Review of Magnetic Shape Memory Polymers and Magnetic Soft Materials

Magnetic soft materials (MSMs) and magnetic shape memory polymers (MSMPs) have been some of the most intensely investigated newly developed material types in the last decade, thanks to the great and versatile potential of their innovative characteristic behaviors such as remote and nearly heatless shape transformation in the case of MSMs. With regard to a number of properties such as shape recovery ratio, manufacturability, cost or programming potential, MSMs and MSMPs may exceed conventional shape memory materials such as shape memory alloys or shape memory polymers. Nevertheless, MSMs and MSMPs have not yet fully touched their scientific-industrial potential, basically due to the lack of detailed knowledge on various aspects of their constitutive response. Therefore, MSMs and MSMPs have been developed slowly but their importance will undoubtedly increase in the near future. This review emphasizes the development of MSMs and MSMPs with a specific focus on the role of the magnetic particles which affect the shape memory recovery and programming behavior of these materials. In addition, the synthesis and application of these materials are addressed.

Lagrange multiplier approach to unilateral indentation problems: Well-posedness and application to linearized viscoelasticity with non-invertible constitutive response

The Boussinesq problem describing indentation of a rigid punch of arbitrary shape into a deformable solid body is studied within the context of a linear viscoelastic model. Due to the presence of a non-local integral constraint prescribing the total contact force, the unilateral indentation problem is formulated in the general form as a quasi-variational inequality with unknown indentation depth, and the Lagrange multiplier approach is applied to establish its well-posedness. The linear viscoelastic model that is considered assumes that the linearized strain is expressed by a material response function of the stress involving a Volterra convolution operator, thus the constitutive relation is not invertible. Since viscoelastic indentation problems may not be solvable in general, under the assumption of monotonically non-increasing contact area, the solution for linear viscoelasticity is constructed using the convolution for an increment of solutions from linearized elasticity. For the axisymmetric indentation of the viscoelastic half-space by a cone, based on the Papkovich–Neuber representation and Fourier–Bessel transform, a closed form analytical solution is constructed, which describes indentation testing within the holding-unloading phase.

Phase Field Modeling of Brittle Fracture Based on the Cell-Based Smooth FEM by Considering Spectral Decomposition

The spectral decomposition of the strain tensor is an essential technique to deal with the fracture problems via phase field method, and some incorrect results may be obtained without it. A novel phase field model for brittle fracture is developed based on cell-based smooth finite element (CS-FEM) and the spectral decomposition is taken into account. In order to describe the nonlinearity behaviors which contain the varied stress and elastic constitutive response caused by spectral decomposition. A second-order stress tensor and a fourth-order constitutive tensor based on decomposition of strain tensor are derived. A fundamental framework of CS-FEM is established to solve the phase field fracture problems, implemented by user-defined element (UEL) subroutine of ABAQUS software. The proposed model is validated by a typical Mode II crack, and the results show that the derived tensors are effective. Phase field parameter, CS-FEM parameter and mesh inhomogeneity are investigated to provide some useful suggestion for further development. Some classical numerical examples are solved by using the present model. The studies demonstrate that the proposed method can successfully overcome mesh distortion; the number of smooth cell does not show influences on the accuracy. Moreover, some results show that this method has the advantage over the standard FEM in convergence and computing efficiency.