems in elasticity and other areas. The successful application of the method to linear problems leads naturally ...to the question of its effectiveness in the nonlinear regime. This work is concerned with extensions of the virtual element method to problems of finite strain plasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered. The formulation is based on minimization of an incremental energy expression, with a novel construction of the stabilization energy for elasto-plasticity. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties.
Variationally consistent phase-field methods have been well established in the recent decade. A wide range of applications to brittle and ductile fracture problems could already demonstrate the ...ability to predict complex crack patterns in three-dimensional geometries. However, current phase-field models to ductile fracture are not formulated for both, material and geometrical non-linearities. In this contribution we present a computational framework to account for three-dimensional fracture in ductile solids undergoing large elastic and plastic deformations. The proposed model is based on a triple multiplicative decomposition of the deformation gradient and an exponential update scheme for the return map in the time discrete setting. This increases the accuracy on the entire range of the ductile material behavior encompassing elastoplasticity, hardening, necking, crack initiation and propagation. The accuracy and convergence properties are further improved by the application of a higher order phase-field regularization and a gradient enhanced plasticity model. To account for the ductile behavior at fracture, a model of the critical fracture energy density depending on the equivalent plastic strain is proposed and validated by experimental data.
•We present a higher order phase-field model to non-linear ductile fracture.•A novel multiplicative triple split of the deformation gradient is introduced.•An exponential update scheme for the return map in the time discrete setting is applied.•To account for ductile fracture a novel model of the critical fracture energy is introduced.•The approach is able to account for the entire range of ductile fracture within non-linear elastoplasticity.
Phase-field methods to regularize sharp interfaces represent a well established technique nowadays. In fracture mechanics, recent works have shown the capability of the method for brittle as well as ...ductile problems formulated within the fully non-linear regime. In this contribution, we introduce a framework to simulate porous-ductile fracture in isotropic thermo-elasto-plastic solids undergoing large deformations. Therefore, a modified Gurson–Tvergaard–Needleman GTN-type plasticity model is combined with a phase-field fracture approach to account for a temperature-dependent growth of voids on micro-scale followed by crack initiation and propagation on macro-scale. The multi-physical formulation is completed by the incorporation of an energy transfer into the thermal field such that the temperature distribution depends on the evolution of the plastic strain and the crack phase-field. Eventually, this physically comprehensive fracture formulation is validated by experimental data.
•We present a novel framework for the simulation of non-linear porous-ductile fracture.•A phase-field fracture approach is combined with a thermoelastoplasticity formulation.•A modified GTN-type model is introduced to account for the growth of micro-voids.•The multi-physical formulation rests on an energy transfer into thermal field.•The capabilities of the analysis for complex material behavior are demonstrated.
A virtual element method for contact Wriggers, P.; Rust, W. T.; Reddy, B. D.
Computational mechanics,
12/2016, Letnik:
58, Številka:
6
Journal Article
Recenzirano
The problem of contact between two elastic bodies is addressed computationally using the virtual element method (VEM). The use of the VEM allows the use of non-matching meshes for the two bodies, and ...hence obviates the need for node-to-node contact on the candidate contact interfaces. The contact constraint is imposed using either a Lagrange multiplier or penalty formulation. A number of numerical examples illustrate the robustness and accuracy of the algorithm.
Meshfree approximation schemes possess a high potential in computer aided engineering due to their large flexibility. Especially the tremendous progress in processor technology within recent years ...relativizes the increase in computation time due to the inherent search algorithm. Nevertheless meshfree approximation schemes are still faced with some challenges, like imposition of Dirichlet boundary conditions, robustness of the algorithm and accuracy. The recent developed Optimal Transportation Meshfree (OTM) method seemed to overcome most of these problems. In this paper the OTM solution scheme is combined with a standard search algorithm in order to allow a simple and flexible computation. However this scheme is not stable for some examples of application. Hence an investigation is conducted which shows that the reason for this instability is due to underintegration. Based on this investigation a remedy to stabilize the algorithm is suggested which is based on well known concepts to control the hourglass effects in the Finite Element Method. In contrast to the original publication, the OTM algorithm is derived here from the principle of virtual work. Local maximum entropy shape functions are used which possess a weak Kronecker-δ property. This enables a direct imposition of Dirichlet boundary conditions if the boundary is convex. The limitations of this basis function are also addressed in this paper. Additionally, the search algorithm presented fulfills basic topological requirements. Several examples are investigated demonstrating the improved behavior of the stabilized OTM algorithm.
The present work establishes a reliable model to describe the influence due to the interfacial transition zone (ITZ) between cement paste and aggregates on the mechanical, thermal and diffusion ...properties of concrete. The mesostructure of concrete consists of aggregates with a random distribution embedded in the cement paste as well as the interface elements with zero-thickness representing the ITZ. In this work, the cohesive zone model (CZM) is used to model the debonding at the ITZ between cement paste and aggregates. Furthermore, a traction-separation law in CZM combined with micromechanically motivated thermal flux-separation relation and diffusion flux-separation relation is developed, thus enabling to describe the temperature jump and humidity jump across the cohesive crack.
The Peridynamic Petrov–Galerkin (PPG) method is a meshfree approach based on the peridynamic integro-differential form of the momentum equation. The spurious oscillations in the common peridynamic ...correspondence formulation are investigated. They occur due to an inadmissible linearized mapping of the family deformation field. This leads to a generalized correspondence formulation, which contains the common formulation as a special case. It is based on the weak form of the peridynamic momentum equation. Test and trial function requirements are examined which ensure an exact imposition of Dirichlet and Neumann boundary conditions and Weighted Least Square (WLS) shape functions as well as Local Maximum Entropy (LME) approximants are utilized to examine the PPG Method. A consistent linearization is provided, which can also be used to speed up common implicit peridynamic correspondence codes. It is used in an implicit quasistatic framework to investigate the impact of different shape function combinations. Test cases show that low-energy modes can be prevented by the PPG Method and highlight the fast convergence and stability.
•An ansatz function based correspondence formulation eliminates low-energy modes.•Ansatz function conditions enforce accurate boundary conditions and convergence.•Consistent linearization enables efficient implicit peridynamic correspondence codes.
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