P. Areias

A gradient model for finite strain elastoplasticity coupled with damage

This paper describes the formulation of an implicit gradient damage model for finite strain elastoplasticity problems including strain softening. The strain softening behavior is modeled through a variant of Lemaitres damage evolution law. The resulting constitutive equations are intimately coupled with the finite element formulation, in contrast with standard local material models. A 3D finite element including enhanced strains is used with this material model and coupling peculiarities are fully described. The proposed formulation results in an element which possesses spatial position variables, nonlocal damage variables and also enhanced strain variables. Emphasis is put on the exact consistent linearization of the arising discretized equations.A numerical set of examples comparing the results of local and the gradient formulations relative to the mesh size influence is presented and some examples comparing results from other authors are also presented, illustrating the capabilities of the present proposal.

Finite element studies of the mechanical behaviour of the diaphragm in normal and pathological cases

The diaphragm is a muscular membrane separating the abdominal and thoracic cavities, and its motion is directly linked to respiration. In this study, using data from a 59-year-old female cadaver obtained from the Visible Human Project, the diaphragm is reconstructed and, from the corresponding solid object, a shell finite element mesh is generated and used in several analyses performed with the ABAQUS 6.7 software. These analyses consider the direction of the muscle fibres and the incompressibility of the tissue. The constitutive model for the isotropic strain energy as well as the passive and active strain energy stored in the fibres is adapted from Humphreys model for cardiac muscles. Furthermore, numerical results for the diaphragmatic floor under pressure and active contraction in normal and pathological cases are presented.

A multiscale multisurface constitutive model for the thermo-plastic behavior of polyethylene

Abstract We present a multiscale model bridging length and time scales from molecular to continuum levels with the objective of predicting the yield behavior of amorphous glassy polyethylene (PE). Constitutive parameters are obtained from molecular dynamics (MD) simulations, decreasing the requirement for ad-hoc experiments. Consequently, we achieve: (1) the identification of multisurface yield functions; (2) the high strain rate involved in MD simulations is upscaled to continuum via quasi-static simulations. Validation demonstrates that the entire multisurface yield functions can be scaled to quasi-static rates where the yield stresses are possibly predicted by a proposed scaling law; (3) a hierarchical multiscale model is constructed to predict temperature and strain rate dependent yield strength of the PE.

A damage-based temperature-dependent model for ductile fracture with finite strains and configurational forces

In this paper we assess a crack propagation criterion based on the notion of configurational force in the spirit of Gurtin (Configurational forces as basic concepts of continuum physics. Applied mathematical sciences. Springer, Berlin, 2000). We extend the theory of Gurtin to finite strain elasto-plastic fracture and in addition take thermal effects into account. The global model is a system of nonlinear and non-smooth equations which are solved directly with a finite element discretization. Comparison with laboratory experiments is provided, thereby showing that the concept of configurational force can be successfully used for computational damage-based fracture tests on ductile materials.

The extended unsymmetric frontal solution for multiple-point constraints

Purpose – The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling. Design/methodology/approach – Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage. Findings – When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced. Research limitations/implications – Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem. Practical implications – A complete software package in Fortran 2...

A simple assumed-strain quadrilateral shell element for finite strains and fracture

This work recovers an established technique for improving quadrilateral shell element performance in both out-of-plane and in-plane bending cases using a mixed formulation. A four-field variational principle is established and we relate, at the discrete level, the Lagrange multipliers and secondary right Cauchy–Green field with the displacement and rotation fields. This is the main contribution of this work. High coarse-mesh accuracy is observed for distorted meshes and the robustness is shown to be adequate for crack propagation simulations. A consistent director normalization is performed, as an alternative to our recent spherical interpolation. Covariant metric components are deduced and exact linearization of the shell element is performed. Full assessment of the element is accomplished, showing similar performance to more costly approaches such as enhanced assumed strain. Patch test is satisfied ab-initio and benchmarks present very accurate results. Numerical experimentation for geometrically and material nonlinear problems is presented, as well as one fracture example using our recently proposed cracked edge technique.

Experimental and Finite Element Analysis of Human Skin Elasticity

In this paper, mechanical properties of human skin are inferred from the information of a suction test using a cutometer test. Experiments with a 2 mm probe are carried out and numerical tests using a finite element program developed by the first author are employed for comparison. Regarding the numerical tests, both axisymmetric and complete 3D models of a silicon sheet were employed with the hyperelastic Yeoh constitutive model.Copyright

Gradient Damage Models in Metal Forming Problems

Reliable metal forming predictions require that fracture indication be available both in processes where it should be avoided and in processes in which fracture is a part of the process itself as in sheet blanking or metal cutting. The present proposal circumvents the necessity of the so‐called “fracture indicators” or fracture criteria by representing fracture through the material model exclusively. The frequent objections to this otherwise attractive are mainly related to the observed defect of mesh dependency. To attenuate this dependency an implicit gradient damage model is used. Therefore a non‐local damage field is introduced, which can be related to a local damage field, by means of a Helmholtz type differential equation. The damage evolution law is based on the improved Lemaitre damage model that treats differently the compressive and tensile response, which is particularly adequate forsituations involving complex strain paths.

Surface-based and solid shell formulations of the 7-parameter shell model for layered CFRP and functionally graded power-based composite structures

ABSTRACT In this study, we present the extension of the so-called 7-parameter shell formulation to layered CFRP and functionally graded power-based composite structures using two different parametrizations: (i) the three-dimensional shell formulation, and (ii) the solid shell approach. Both numerical strategies incorporate the use of the Enhanced Assumed Strain (EAS) and the Assumed Natural Strain (ANS) methods to alleviate locking pathologies and are implemented into the FE code ABAQUS. The applicability of the current developments is demonstrated by means of several benchmark examples, whose results are compared with reference solutions using shell elements of ABAQUS, exhibiting an excellent level of accuracy

A Second Order Approach For Finite Deformation Implicit Contact Analysis, Including Friction, In Deformable Bodies

Forming processes involve unilateral contact action from tools into workpiece. Also self‐contact may emerge in a variety of situations, some of which are technically undesirable. Additionally, it is known that the consideration of tool deformation may also be important in certain circumstances. Nevertheless the finite deformation implicit contact analysis, including friction, of 3D deformable bodies is not yet fully developed and robust to be applied in large‐scale applications.The non‐penetration of the solids between each other (and themselves) and the arising friction effects between the interacting surfaces due to interaction of micro‐asperities in tangential movement are here addressed. The finite element treatment of the non‐penetration is commonly based on the imposition of inequality constraints. The proposed method, in the context of an implicit solution, allows the combination of both the standard Rockafellar method for extending the Augmented Lagrangian to inequality constraints and a second or...