Constitutive Formulation Research Articles

Simulation of Autogenous Self‐Healing in Lime‐Based Mortars

ABSTRACTThroughout history, architectural heritage has been constructed using masonry, clay or stone elements, and lime‐based mortars. Over time, old buildings are subjected to different degrees of movement and degradation, leading to the formation of microcracks. Water dissolves and transports lime in mortar, but when the water evaporates, the lime is deposited and heals cracks in a process known as autogenous healing. Lime‐based mortars can regain some mechanical properties due to their healing capacity, given certain conditions. In the present work, a constitutive formulation has been developed to simulate cracking and healing in lime‐based mortars. The proposed model captures the residual displacements within cracks, associated with interacting crack surface asperities, as well as the healing effect on mechanical properties. A new approach is described which expresses these mechanisms mathematically within a micromechanical formulation. The proposed model was validated by comparing the outputs with experimental data. The results show that the new continuum micromechanical damage‐healing model could capture the damage‐healing cycle with good accuracy.

Non-invasive regional parameter identification of degenerated human meniscus

Accurate identification of local changes in the biomechanical properties of the normal and degenerative meniscus is critical to better understand knee joint osteoarthritis onset and progression. Ex-vivo material characterization is typically performed on specimens obtained from different locations, compromising the tissue's structural integrity and thus altering its mechanical behavior. Therefore, the aim of this in-silico study was to establish a non-invasive method to determine the region-specific material properties of the degenerated human meniscus. In a previous experimental magnetic resonance imaging (MRI) study, the spatial displacement of the meniscus and its root attachments in mildly degenerated (n = 12) and severely degenerated (n = 12) cadaveric knee joints was determined under controlled subject-specific axial joint loading. To simulate the experimental response of the lateral and medial menisci, individual finite element models were created utilizing a transverse isotropic hyper-poroelastic constitutive material formulation. The superficial displacements were applied to the individual models to calculate the femoral reaction force in an inverse finite element analysis. During particle swarm optimization, the four most sensitive material parameters were varied to minimize the error between the femoral reaction force and the force applied in the MRI loading experiment. Individual global and regional parameter sets were identified. In addition to in-depth model verification, prediction errors were determined to quantify the reliability of the identified parameter sets. Both compressibility of the solid meniscus matrix (+141 %, p ≤ 0.04) and hydraulic permeability (+53 %, p ≤ 0.04) were significantly increased in the menisci of severely degenerated knees compared to mildly degenerated knees, irrespective of the meniscus region. By contrast, tensile and shear properties were unaffected by progressive knee joint degeneration. Overall, the optimization procedure resulted in reliable and robust parameter sets, as evidenced by mean prediction errors of <1 %. In conclusion, the proposed approach demonstrated high potential for application in clinical practice, where it might provide a non-invasive diagnostic tool for the early detection of osteoarthritic changes within the knee joint.

Rate-dependent constitutive behavior and mechanism of CMDB under tension loading

The composite modified double-base propellants (CMDB) were experimentally investigated for mechanical behavior under wide tension strain rate loading from 0.0001 s−1 to 2500 s−1, based on Instron mechanical machine and modified Hopkinson tension bar technique. Stress-strain curves were obtained for its strain rate effect and integrality evaluation. The results indicated that CMDB presents high rate-dependence with flow stress distinctly increase as loading strain rate increasing. A succinct constitutive formulation is established with only five parameters, to characterize well the rate-dependence and strain hardening behavior. The fracture morphologies were investigated by scanning electron microscopy, and it is indicated that they are also rate-dependent: the cavitation and matrix damage induced from matrix deformation work less but more RDX particles fractures with strain rate increasing. Equivalent unit cell model with brittle cracking was established to simulate the mechanical behavior and failure characteristics of CMDB. The results reveal that with increasing loading strain rates, CMDB presents a tough-brittle transition, with less cavitation and matrix damage induced by matrix deformation, while more RDX particles fracture. Series of simulated results confirm qualitatively the experimental observations, and the obtained stress contours facilitate to validate the observed characteristics and propose reasonable mechanisms.

A novel scale-bridging method for MSMA linking continuum thermodynamics constitutive formulations to lumped system-level models

This work introduces a novel scale-bridging method between a continuum thermodynamics constitutive model and a lumped system-level model for magnetic shape memory alloys (MSMA). With this method, system models for real-time operations are generated based on virtual experiments using the constitutive model. The proposed method addresses the fact that, while constitutive models for MSMA typically only require small sets of parameters as input, their evaluation is still computationally expensive. System models for control engineering, however, require extensive experimental parameterization, while their evaluation is highly time-efficient. The proposed scale-bridging method has the potential to combine a small parameterization effort and a low computational cost of the real-time system model. Additionally, the constitutive model is utilized to investigate whether it can determine the individual behavior of MSMA samples. This is important since the inherent model parameters, while valid for ideal single crystals, deviate for non-ideal MSMA sample behavior. To this end, the MSMA constitutive model, based on a global variational principle originally proposed by Kiefer et al is supplemented by various extensions, including a more robust algorithmic treatment. A parameter identification procedure is introduced to optimize the constitutive model parameters based on an outer hysteresis curve for a particular load case. By conducting virtual experiments with the constitutive model, data sets are generated to parameterize Preisach hysteresis models as numerical approximations of the constitutive models. The resulting hysteresis models are compared with physical experiments using an MSMA test bench for different load cases. It is shown that the proposed scale-bridging method successfully generates hysteresis models derived from constitutive models. While maintaining accuracy comparable to strictly phenomenological models across various load cases (as validated through physical MSMA test bench experiments), these models require significantly less parameterization effort than classical system models. This translates to faster model creation and broader applicability.

Uniaxial material model with softening for simulating the cyclic behavior of steel tubes in concrete‐filled steel tube beam‐columns

AbstractThis paper presents a new uniaxial constitutive material formulation with softening for simulating the inelastic behavior of steel rectangular tubes in concrete‐filled steel tube (CFST) members. The primary behavioral characteristics of the steel tube in CFST members are isolated and pronounced through a carefully designed experimental campaign with CFST specimens subjected to uniaxial strain‐based loading protocols. The model is expressed in an effective stress–strain domain, where the effective uniaxial strain is defined as the uniaxial displacement within a dissipative zone over a predefined length. In the pre‐peak state, the proposed model can effectively capture the combined kinematic/isotropic hardening and Bauschinger effect—characteristic of mild structural steels—within the framework of rate‐independent plasticity. In the post‐peak state, the proposed model traces strength deterioration due to outward local buckling, which is a characteristic nonlinear geometric instability in CFST members due to the presence of the filled concrete in the steel tube. The proposed constitutive formulation incorporates a softening branch that exponentially decays to trace the stabilization of the outward buckling wave within the buckling region in successive inelastic loading cycles. Cyclic deterioration of the effective stress is explicitly considered via an energy‐based rule. The proposed model is calibrated to a CFST dataset. Regression equations are proposed for predicting the input model parameters. These equations cover a wide range of geometric parameters and structural steel materials in CFST members. Comparisons with prior tests on actual CFST beam‐columns under planar symmetric cyclic loading suggest that conventional 2‐dimensional displacement‐based beam‐column elements can predict the full‐range of the hysteretic behavior of the CFST members with the proposed constitutive formulation including cases where the post‐peak response of CFST members exhibits negative stiffness.

Criterion for unhomogeneous yielding of porous materials

A criterion is developed for the unhomogeneous yielding of materials containing arbitrarily oriented ellipsoidal voids. The criterion is built upon classical estimates for pure pressure and pure shear. A data-driven approach is then followed to incorporate the effects of void shape and orientation. A large number of micromechanical unit cell results are used to calibrate the yield criterion. A key feature of the criterion is that it predicts a significant reduction of the effective shear yield strength due to mere void inclination, with the reduction increasing with the void dimension perpendicular to the shear. The coupling between tension and shear deformation results in an apparent rotation of the yield surface, which provides a sound micromechanical basis for predicting void closure in shear among other new features. Once supplemented with evolution equations of relevant internal parameters, the resulting constitutive formulation will enable ductile failure simulations heretofore impossible to carry out on a sound physical basis for general loading conditions.

Instability in Computational Models of Vascular Smooth Muscle Cell Contraction

PurposeThrough their contractile and synthetic capacity, vascular smooth muscle cells (VSMCs) can regulate the stiffness and resistance of the circulation. To model the contraction of blood vessels, an active stress component can be added to the (passive) Cauchy stress tensor. Different constitutive formulations have been proposed to describe this active stress component. Notably, however, measuring biomechanical behaviour of contracted blood vessels ex vivo presents several experimental challenges, which complicate the acquisition of comprehensive datasets to inform complex active stress models. In this work, we examine formulations for use with limited experimental contraction data as well as those developed to capture more comprehensive datasets.MethodsFirst, we prove analytically that a subset of constitutive active stress formulations exhibits unstable behaviours (i.e., a non-unique diameter solution for a given pressure) in certain parameter ranges, particularly for large contractile deformations. Second, using experimental literature data, we present two case studies where these formulations are used to capture the contractile response of VSMCs in the presence of (1) limited and (2) extensive contraction data.ResultsWe show how limited contraction data complicates selecting an appropriate active stress model for vascular applications, potentially resulting in unrealistic modelled behaviours.ConclusionOur data provide a useful reference for selecting an active stress model which balances the trade-off between accuracy and available biomechanical information. Whilst complex physiologically motivated models’ superior accuracy is recommended whenever active biomechanics can be extensively characterised experimentally, a constant 2nd Piola-Kirchhoff active stress model balances well accuracy and applicability with sparse contractile data.

M‐AGC tangent visco‐plastic operator with hardening/softening, and application to the visco‐plastic relaxation analysis of stable and unstable problems using fracture‐based geomechanical interfaces

AbstractA previous perfect visco‐plastic constitutive formulation of the Perzyna type incorporating the concepts of prescribed stress increments and m‐AGC tangent operator (m‐Assumed algorithmic generalized compliance tangent operator) is extended to the case of Hardening/Softening (H/S). This extension is possible thanks to the closed‐form solution developed for the evolution of the loading function during a visco‐plastic time step. The formulation is then applied to constitutive modeling of zero‐thickness interfaces on the basis of a well‐established fracture‐based elasto‐plastic formulation, which in this manner is extended to visco‐plasticity. The resulting model is implemented in the finite element (FE) and small‐strain context by using both a standard Newton Raphson scheme for physical visco‐plasticity in which visco‐plastic time corresponds to physical time, and a Visco‐Plastic Relaxation (VPR) scheme, in which time corresponds to a fictitious time governing the transition from the elastic to the inviscid elasto‐plastic response. The numerical implementation is verified satisfactorily for common loading cases at interfaces such as pure tension (mode I) opening and shear‐compression (mixed‐mode) cracking/sliding, showing that the visco‐plastic results match the predictions of the fracture mechanics inviscid model in the long term. In addition, it is also shown that the VPR strategy developed is capable of providing temporary stability while the equilibrium path is recovered during instability events such as a snap‐back in the load‐displacement curve. This feature opens the door to a number of potential advanced applications of the formulation developed in the geomechanical context.

The role of the extracellular matrix in the reduction of lateral force transmission in muscle bundles: A finite element analysis

Background and objectiveAging is associated with a reduction in muscle performance, but muscle weakness is characterized by a much greater loss of force loss compared to mass loss. The aim of this work is to assess the contribution of the extracellular matrix (ECM) to the lateral transmission of force in humans and the loss of transmitted force due to age-related modifications. MethodsFinite element models of muscle bundles are developed for young and elderly human subjects, by considering a few fibers connected through an ECM layer. Bundles of young and elderly subjects are assumed to differ in terms of ECM thickness, as observed experimentally. A three-element-based Hill model is adopted to describe the active behavior of muscle fibers, while the ECM is modeled assuming an isotropic hyperelastic neo-Hookean constitutive formulation. Numerical analyses are carried out by mimicking, at the scale of a bundle, two experimental protocols from the literature. ResultsWhen comparing numerical results obtained for bundles of young and elderly subjects, a greater reduction in the total transmitted force is observed in the latter. The loss of transmitted force is 22 % for the elderly subjects, while it is limited to 7.5 % for the young subjects. The result for the elderly subjects is in line with literature studies on animal models, showing a reduction in the range of 20–34 %. This can be explained by an alteration in the mechanism of lateral force transmission due to the lower shear stiffness of the ECM in elderly subjects, related to its higher thickness. ConclusionsComputational modeling allows to evaluate at the bundle level how the age-related increase of the ECM amount between fibers affects the lateral transmission of force. The results suggest that the observed increase in ECM thickness in aging alone can explain the reduction of the total transmitted force, due to the impaired lateral transmission of force of each fiber.

A finite deformation formulation for amorphous glassy polymers under moderate and impact strain rates: Application to adhesive films

This work describes a novel finite strain hypo-elastic formulation for amorphous thermoset polymers working in the glassy regime. The constitutive formulation is able to describe time and pressure-dependent behaviour under loading rates ranging from quasi-static to impact-type loading conditions and to account for thermo-mechanical coupling effects. A non-linear pressure dependent potential function is introduced to capture the non-associative visco-plastic potential flow for volumetric plastic strain control. The formulation also incorporates an internal state or deformation resistance variable to enable the description of the polymer hardening — softening behaviour, as well as a novel relation for the dissipative fraction of the plastic work in terms of the equivalent accumulated plastic strain. The constitutive model is formulated within a finite strain kinematics framework, and full details of its numerical implementation into the finite element method using a fully implicit Euler Backward algorithm are given. Model calibration is carried out for three different thermosetting resins (PR520 and RTM6 Epoxies, and MMA adhesives).To illustrate the model capabilities, two case studies are investigated: (i) the de-formation behaviour of epoxy under moderate and impact-type loading conditions under isothermal and fully adiabatic conditions, and (ii) the fracture behaviour of adhesive layers used to bond stiff metallic substrates. Results on RTM6 epoxy show that at, e.g., 60% true strain, 48.5% of the rate of plastic work is dissipative, and that the corresponding predicted increase in temperature due to the locally dissipated heat is consistent with published calorimetry data on a similar thermoset polymer. It was also found that, by coupling the proposed constitutive model with a cohesive zone model, it was possible to predict accurately the effect of an MMA adhesive layer thickness and pressure-dependency on the growth of an interfacial crack between the MMA adhesive and the metallic substrates. The proposed model should constitute a generic phenomenological formulation for the mechanical behaviour prediction of a wide range of thermoset polymers under confined and quasi-adiabatic conditions such as in composites and adhesive joints.

Numerical simulation of three dimensional concrete printing based on a unified fluid and solid mechanics formulation

Deformation control constitutes one of the main technological challenges in three dimensional (3D) concrete printing, and it presents a challenge that must be addressed to achieve a precise and reliable construction process. Model-based information of the expected deformations and stresses is required to optimize the construction process in association with the specific properties of the concrete mix. In this work, a novel thermodynamically consistent finite strain constitutive model for fresh and early-age 3D-printable concrete is proposed. The model is then used to simulate the 3D concrete printing process to assess layer shapes, deformations, forces acting on substrate layers and prognoses of possible structural collapse during the layer-by-layer buildup. The constitutive formulation is based on a multiplicative split of the deformation gradient into elastic, aging and viscoplastic parts, in combination with a hyperelastic potential and considering evolving material properties to account for structural buildup or aging. One advantage of this model is the stress-update-scheme, which is similar to that of small strain plasticity and therefore enables an efficient integration with existing material routines. The constitutive model uses the particle finite element method, which serves as the simulation framework, allowing for modeling of the evolving free surfaces during the extrusion process. Computational analyses of three printed layers are used to create deformation plots, which can then be used to control the deformations during 3D concrete printing. This study offers further investigations, on the structural level, focusing on the potential structural collapse of a 3D printed concrete wall. The capability of the proposed model to simulate 3D concrete printing processes across the scales—from a few printed layers to the scale of the whole printed structure—in a unified fashion with one constitutive formulation, is demonstrated.

Modelling time-dependent relaxation behaviour using physically based constitutive framework

The application of interrupted die motion during the deformation process in a servo press cycle is known to enhance the forming limit of metallic materials. This observation is generally attributed to the transient effects associated with stress relaxation phenomenon. However, attempts to model stress relaxation behaviour using physically based constitutive formulations in the finite element method are scarce. In this work, a modified version of the Kocks–Mecking–Estrin (KME) dislocation density model is used to evaluate the substructural changes during relaxation. An ‘uncoupled’ elasto-viscoplastic approach is employed to accommodate the plastic strain rate effect. This modelling approach is implemented in the commercial finite element software via a user material subroutine. The model is validated through simulations of interrupted uniaxial tensile tests for aluminium alloy AA7075 under two different aging conditions. The implemented model is shown to closely capture the experimental results and account for changes in dislocation density and the athermal component of flow stress during relaxation. Subsequently, the model is applied to simulate monotonic and interrupted hole expansion tests (HET), and the results are discussed qualitatively.

Cyclic response of granular soils evaluated through a strain hardening model incorporated into the generalized plasticity framework

ABSTRACT In this study, constitutive behavior of granular soils is modeled through a generalized plasticity-based theoretical framework. The soil hardening is addressed by a novel relationship proposed to calculate plastic strains and their evolution during loading history. The model is effective in predicting the response and incorporating it into a numerical scheme. Focus is given to stress ratios yielding liquefaction in a few stress cycles. The proposed hardening law is based upon a combined deviatoric-volumetric hardening rule updating the stress-strain relationship and plastic strain vector. Numerous undrained monotonic and cyclic triaxial tests are simulated for verification of the constitutive formulation. Results indicate that the developed model for sand-like cohesionless soils proves to match fairly well with the available experimental data. Plastic strains are calculated accurately and accumulated pore pressures are well captured. Triaxial test simulations exhibit a successfully improved way of capturing the essential static and cyclic behavior of granular soils.

Laun's rule for predicting the first normal stress coefficient in complex fluids: A comprehensive investigation using fractional calculus

Laun's rule [H. M. Laun, “Prediction of elastic strains of polymer melts in shear and elongation,” J. Rheol. 30, 459–501 (1986).] is commonly used for evaluating the rate-dependent first normal stress coefficient from the frequency dependence of the complex modulus. We investigate the mathematical conditions underlying the validity of Laun's relationship by employing the time-strain–separable Wagner constitutive formulation to develop an integral expression for the first normal stress coefficient of a complex fluid in steady shear flow. We utilize the fractional Maxwell liquid model to describe the linear relaxation dynamics compactly and accurately and incorporate material nonlinearities using a generalized damping function of Soskey–Winter form. We evaluate this integral representation of the first normal stress coefficient numerically and compare the predictions with Laun's empirical expression. For materials with a broad relaxation spectrum and sufficiently strong strain softening, Laun's relationship enables measurements of linear viscoelastic data to predict the general functional form of the first normal stress coefficient but often with a noticeable quantitative offset. Its predictive power can be enhanced by augmenting the original expression with an adjustable power-law index that is based on the linear viscoelastic characteristics of the specific material being considered. We develop an analytical expression enabling the calculation of the optimal power-law index from the frequency dependence of the viscoelastic spectrum and the strain-softening characteristics of the material. To illustrate this new framework, we analyze published data for an entangled polymer melt and for a semiflexible polymer solution; in both cases our new approach shows significantly improved prediction of the experimentally measured first normal stress coefficient.

Numerical modeling of the abdominal wall biomechanics and experimental analysis for model validation.

The evaluation of the biomechanics of the abdominal wall is particularly important to understand the onset of pathological conditions related to weakening and injury of the abdominal muscles. A better understanding of the biomechanics of the abdominal wall could be a breakthrough in the development of new therapeutic approaches. For this purpose, several studies in the literature propose finite element models of the human abdomen, based on the geometry of the abdominal wall from medical images and on constitutive formulations describing the mechanical behavior of fascial and muscular tissues. The biomechanics of the abdominal wall depends on the passive mechanical properties of fascial and muscle tissue, on the activation of abdominal muscles, and on the variable intra-abdominal pressure. To assess the quantitative contribution of these features to the development and validation of reliable numerical models, experimental data are fundamental. This work presents a review of the state of the art of numerical models developed to investigate abdominal wall biomechanics. Different experimental techniques, which can provide data for model validation, are also presented. These include electromyography, ultrasound imaging, intraabdominal pressure measurements, abdominal surface deformation, and stiffness/compliance measurements.

Mechanical Behaviour of Plantar Adipose Tissue: From Experimental Tests to Constitutive Analysis.

Plantar adipose tissue is a connective tissue whose structural configuration changes according to the foot region (rare or forefoot) and is related to its mechanical role, providing a damping system able to adsorb foot impact and bear the body weight. Considering this, the present work aims at fully describing the plantar adipose tissue's behaviour and developing a proper constitutive formulation. Unconfined compression tests and indentation tests have been performed on samples harvested from human donors and cadavers. Experimental results provided the initial/final elastic modulus for each specimen and assessed the non-linear and time-dependent behaviour of the tissue. The different foot regions were investigated, and the main differences were observed when comparing the elastic moduli, especially the final elastic ones. It resulted in a higher level for the medial region (89 ± 77 MPa) compared to the others (from 51 ± 29 MPa for the heel pad to 11 ± 7 for the metatarsal). Finally, results have been used to define a visco-hyperelastic constitutive model, whose hyperelastic component, which describes tissue non-linear behaviour, was described using an Ogden formulation. The identified and validated tissue constitutive parameters could serve, in the early future, for the computational model of the healthy foot.

A shear history model for capturing the liquefaction resistance of sands at various cyclic stress ratios

Various constitutive formulations have been developed over the years to reproduce the cyclic resistance of sands. A common challenge for existing models is the accurate simulation of the cyclic strength of sands for a wide range of initial conditions and different cyclic stress levels when adopting a single calibration. Many liquefaction models tend to overpredict the resistance of the soil under large-amplitude loading, while underestimating the strength at low-amplitude cyclic shearing. This manifests itself in slopes of simulated cyclic resistance ratio curves (CRR-curves) which are steeper than experimental studies indicate. This paper provides a discussion on the effects of large-amplitude and low-amplitude cyclic shearing on a granular material based on micromechanical and experimental investigations presented in the literature. A constitutive model with a shear-history threshold is proposed, which accounts for a shift of the apparent angle of phase transformation under cyclic loading. In addition, a novel expression for a deviatoric fabric tensor is introduced to describe the evolution of shear-induced fabric anisotropy while a soil is dilating and contracting. Combining these two features in one formulation within the bounding surface plasticity framework enables an accurate prediction of cyclic strength of sands under a wide range of cyclic stress ratios.

Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

SummaryA multiscale model for saturated porous media is proposed, based on the concept of representative volume element (RVE). The physics between macro and micro‐scales is linked in terms of virtual power measures given by the general theory of poromechanics. Then, applying the so‐called Principle of Multiscale Virtual Power, together with suitable admissible constraints on micro‐scale displacement and pore pressure fields, a well‐established variational framework is obtained. This setting allows deriving the weak form of micro‐scale balance equations as well as the homogenization rules for the macro‐scale stress‐like variables and body forces. Whenever the micro‐scale mechanical constitutive functionals admit, as input arguments, the full‐order expansion of the micro‐scale pore pressure field, a size effect is inherited on the macro‐scale material response. The current literature attributes this issue to the so‐called “dynamical” or “second‐order” term of the homogenized flux velocity. It has been commonly suggested that the influence of this term is negligible by assuming infinitely small micro‐scale dimensions. However, such an idea compromises the fundamental notion of the existence of RVE for highly heterogeneous media. In this work, we show that the micro‐scale size dependence can be consistently eliminated by a simple constitutive‐like assumption. Accordingly, slight and selective redefinitions in the input arguments of micro‐scale material laws are proposed, leading to a constitutive formulation that allows the combination of micro‐scale variables with different orders of expansion. Just at this specific (constitutive) level, a reduced‐order expansion is selectively adopted for the micro‐scale pore pressure field. Thus, the RVE notion is restored while still retaining the major effects of the “dynamical” component of the homogenized flux velocity. The proposed formulation is implemented within a finite element squared (FE) environment. Some numerical experiments are presented showing the viability of the methodology, including comparisons against analytical, mono‐scale and DNS solutions.

On different classes of constitutive descriptions in finite electro‐mechanics: Computational modelling of isotropic and anisotropic electro‐active materials

AbstractVarious 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 coupling algorithm of ordinary and non-ordinary state-based peridynamic models for fracture analysis in brittle and ductile materials

In this work, a novel coupling algorithm of the ordinary state-based peridynamic (OSB-PD) model and non-ordinary state-based peridynamic (NOSB-PD) model is provided under the peridynamic framework. The salient advantages of both OSB-PD and NOSB-PD models can be simultaneously inherited in this coupling model and approach. The feasibility of coupling these two models is first analyzed by demonstrating the numerical equivalence of their constitutive formulations in isotropic elastic and elastoplastic problems, and the detailed numerical implementation strategy of coupling formulation is given as well. With the coupling model in this study, the main calculation procedure of numerical simulations is accomplished in OSB-PD, while the damage and failure analysis is conducted in NOSB-PD. Moreover, different failure criteria are introduced in this coupling model to describe the damage and failure of brittle and metallic materials. Several typical examples, including the mode I and mixed mode I/II fracture of brittle materials, and the ductile fracture and impact failure of metallic materials, are conducted to demonstrate the robustness and accuracy of the presented coupling model and approach.