Thomas Pence | Michigan State University (original) (raw)

Papers by Thomas Pence

Proceedings of the 1996 MRS Fall Symposium, 1997

Applied Mechanics Reviews, Sep 1, 2021

Collagen is the most abundant protein in mammals, often serving as the main load bearing constitu... more Collagen is the most abundant protein in mammals, often serving as the main load bearing constituent in soft tissues. Collagen undergoes continuous remodeling processes in which present collagen degrades, and new collagen is formed and deposited. Experiments find that modestly strained fibrillar collagen is often stabilized to enzymatic degradation, a mechanism that is essential in approaching and maintaining a homeostatic balance in the tissue remodeling process for healthy tissue. At larger strains, this decline in the collagen degradation rate may be reversed. This article reviews different modeling approaches that seek to account for the effect of straining on collagen remodeling, both with respect to collagen amount and to resulting mechanical properties. These models differ in the considered length scale starting from the molecular scale up to the larger continuum scale.

International Journal of Non-linear Mechanics, Nov 1, 2018

By incorporating local volume change as a parametric constraint into the conventional theory of h... more By incorporating local volume change as a parametric constraint into the conventional theory of hyperelasticity it is possible to model a variety of swelling affects. Here we examine the finite strain swelling of a soft solid plug within a rigid tube of circular cross section. The eventual channel wall contact as the swelling proceeds generates a confinement pressure that increases as the plug expands. The contact problem for a solid cylinder plug is one of homogeneous deformation, allowing the pressure-swelling response of classical hyperelastic models to be contrasted with hyperelastic models that display limited chain extensibility. We then examine a cylindrical plug that itself contains an internal channel. Wall contact now gives a deformation in which swelling combines axial lengthening with internal channel narrowing. Of particular interest is the closing behavior as the swelling proceeds. Treating the associated boundary value problem provides asymptotic expressions for the channel radius closing and the contact pressure in the large swelling regime.

Mechanics Research Communications, Sep 1, 2021

Abstract Collagen is a load bearing constituent in many soft tissues, which undergoes remodeling ... more Abstract Collagen is a load bearing constituent in many soft tissues, which undergoes remodeling processes that are mediated by mechanical stimuli. Experiments suggest that fiber stretching tends to suppress the enzymatic degradation of the collagen fibers. This article presents a mechanical model that describes how this impacts overall collagen density. It specifically accounts for processes that involve ongoing change to the local stretch as the remodeling incorporates new fibers into the overall collagen network. The governing integral expression allows calculation of the local fiber density as determined by a specified deformation without the need to know or to specify either the stiffness or the force loading of the material under consideration. Fiber density homeostasis is disrupted by sudden changes in stretch, and regain of homeostasis is characterized by three characteristic times and hence two dimensionless groups.

Biomechanics and Modeling in Mechanobiology, Jun 21, 2018

A continuum mechanics constitutive model is presented for the interaction between swelling and co... more A continuum mechanics constitutive model is presented for the interaction between swelling and collagen remodeling in biological soft tissue. The model is inherently two-way: swelling stretches the collagen fibers which affects their rate of degradation-the remodeled fibrous microarchitecture provides selective directional stiffening that causes the swollen tissue to expand more in the unreinforced directions. The constitutive model specifically treats stretch-stabilization wherein the rate of enzymatic-induced degradation of collagen is a decreasing function of fiber stretch. New collagen replacement takes place in a generally swollen environment, and this synthesis is tracked as a function of time by means of a time integration scheme that accounts for the historical sequence of collagen recreation. The model allows for the specification of the collagen pre-stretch at the time of first synthesis, thus allowing for the consideration of either initially limp replacement fiber or initially pre-tensioned replacement fiber. Loading and swelling that occurs on time scales that are commensurate with the natural time scales for fiber degradation and replacement lead to the consideration of time-integral constitutive equations. Loading and swelling that take place on time scales that are very different from that of the remodeling time scales provide a simplified treatment in which there are definite notions of a short-time instantaneous response and also a large-time approach to a steady-state condition of homeostasis. Keywords Collagen • Swelling • Fiber remodeling • Hyperelasticity • Homeostasis List of symbols β (Equation 5)-population density of the fibers γ (Equation 22)-stiffness parameter for the protofibers ζ (Equation 5)-fiber survival kernel η(Λ) (Equations 23, 24)-fiber dissolution rate κ o Reference configuration, natural configuration of the matrix κ(t) Deformed configuration at time t κ f (τ) Natural fiber configuration at time of fiber creation τ B Heiko Topol

A theoretical and numerical model for the degradation of solid materials in combustion is develop... more A theoretical and numerical model for the degradation of solid materials in combustion is developed. As solid materials are heated by the flame, they undergo an internal thermo-chemical breakdown process known as pyrolysis. As the pyrolysis front propagates into the sample, a charring layer is left behind which contains voids, fractures and defects. Cracks propagate to release tensile stresses accumulated when the sample is losing mass. The crack front may precede the pyrolysis front into the sample. Crack patterns and fracture behaviors vary depending on material properties and heating level and distribution. Cracks cause loss of material integrity by forming isolated loops or fragments. Cracks concentrate the stresses and reduce material ability to withstand external loads. Cracks expose uncharred materials to flame, accelerating combustion. The process is highly nonlinear: crack patterns display fractal behavior. Dimensionless groups that define the model are examined: each yields different crack patterns.

As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually de... more As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually degrading into residual char and forming defects such as voids, fissures and cracks. The material degradation process, which is coupled to the crack formation process, is described using a theoretical model and is numerically simulated using the finite-element method for a generic, charring, rubber-like material. In this model, a slab of material is subjected to an external, localized heat flux and, as the material degrades, cracks form when the local principal stress exceeds a defined cracking threshold. The magnitude of the cracking threshold σc is systematically varied in order to examine its influences on crack initiation, evolution, distribution and behaviour over time. When σc exceeds the maximum principal stress for the entire process, σm, then no cracks are generated. We quantify how the average crack spacing, total crack length and crack initiation time depend upon the ratio σc/σm. Two characteristic domains of crack formation behaviour are identified from the crack initiation behaviour. Correlations are produced for the crack length evolution and final crack length values as functions of σc/σm. Crack intersection patterns and behaviour are described and characterized.

Journal of Mechanics of Materials and Structures, Feb 26, 2020

Spherical shells with porohyperelastic walls that contain mobile liquid are examined for the purp... more Spherical shells with porohyperelastic walls that contain mobile liquid are examined for the purpose of determining how the in-wall liquid distribution affects the overall mechanical response. Attention is restricted to spherical symmetry and to Mooney-Rivlin type material models that are generalized so as to incorporate swelling. In this setting, different distributions of the same amount of liquid are examined for their effect on the sphere's pressure-expansion behavior. Liquid distributions that are essentially uniform are found to give the most compliant response. In contrast, nonuniform liquid distributions that concentrate liquid near either the inner or outer wall are found to stiffen the overall behavior. Liquid redistribution can also alter the basic monotonicity properties of the resulting inflation graphs, possibly leading to various limited burst events.

Journal of The Mechanical Behavior of Biomedical Materials, 2021

A variety of biochemical and physical processes participate in the creation and maintenance of co... more A variety of biochemical and physical processes participate in the creation and maintenance of collagen in biological tissue. Under mechanical stimuli these collagen fibers undergo continuous processes of morphoelastic change. The model presented here is motivated by experimental reports of stretch-stabilization of the collagen fibers to enzymatic degradation. The fiber structure is modeled in terms of a fiber density evolution that is regulated by means of a fixed creation rate and a mechano-sensitive dissolution rate. The theory accounts for the possibly different natural configurations of the fiber unit constituents and the ground substance matrix. It also generalizes previous theoretical descriptions so as to account for finite survival times of the individual fiber units. Special consideration is given to steady state fiber-remodeling processes in which fiber creation and dissolution are in balance. Fiber assembly processes that involve prestretching the fiber constituents yield a homeostatic stress response with a characteristic fiber tone. Fiber density returns to homeostasis after mechanical disruption when sufficient time has passed.

Journal of Engineering Mathematics, May 25, 2017

We study how fiber-reinforced materials will naturally undergo swelling deformations in which a r... more We study how fiber-reinforced materials will naturally undergo swelling deformations in which a relatively greater stretch occurs transverse to the fibers than in the fiber direction. This means that a pattern of initially curved fibers prior to swelling will tend to straighten out as swelling proceeds. This can lead to swelling-induced deformations with a high degree of localized shearing and significant overall twisting. Such a process is examined for a plane strain swelling deformation that combines twist with radial expansion. Analytical results are obtained for both types: small and large swelling. Of particular interest is the relation of the extensible fiber theory to a theory for inextensible fibers. We examine the extent to which the former approaches the latter in the limit as the fibers are taken to be progressively stiffer.

Journal de physique, Dec 1, 1995

It is now well established that titanium-nickel alloys fabricated as thin films by physical vapor... more It is now well established that titanium-nickel alloys fabricated as thin films by physical vapor deposition can display the same transformation and shape-memory effects as their ingot-metallurgy counterparts. As such they may find important application to microelectromechanical and biomechanical systems. Furthermore, we show here that titanium-nickel films may be directly processed so as to possess extremely fine austenite grain size and very high strength. These films display classical transformational superelasticity, including high elastic energy storage capacity, the expected dependence of martensite-start temperature on transformation enthalpy, and large, fully recoverable anelastic strains at temperatures above Af. Processing depends on elevated substrate temperatures during deposition, which may be manipulated within a certain range to control both grain size and crystallographic texture. It is also possible to deposit crystalline titanium-nickel films onto polymeric substrates, making them amenable to lithographic patterning into actuator elements that are well-suited to electrical excitation of the martensite reversion transformation. Finally, isothermal annealing of nickel-rich films, under conditions of controlled extrinsic residual stress, leads to topotaxial orientation of Ni 4 Ti 3-type precipitates, and the associated possibility of twoway memory effects. Much work remains to be done, especially with respect to precise control of composition. 'We offer this descriptor as an alternative to the conventional term 'thermoelastic', as it is suggestive of both thermally-driven shape-strains and anelastic strain energy storage capability, and avoids confusion with another standard usage of 'thermoelastic' referring to purely elastic distortions associated with temperature gradients.

Gauss described number theory as the queen of mathematics. Indeed, the amount of mathematics inve... more Gauss described number theory as the queen of mathematics. Indeed, the amount of mathematics invented for arithmetic reasons is truly astonishing. To name just a few examples: • A large part of complex analysis (Cauchy, Riemann, Weierstraß, Hadamard, Hardy-Littlewood,. . .); • The theory of divisors (Kummer, Dedekind) and of ideals (E. Noether); • The theory of Riemann surfaces (Riemann,. . .); • The non-analytic version of the Riemann-Roch theorem for curves (F. K. Schmidt); • The refoundation of Italian algebraic geometry on the basis of commutative algebra (Weil); 1 • The theory of abelian varieties (Weil); • Part of the theory of linear representations of finite groups (Artin, Brauer); • A large part of homological algebra: group cohomology, the theory of sheaves on a general site (Cartan, Eilenberg, Serre, Tate, Grothendieck,. . .); • Part of the theory of schemes (Grothendieck); • The development of étale cohomology (M. Artin, Grothendieck, Verdier, Deligne.. .) and then crystalline cohomology (Grothendieck, Berthelot, Ogus, Bloch, Deligne, Illusie,. . .); • Part of the theory of derived categories (Grothendieck, Verdier); • The six operations formalism (Grothendieck); • Monodromy theory in the world of schemes (Grothendieck, Serre, Deligne, Katz,. . .); and, of course, the theory of motives! 1 van der Waerden and Zariski also participated in this movement, for different reasons. for the hardest one: the "Riemann hypothesis". I also give an overview of Dwork's p-adic proof of the rationality of zeta functions of varieties over a finite field (obtained before the development of Grothendieck's cohomological methods!). Chapter 4 returns to more elementary mathematics, introducing Dirichlet, Hecke, and Artin L-functions. I give a proof of Dirichlet's theorem on arithmetic progressions, by the method expounded by Serre in [Ser3]; it would

Wiley eBooks, Jul 15, 2002

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, Sep 1, 2019

As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually de... more As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually degrading into residual char and forming defects such as voids, fissures and cracks. The material degradation process, which is coupled to the crack formation process, is described using a theoretical model and is numerically simulated using the finiteelement method for a generic, charring, rubber-like material. In this model, a slab of material is subjected to an external, localized heat flux and, as the material degrades, cracks form when the local principal stress exceeds a defined cracking threshold. The magnitude of the cracking threshold σ c is systematically varied in order to examine its influences on crack initiation, evolution, distribution and behaviour over time. When σ c exceeds the maximum principal stress for the entire process, σ m , then no cracks are generated. We quantify how the average crack spacing, total crack length and crack initiation time depend upon the ratio σ c /σ m. Two characteristic domains of crack formation behaviour are identified from the crack initiation behaviour. Correlations are produced for the crack length evolution and final crack length values as functions of σ c /σ m. Crack intersection patterns and behaviour are described and characterized.

MRS Proceedings, 1996

ABSTRACTThin films of thermoelastic titanium-nickel are of interest as a material basis for force... more ABSTRACTThin films of thermoelastic titanium-nickel are of interest as a material basis for force-producing elements in microelectromechanical systems, and for active phases in mechanically-adaptive composite materials. The successful introduction of this material system into such application areas will depend on development of reliable thin film deposition protocols, together with the refinement of analytical models which successfully predict the response of active microstructures to a variety of dynamic thermal and mechanical stimuli. In the present paper we review some of our recent experimental and theoretical work which bear on these problems. With respect to thin film fabrication techniques we focus on problems of composition control and the manipulation of microstructure, with particular emphasis on opportunities afforded by amorphous precursor phases formed during low temperature processing, and the fine-grained, thermally stable crystalline microstructures obtainable using hot-substrate deposition. The films resulting from either approach retain the important thermomechanical response features of the well-known bulk-alloy system: shape memory and transformational superelasticity. The response can be modeled in terms of a continuum description augmented with internal variables that track fractional partitioning of the material between austenite and variants of the martensite.

International Journal of Solids and Structures, Oct 1, 2017

Abstract The incompressible hyperelastic Mooney-Rivlin constitutive model allows for pressure-inf... more Abstract The incompressible hyperelastic Mooney-Rivlin constitutive model allows for pressure-inflation response of spherical shells that could either be globally stable (a monotonic pressure-radius graph) or could instead involve instability jumps of various kinds as pressurization proceeds. The latter occurs when the pressure-radius graph is not monotonic, allowing for a snap-through bifurcation that gives a sudden burst of inflation. For a given structure (shell thickness) composed of a specific material (a parameter choice in the M–R constitutive model), the form of the pressure-radius graph becomes fixed, enabling the determination of whether and when such a burst will be triggered. Internal swelling of the material that makes up the shell wall will generally change the response. Not only does it alter the quantitative pressure-inflation relation but it can also change the qualitative stability response, allowing burst phenomena for certain ranges of swelling and preventing burst phenomena for other ranges of swelling. This paper provides a systematic framework for predicting how such swelling ranges depend on structural geometry and material parameters.

Combustion Theory and Modelling, Jun 1, 2020

A model is developed for the formation and propagation of cracks in a material sample that is hea... more A model is developed for the formation and propagation of cracks in a material sample that is heated at its top surface, pyrolyses, and then thermally degrades to form char. In this work the sample is heated uniformly over its entire top surface by a hypothetical flame (a heat source). The pyrolysis mechanism is described by a one-step overall reaction that is dependent nonlinearly on the temperature (Arrhenius form). Stresses develop in response to the thermal degradation of the material by means of a shrinkage strain caused by local mass loss during pyrolysis. When the principal stress exceeds a prescribed threshold value, the material forms a local crack. Cracks are found to generally originate at the surface in response to heating, but occasionally they form in the bulk, away from ever-changing material boundaries. The resulting cracks evolve and form patterns whose characteristics are described. Quantities examined in detail are: the crack spacing in the pyrolysis zone; the crack length evolution; the formation and nature of crack loops which are defined as individual cracks that have joined to form loops that are disconnected from the remaining material; the formation of enhanced pyrolysis area; and the impact of all of the former quantities on mass flux. It is determined that the mass flux from the sample can be greatly enhanced over its nominal (non-cracking) counterpart. The mass efflux profile qualitatively resembles those observed in Cone Calorimeter tests.

$Research paper thumbnail of Reflection and Refraction of Anti-Plane Shear Waves from a Moving Phase Boundary$

The reflection and refraction of anti-plane shear waves from an interface separating halfspaces w... more The reflection and refraction of anti-plane shear waves from an interface separating halfspaces with different moduli is well understood in the linear theory of elasticity. Namely, an oblique incident wave gives rise to a reflected wave that departs at the same angle and to a refracted wave that, after transmission through the interface, departs at a possibly different angle. Here we study similar issues for a material that admits mobile elastic phase boundaries in anti-plane shear. We consider an energy minimal equilibrium state in anti-plane shear involving a planar phase boundary that is perturbed due to an incident wave of small magnitude. The phase boundary is allowed to move under this perturbation. As in the linear theory, the perturbation gives rise to a reflected and a refracted wave. The orientation of these waves is independent of the phase boundary motion and determined as in the linear theory. However, the phase boundary motion affects the amplitudes of the departing waves. Perturbation analysis gives these amplitudes for general small phase boundary motion, and also permits the specification of the phase boundary motion on the basis of additional criteria such as a kinetic relation. A standard kinetic relation is studied to quantify the subsequent energy partitioning and dissipation on the basis of the properties of the incident wave.

MRS Proceedings, 1994

Deposition of crystalline titanium-nickel shape-memory alloys on polymeric substrates is complica... more Deposition of crystalline titanium-nickel shape-memory alloys on polymeric substrates is complicated by the elevated temperatures that must be withstood either during deposition or during post-deposition crystallization anneals. In this paper we report results on thin films of titanium-nickel, with Ni-rich compositions, which were prepared by dc magnetron sputtering onto quartz substrates, and onto thin polyimide membranes, at various elevated substrate temperatures between 623K and 703K. All of the as-deposited films possessed ordered bcc microstructures and had nano-scale grain sizes. Films deposited at the higher end of the temperature range displayed familiar two-step transformation behavior in electrical resistivity experiments, with transformation temperatures that were stable with respect to annealing for 22-hrs at 700K. Classic shape-memory was observed for a bilayer consisting of an 7.6 Vtm thick Kapton® polyimide sheet onto which 3 ýtm of near-equiatomic TiNi had been sputtered at 703K. By applying a pattern-etch technique to the metallized polymer we were able to fabricate a prototype electrically-excitable thin-film actuating element, potentially applicable to microelectromechanical and biomechanical systems.

Proceedings of the 1996 MRS Fall Symposium, 1997

Applied Mechanics Reviews, Sep 1, 2021

International Journal of Non-linear Mechanics, Nov 1, 2018

Mechanics Research Communications, Sep 1, 2021

Biomechanics and Modeling in Mechanobiology, Jun 21, 2018

Journal of Mechanics of Materials and Structures, Feb 26, 2020

Journal of The Mechanical Behavior of Biomedical Materials, 2021

Journal of Engineering Mathematics, May 25, 2017

Journal de physique, Dec 1, 1995

Wiley eBooks, Jul 15, 2002

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, Sep 1, 2019

As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually de... more As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually degrading into residual char and forming defects such as voids, fissures and cracks. The material degradation process, which is coupled to the crack formation process, is described using a theoretical model and is numerically simulated using the finiteelement method for a generic, charring, rubber-like material. In this model, a slab of material is subjected to an external, localized heat flux and, as the material degrades, cracks form when the local principal stress exceeds a defined cracking threshold. The magnitude of the cracking threshold σ c is systematically varied in order to examine its influences on crack initiation, evolution, distribution and behaviour over time. When σ c exceeds the maximum principal stress for the entire process, σ m , then no cracks are generated. We quantify how the average crack spacing, total crack length and crack initiation time depend upon the ratio σ c /σ m. Two characteristic domains of crack formation behaviour are identified from the crack initiation behaviour. Correlations are produced for the crack length evolution and final crack length values as functions of σ c /σ m. Crack intersection patterns and behaviour are described and characterized.

MRS Proceedings, 1996

International Journal of Solids and Structures, Oct 1, 2017

Combustion Theory and Modelling, Jun 1, 2020

$Research paper thumbnail of Reflection and Refraction of Anti-Plane Shear Waves from a Moving Phase Boundary$

MRS Proceedings, 1994