Computer modelling and experimental investigation of phase change hysteresis of PCMs: The state-of-the-art review

Phase-Field Material Point Method for dynamic brittle fracture with isotropic and anisotropic surface energy

The research progress on phase change hysteresis affecting the thermal characteristics of PCMs: A review

A multiaxial degrading hysteretic model is developed, enabling consistent multiaxial yield/capacity surface evolution with degradations, and is appropriately incorporated in a finite-elemen...

Hysteretic Beam Finite-Element Model Including Multiaxial Yield/Capacity Surface Evolution with Degradations

Modeling RC column flexural failure modes under intensive seismic loading

This work presents the development of a hysteretic beam element in the context of the finite element method, that is suitable for the inelastic dynamic analysis of framed structures. The formulation proposed is able to capture the main characteristics of hysteresis in structural systems and mainly accounts for stiffness degradation, strength deterioration and pinching phenomena, as well as for non-symmetrical yielding that often characterizes their behavior. The proposed formulation is based on the decoupling of deformations into elastic and hysteretic parts by considering additional hysteretic degrees of freedom, i.e., the hysteretic curvatures and hysteretic axial deformations. The direct stiffness method is employed to establish global matrices and determine the mass and viscous damping, as well as the elastic stiffness and the hysteretic matrix of the structure that corresponds to the newly added hysteretic degrees of freedom. All the governing equations of the structure, namely the linear global equations of motion and the nonlinear evolution equations at elemental level that account for degradations and pinching, are solved simultaneously. This is accomplished by converting the system of equations into state space form and implementing a variable-order solver based on numerical differentiation formulas (NDFs) to determine the solution. Furthermore, hysteretic loops and degradation phenomena are easily controlled by modifying the model parameters at the element level enabling simulations of a more realistic response. Numerical results are presented and compared against experimental results and other finite element codes to validate the proposed formulation and verify its ability to simulate complex hysteretic behavior exhibiting cyclic degradations.

Hysteretic beam element with degrading smooth models

The material point method (MPM) is an advancement of particle in cell method, in which Lagrangian bodies are discretized by a number of material points that hold all the properties and the state of the material. All internal variables, stress, strain, velocity, etc., which specify the current state, and are required to advance the solution, are stored in the material points. A background grid is employed to solve the governing equations by interpolating the material point data to the grid. The derived momentum conservation equations are solved at the grid nodes and information is transferred back to the material points and the background grid is reset, ready to handle the next iteration. In this work, the standard explicit MPM is extended to account for smooth elastoplastic material behavior with mixed isotropic and kinematic hardening and stiffness and strength degradation. The strains are decomposed into an elastic and an inelastic part according to the strain decomposition rule. To account for the different phases during elastic loading or unloading and smoothening the transition from the elastic to inelastic regime, two Heaviside-type functions are introduced. These act as switches and incorporate the yield function and the hardening laws to control the whole cyclic behavior. A single expression is thus established for the plastic multiplier for the whole range of stresses. This overpasses the need for a piecewise approach and a demanding bookkeeping mechanism especially when multilinear models are concerned that account for stiffness and strength degradation. The final form of the constitutive stress rate–strain rate relation incorporates the tangent modulus of elasticity, which now includes the Heaviside functions and gathers all the governing behavior, facilitating considerably the simulation of nonlinear response in the MPM framework. Numerical results are presented that validate the proposed formulation in the context of the MPM in comparison with finite element method and experimental results.

Hysteretic behavior using the explicit material point method

Abstract. The material point method (MPM) is one of the latest developments in particle in cell methods (PIC). The structure is discretized into a number of material points that hold all the state variables of the system [1] such as stress, strain, velocity, displacement etc. These properties are then mapped to a temporary background grid and the governing equations are solved. The momentum conservation equations (together with energy and mass conservation considerations) are solved at the grid nodes. The state variables of the particles are then updated by transferring the solutions from the grid nodes back to the material points. Since the background grid is used only to solve the governing equations at the end of each computational step it can be reset to its undistorted form and thus mesh distortion and element entanglement are avoided.

Material point method for deteriorating inelastic structures

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Hysteretic model for the explicit material point method

The Material Point Method (MPM) is an extension of particle in cell methods (PIC) for solid mechanics problems. The structure is discretized into a set of material points that hold all the state variables of the system [1] such as stress, strain, velocities etc. A background grid is employed and the variables are mapped to the nodes of the grid. The momentum conservation equations with energy and mass conservation considerations are solved at the grid nodes and the updated state variables are again mapped back to the material points updating their positions and velocities. The background grid is used only to solve the governing equations at the end of each computational step and then it is reset back to its original undeformed configuration. It is used only as a scratchpad for calculations and thus mesh distortion that constitutes a problem in Finite Element simulations is avoided. In this work the explicit formulation of the MPM is employed. According to the strain decomposition rule the strains are uncoupled into an elastic and an inelastic part. The constitutive law follows a Bouc-Wen [3] type formulation and provides a smooth transition to the inelastic regime. In the same manner a damage driving variable is introduced as a function of the total strain. The incremental damage behavior is smoothed similarly to the plasticity formulation following their common mathematical structure [2]. The above formulation is incorporated in the expression of the tangent modulus of elasticity as Heaviside type functions that control the inelastic behavior and damage at elemental level. Results are presented that validate and verify the proposed formulation in the context of the Material Point Method.

Christos D. Sofianos

Papers

Hysteretic beam element with degrading smooth models

Hysteretic behavior using the explicit material point method

Material point method for deteriorating inelastic structures

Hysteretic model for the explicit material point method

Smooth plasticity and damage model for the material point method