Constitutive Formulations for Network Materials

Various constitutive formulations can be employed to simulate the coupled behaviour of electro‐active polymers (EAP). Those distinct mathematical descriptions vary with respect to the manner in which the electric field is coupled to the deformation. However, in principle, they are all capable of emulating the finite coupled response of EAP. The underlying coupling mechanism of largely deformable materials can be identified through experimental characterization. This contribution addresses the constitutive and finite element modelling of the actuation response of both isotropic and anisotropic EAP, where different material formulations are considered and implemented within a finite element framework. Those various material formulations are mathematically treated and employed to simulate electro‐mechanical experiments of dielectric materials. Existing coupled electro‐mechanical tests of active materials are referred to, where it is sought to employ different constitutive models to fit the experimental observations. Within the undertaken study, the capability of different descriptions to predict electro‐mechanical instabilities is evaluated. Regarding the numerical implementation of the model, it is referred to an electro‐mechanical Q1P0 finite element formulation. After performing the study and fitting experimental results associated to isotropic materials, the actuation response of several anisotropic EAP‐based structures is emulated.

A constitutive formulation and numerical procedure to model rate effects on porous materials at finite strains

A theoretical homogenized constitutive model formulation for matrix composite materials reinforced with curved fibers

Highly variable deformations of a human anterior cruciate ligament (ACL) cannot be adequately quantified by one-dimensional, localized measurements and/or analyses. This paper describes a new structurally-motivated phenomenological approach. Such assumption was made that the ACL ligament can be idealized as being composed of a homogeneous matrix in which two non-interacting families of densely distributed extensible fibers are embedded. A non-linear stress-strain characteris- tic exhibited by multiple collagen fibers was represented by the multi-linear curve. Then a constitutive equation for the ACL composite was formulated. Using the finite element method, finite deformation and stress distribution of the ACL as a function of knee flexion were introduced through simulation.

Methods in entropic thermomechanics

Constitutive relations and finite element formulations for elastic-plastic and rigid-plastic materials in sheet metal forming analysis are reviewed. In the present study an elastic-plastic material model and a Total Lagrangian finite element formulation is used. Arbitrarily shaped punches and dies can be treated. The interface contact forces between the tools and the metal sheet are assumed to be either of Coulomb friction type or simply a constant shear stress. The effects of various material parameters and friction in the strain distribution in hemispherical punch stretching have been investigated numerically and are shown in diagrams. A few experimentally determined strain distributions are shown and are compared with results from finite element calculations.

Elements of constitutive model formulation for simple materials within a thermodynamic, finite deformation framework are reviewed, especially as related to the rational mechanics approach. Selected applications to anisothermal viscoelasticity, viscoplasticity, elasticity and damage mechanics are described.

A theoretical and numerical comparison of three finite strain finite element formulations for elastic-viscoplastic materials

Constitutive and failure behaviour in selective laser melted stainless steel for microlattice structures

An alternate constitutive formulation for visco-elastic materials, with particular emphasis on macromolecular viscoelastic fluids, is presented by generalizing Maxwell's idealized separation of elastic and relaxation mechanisms. The notion ofrelative rate of change of elastic stress is identified, abstracted, and formulated with the help of the established theory of finitely elastic isotropic materials. This given a local rate-type constitutive relation for an elastic mechanism in a simple material. For the simplest class of viscoelastic polymer melts, the notion of rate of change of elastic stress and its damped accumulation is identified and formulated. Under conditions of moderate strain rates, this scheme implies the reliable K-BKZ model for a class of polymer melts. An obvious extension generalizes the remaining classical spring-dashpot models.

Piezoelectric stack actuators have been used in structural acoustic controls, and active vibration isolation systems. In recent tests of heavy duty vibration isolation systems, it has been found that piezoelectric stack actuators under large loadings and high driving voltages can produce substantial heat to cause failure. This paper presents preliminary results of a research effort that was set out to investigate the heat production and thermal effects on the actuator performance In the paper, a general constitutive formulation of piezoelectric materials is presented starting from the first law of thermal dynamics. the constitutive equations involve thermoelastic, pyroelectric and, of course, piezoelectric effect. A variational principle based on Oden's approach is then developed. As a special case, the equations of motion for a circular multilayer stack piezoelectric actuator are derived from the variational principle. Numerical results of blocked force and free stroke of the actuator are presented in the paper. The effects of various parameters on these two common specifications of solid state actuators are studied.

A model incorporating damage evolution to predict the penetration behavior of a ceramic target subjected to the long projectile impact

Micro–macro constitutive modeling and finite element analytical-based formulations for fibrous materials: A multiscale structural approach for crimped fibers

Aspects of plastic anisotropy in damage accumulation are considered for a class of hexagonal crystals that deform by combined slip and twinning. Focus is placed on crystallographic aspects that are currently absent from constitutive formulations of ductile damage. To this end, three-dimensional finite-element calculations are carried out using a cubic unit cell containing a single void embedded in a crystal matrix. Plastic flow in the latter is described using crystal plasticity with parameters representative of single crystal pure magnesium. The effect of void oblateness is analyzed in some detail, as voids often form as blunted microcracks in Mg alloys. The analyses reveal two aspects peculiar to twinning-mediated void growth: (1) insensitivity of the effective stress-strain response to void oblateless and (2) a plastic auxetic effect. Both aspects manifest under certain circumstances. Some implications in terms of incorporating the uncovered crystallographic aspects in coupled plasticity-damage formulations of anisotropic materials are discussed.

Constitutive models for random fiber network materials: A review of current status and challenges