Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids

A thermoviscoelastic constitutive model is developed for amorphous shape memory polymers (SMP) based on the hypothesis that structural and stress relaxation are the primary molecular mechanisms of the shape memory effect and its time-dependence. This work represents a new and fundamentally different approach to modeling amorphous SMPs. A principal feature of the constitutive model is the incorporation of the nonlinear Adam–Gibbs model of structural relaxation and a modified Eyring model of viscous flow into a continuum finite–deformation thermoviscoelastic framework. Comparisons with experiments show that the model can reproduce the strain–temperature response, the temperature and strain-rate dependent stress–strain response, and important features of the temperature dependence of the shape memory response. Because the model includes structural relaxation, the shape memory response also exhibits a dependence on the cooling and heating rates.

A thermoviscoelastic model for amorphous shape memory polymers: Incorporating structural and stress relaxation

Some fundamental issues in the formulation of constitutive theories of material response based on the multiplicative decomposition of the deformation gradient are reviewed, with focus on finite deformation thermoelasticity, elastoplasticity, and biomechanics. The constitutive theory of isotropic thermoelasticity is first considered. The stress response and the entropy expression are derived in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. Basic kinematic and kinetic aspects of the phenomenological and single crystal elastoplasticity within the framework of the multiplicative decomposition are presented. Attention is given to additive decompositions of the stress and strain rates into their elastic and plastic parts. The constitutive analysis of the stress-modulated growth of pseudo-elastic soft tissues is then presented. The elastic and growth parts of the deformation gradient and the rate of deformation tensor are defined and used to construct the corresponding rate-type biomechanic theory. The structure of the evolution equation for growth-induced stretch ratio is discussed. There are 112 references cited in this review article. DOI: 10.1115/1.1591000 The objective of this survey is to give an overview of the application of the multiplicative decomposition of the deformation gradient in constitutive theories of finite deformation thermoelasticity, elastoplasticity, and biomechanics. The multiplicative decomposition of the deformation gradient is based on an intermediate material configuration, which is obtained by a conceptual destressing of the currently deformed material configuration to zero stress. The significance of such configuration for material modeling was pointed out ˙

/pdf/constitutive-theories-based-on-the-multiplicative-3tssc4xxhk.pdf

Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics

This essay investigates the temperature dependence of the mechanical properties of a filler-loaded tread compound experimentally and proposes a physically based method to represent this behaviour in the framework of non-linear continuum thermomechanics. To this end, we realise a series of monotonic and cyclic strain controlled tests on cylindrical specimens in tension at different temperature levels. The experimental data show the isothermal mechanical behaviour to be mainly influenced by non-linear elasticity in combination with non-linear rate dependence and weak equilibrium hysteresis. We observe that the rate sensitivity of the material depends strongly on the temperature : at low temperature levels, the rate sensitivity is essentially higher than at high temperatures. The elastic properties of the material depend comparatively less on the temperature. Nevertheless, higher temperature levels lead to higher equilibrium stresses. In order to represent the material behaviour, we start with a multiplicative split of the deformation gradient into a mechanical and a thermal part as proposed by Lu and Pister (1975). Physically, this idea corresponds to a stress-free thermal expansion followed by an isothermal stress-producing deformation. We suppose the thermal part of the deformation gradient to be isotropic. As a consequence of this, the velocity gradient decomposes additively into a pure thermal and a pure mechanical part. By using these elements, we exploit the Clausius Duhem inequality and assume the so-called ‘mechanical second Piola Kirchhoff stress tensor’ to be a functional of the ‘mechanical Green's strain tensor’. In a further step, we define this functional by a system of constitutive equations which are based on a rheological model. The evolution equations for the internal variables are formulated by using the concept of dual variables proposed by Haupt and Tsakmakis (1989, 1996). The rate sensitivity is modelled by a stress and temperature dependent viscosity function. The elastic part of the equilibrium stress is described by entropy elasticity in combination with a modified Mooney Rivlin strain energy function. The equilibrium hysteresis effects are represented by rate independent plasticity in arclength representation as proposed by Valanis (1971). The constitutive model is compatible with the dissipation principle of thermodynamics and describes the general trend of the experimental data fairly well.

On the large deformation behaviour of reinforced rubber at different temperatures

Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models

Decomposition of deformation and representation of the free energy function for isotropic thermoelastic solids

During the drilling and repairing of wells, the pipe string transfer equipment has a high work frequency. The movement accuracy, response speed, and controllability of the equipment have significant impacts on the stability. In this paper, we propose an analysis method of mechanical arms to lift pipe strings using a rigid–flexible coupling model. With the mechanical arm as a flexible body and the mechanical hand as a rigid body, a numerical calculation model of the rigid-flexible coupling of the system was established based on the Lagrangian equation. ADAMS and Ansys software were applied to numerical simulations of this system to investigate the lifting characteristics, the influence of the operation parameters and structure parameters, and the contact collision analysis of the mechanical arm. The conditions of rigid–flexible modeling for the multi-body system and the main factors affecting the vibration characteristics of the flexible arm are described. We conclude that the arm should be modeled as a rigid body if the structure parameter [w/l] (elastic deformation/length) is between 1/650 and 1/1000, the system can be modeled as a rigid–flexible coupling if [w/l] is between 1/400 and 1/650, and the arm should be modeled as a flexible body and the influence and compensation of the control method should be considered if [w/l] is between 1/250 and 1/400.

/pdf/a-study-of-the-vibration-characteristics-of-flexible-sv6wi22c.pdf

A Study of the Vibration Characteristics of Flexible Mechanical Arms for Pipe String Transportation in Oilfields

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Decomposition of deformation and representation of the free energy function for isotropic thermoelastic solids

A Study of the Vibration Characteristics of Flexible Mechanical Arms for Pipe String Transportation in Oilfields